PM SHRI KENDRIYA VIDYALAYA GACHIBOWLI, GPRA CAMPUS, HYD-32

SAMPLE PAPER TEST 01 FOR BOARD EXAM 2025

SUBJECT: MATHEMATICS MAX. MARKS : 80

CLASS : X DURATION : 3 HRS
General Instruction:
1. This Question Paper has 5 Sections A-E.
2. Section A has 20 MCQs carrying 1 mark each.
3. Section B has 5 questions carrying 02 marks each.
4. Section C has 6 questions carrying 03 marks each.
5. Section D has 4 questions carrying 05 marks each.
6. Section E has 3 case based integrated units of assessment (04 marks each) with sub-parts of the
values of 1, 1 and 2 marks each respectively.
7. All Questions are compulsory. However, an internal choice in 2 Qs of 5 marks, 2 Qs of 3 marks and
2 Questions of 2 marks has been provided. An internal choice has been provided in the 2marks
questions of Section E
8. Draw neat figures wherever required. Take π =22/7 wherever required if not stated.
SECTION – A
Questions 1 to 20 carry 1 mark each.

1. Two circles touch each other externally at C and AB is common tangent of circles, then ∠ACB is
(a) 70° (b) 60° (c) 100° (d) 90°
2. The pair of linear equations 2x + 3y = 5 and 4x + 6y = 10 is
(a) inconsistent (b) consistent (c) dependent consistent (d) none of these
3. Nature of roots of quadratic equation 2x2 – 4x + 3 = 0 is
(a) real (b) equal (c) not real (d) none of them

4. If ∆ABC ~ ∆EDF and ∆ABC is not similar to ∆DEF, then which of the following is not true?
(a) BC. EF = AC. FD (b) AB. EF = AC. DE
(c) BC. DE = AB. EF (d) BC. DE = AB. FD

5. If the circumference of a circle and the perimeter of a square are equal, then
(a) Area of the circle = Area of the square
(b) Area of the circle > Area of the square
(c) Area of the circle < Area of the square
(d) Nothing definite can be said about the relation between the areas of the circle and square.

6. The sum of the lower limit of median class and the upper limit of the modal class of the following
data is:
Marks 0 – 10 10 – 20 20 – 30 30 – 40 40 – 50 50 – 60
No. of students 8 10 12 22 30 18
(a) 70 (b) 80 (c) 90 (d) 100
7. The radius of the largest right circular cone that can be cut out from a cube of edge 4.2 cm is
(a) 2.1 cm (b) 4.2 cm (c) 3.1 cm (d) 2.2 cm

8. Volume and surface area of a solid hemisphere are numerically equal. What is the diameter of
hemisphere?
(a) 9 units (b) 6 units (c) 4.5 units (d) 18 units

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9. In the ∆ABC, DE ∥ BC and AD = 3x − 2, AE = 5x − 4, BD = 7x − 5, CE = 5x − 3, then find the
value of x
(a) 1 (b) 7/10 (c) both (a) & (b) (d) none of these

10. A card is selected at random from a well shuffled deck of 52 cards. The probability of its being a
face card is
(a) 3/26 (b) 3/13 (c) 2/13 (d) 1/2
7
11. In ABC right angled at B, sin A = , then the value of cos C is ………….
25
7 24 7 24
(a) (b) (c) (d)
25 25 24 7
5sin   3cos 
12. If 5 tan θ = 4, then the value of is
5sin   2 cos 
(a) 1/6 (b) 1/7 (c) 1/4 (d) 1/5

13. Given that sin α = 1/2 and cos β = 1/2, then the value of (β – α) is
(a) 0° (b) 30° (c) 60° (d) 90°

14. Two identical solid hemispheres of equal base radius are stuck along their bases. The total surface
area of the combination is
(a) πr2 (b) 2πr2 (c) 3πr2 (d) 4πr2

15. If two positive integers p and q can be expressed as p = ab2 and q = a3b; a, b being prime numbers,
then LCM (p, q) is
(a) ab (b) a2b2 (c) a3b2 (d) a3b3

16. The perimeter of a triangle with vertices (0, 4), (0, 0) and (3, 0) is
(a) 5 units (b) 12 units (c) 11 units (d) (7 + √5) units

17. The zeroes of the polynomial x2 – 3x – m(m + 3) are

(a) m, m + 3 (b) –m, m + 3 (c) m, – (m + 3) (d) –m, – (m + 3)

18. The area of a quadrant of a circle, whose circumference is 22 cm, is

11 77 77 77
(a) cm2 (b) cm2 (c) cm2 (d) cm2
8 8 2 4
Direction : In the question number 19 & 20 , A statement of Assertion (A) is followed by a
statement of Reason(R) . Choose the correct option

19. Assertion (A): 6n never ends with the digit zero, where n is natural number.
Reason (R): Any number ends with digit zero, if its prime factor is of the form 2m × 5n, where m, n
are natural numbers.
(a) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of
Assertion (A).
(b) Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of
Assertion (A).
(c) Assertion (A) is true but Reason (R) is false.
(d) Assertion (A) is false but Reason (R) is true.

20. Assertion (A): The value of y is 3, if the distance between the points P(2, -3) and Q(10, y) is 10.
Reason (R): Distance between two points is given by ( x2  x1 )2  ( y2  y1 )2

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 (a) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of
Assertion (A)
(b) Both assertion (A) and reason (R) are true and reason (R) is not the correct explanation of
Assertion (A)
(c) Assertion (A) is true but reason(R) is false.
(d) Assertion (A) is false but reason(R) is true.

SECTION-B
Questions 21 to 25 carry 2M each
21. Two concentric circles are of radii 5 cm and 3 cm. Find the length of the chord of the larger circle
which touches the smaller circle.

1
22. If sin (A + B) = √3/2 and sin (A – B) = , 0 ≤ A + B ≤ 90° and A > B, then find A and B.
2
OR
(1  sin  )(1  sin  )
If tan θ =3/4, evaluate
(1  cos  )(1  cos  )

23. Find the area of the sector of a circle with radius 4 cm and of angle 30°. Also, find the area of the
corresponding major sector. (Use π = 3.14)
OR
What is the angle subtended at the centre of a circle of radius 10 cm by an arc of length 5π cm?

24. For what values of k will the following pair of linear equations have infinitely many solutions? kx
+ 3y – (k – 3) = 0 and 12x + ky – k = 0

25. In the given figure, AP = 3 cm, AR = 4.5 cm, AQ = 6 cm, AB = 5 cm, AC = 10 cm. Find the length
of AD

SECTION-C
Questions 26 to 31 carry 3 marks each

26. The area of a rectangle gets reduced by 9 square units, if its length is reduced by 5 units and breadth
is increased by 3 units. If we increase the length by 3 units and the breadth by 2 units, the area
increases by 67 square units. Find the dimensions of the rectangle.

sin   cos   1
27. Prove that  sec   tan 
sin   cos   1

28. Two dice are thrown at the same time. What is the probability that the sum of the two numbers
appearing on the top of the dice is (i) 5? (ii) 10? (iii) at least 9?

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29. In the below figure, XY and X′Y′ are two parallel tangents to a circle with centre O and another
tangent AB with point of contact C intersecting XY at A and X′Y′ at B. Prove that ∠AOB = 90°.

OR
In the below figure, two equal circles, with centres O and O', touch each other at X. OO' produced
meets the circle with centre O' at A. AC is tangent to the circle with centre O, at the point C. O'D is
DO '
perpendicular to AC. Find the value of .
CO

30. Four bells toll at an interval of 8, 12, 15 and 18 seconds respectively. All the four begin to toll
together. Find the number of times they toll together in one hour excluding the one at the start.

31. Find the zeroes of the quadratic polynomial 6x2– 3 – 7x and verify the relationship between the
zeroes and the coefficients of the polynomial.
OR
Find the quadratic polynomial sum and product of whose zeros are –1 and –20 respectively. Also
find the zeroes of the polynomial so obtained.

SECTION-D
Questions 32 to 35 carry 5M each

32. If the median of the following distribution is 58 and sum of all the frequencies is 140. What is the
value of x and y?
Class 15 – 25 25 – 35 35 – 45 45 – 55 55 – 65 65 – 75 75 – 85 85 – 95
Frequency 8 10 x 25 40 y 15 7

33. A toy is in the form of a hemisphere surmounted by a right circular cone of the same base radius as
that of the hemisphere. If the radius of the base of the cone is 21 cm and its volume is 2/3 of the
volume of the hemisphere, calculate the height of the cone and the surface area of the toy.
OR
A vessel full of water is in the form of an inverted cone of height 8 cm and the radius of its top,
which is open, is 5 cm. 100 spherical lead balls are dropped into the vessel. One fourth of the water
flows out of the vessel. Find the radius of a spherical ball.

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34. A motor boat whose speed is 18 km/h in still water takes 1 hour more to go 24 km upstream than to
return downstream to the same spot. Find the speed of the stream.
OR
An express train takes 1 hour less than a passenger train to travel 132 km between Mysore and
Bangalore (without taking into consideration the time they stop at intermediate stations). If the
average speed of the express train is 11km/h more than that of the passenger train, find the average
speed of the two trains.
35. State and prove Basic Proportional Theorem.

SECTION-E (Case Study Based Questions)

Questions 36 to 38 carry 4M each

36. Ananya saves Rs. 24 during the first month Rs. 30 in the second month and Rs. 36 in the third
month. She continues to save in this manner.

On the basis of above information answer the following questions.

(i) Whether the monthly savings of Ananya form an AP or not? If yes then write the first term and
common difference.
(ii) What is the amount that she will save in 15th month?
(iii) In which month, will she save Rs. 66?
OR
What is the common difference of an AP whose nth term is 8 – 5n?

37. A person/observer on the sea coast observes two ships in the sea, both the ships are in same straight
path one behind the other.
If the observer is on his building of height 20 meters (including observer) and he observes the angle
of depression of two ships as 45° and 60° respectively.

On the basis of above information answer the following questions.

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 (i) If a person observes a ship whose angle of depression is 60° then how much distance is the ship
away from the building?
(ii) If a person observes another ship whose angle of depression is 45° then how much distance that
ship is away from the building?
(iii) If a person observes the ship whose angle of depression changes from 60° to 30° then how far
be ship from the building if the observer is at 20 m of height (including him)?
OR
At a time when a person observes two ships whose angle of depressions are 60° and 45° the
distance between the ships is (in meter).

38. The top of a table is shown in the figure given below:

p
On the basis of above information answer the following questions.
(i) Find the distance between points A and B.
(ii) Write the co-ordinates of the mid point of line segment joining points M and Q.
(iii) If G is taken as the origin, and x, y axis put along GF and GB, then find the point denoted by
coordinates (4, 2) and (8, 4).

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 OR
Find the coordinates of H, G and also find the distance between them.

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PM SHRI KENDRIYA VIDYALAYA GACHIBOWLI, GPRA CAMPUS, HYD-32
SAMPLE PAPER TEST 02 FOR BOARD EXAM 2025

SUBJECT: MATHEMATICS MAX. MARKS : 80

CLASS : X DURATION : 3 HRS
General Instruction:
1. This Question Paper has 5 Sections A-E.
2. Section A has 20 MCQs carrying 1 mark each.
3. Section B has 5 questions carrying 02 marks each.
4. Section C has 6 questions carrying 03 marks each.
5. Section D has 4 questions carrying 05 marks each.
6. Section E has 3 case based integrated units of assessment (04 marks each) with sub-parts of the
values of 1, 1 and 2 marks each respectively.
7. All Questions are compulsory. However, an internal choice in 2 Qs of 5 marks, 2 Qs of 3 marks and
2 Questions of 2 marks has been provided. An internal choice has been provided in the 2marks
questions of Section E
8. Draw neat figures wherever required. Take π =22/7 wherever required if not stated.
SECTION – A
Questions 1 to 20 carry 1 mark each.

1. If α and β are the zeros of a polynomial f(x) = px2 – 2x + 3p and α + β = αβ, then p is
(a)-2/3 (b) 2/3 (c) 1/3 (d) -1/3

2. Let p be a prime number. The quadratic equation having its roots as factors of p is
(a) x2 –px + p = 0 (b) x2 – (p + 1)x + p = 0
(c) x2 + (p + 1)x +p = 0 (d) x2 – px + p + 1= 0

3. In an A.P., if the first term a = 7, nth term an 84 and the sum of first n terms Sn = 2093/2, then n is
equal to:
(a) 22 (b) 24 (c) 23 (d) 26

4. Let a and b be two positive integers such that a = p3q4 and b = p2q3 , where p and q are prime
numbers. If HCF(a, b) = pmqn and LCM(a, b) = prqs, then (m + n)(r + s) =
(a) 15 (b) 30 (c) 35 (d) 72

5. If the probability of a player winning a game is 0.79, then the probability of his losing the same
game is:
(a) 1.79 (b) 0.31 (c) 0.21% (d) 0.21

6. If sinθ + cosθ = √2, then tanθ + cot θ =

(a) 1 (b) 2 (c) 3 (d) 4
7. From the data l, 4, 7, 9, 16, 21, 25, if all the even numbers are removed, then the probability of
getting at random a prime number from the remaining is :
(a) 2/5 (b) 1/5 (c) 1/7 (d) 2/7
8. For the following distribution:
Class 0-5 5-10 10-15 15-20 20-25
Frequency 10 15 12 20 9
the sum of lower limits of the median class and modal class is
(a) 15 (b) 25 (c) 30 (d) 35
9. AD is a median of ∆ABC with vertices A(5, –6), B(6, 4) and C(O, O). Length AD is equal to :
(a) √68 units (b) 2√15 units (c) √101 units (d) 10 units

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 5sin   2 cos 
10. If 5 tanβ = 4, then 
5sin   2cos 
(a) 1/3 (b) 2/5 (c) 3/5 (d) 6

11. The zeroes of a polynomial x2 + px + q are twice the zeroes of the polynomial 4x2 – 5x – 6. The
value of p is :
(a) –5/2 (b) 5/2 (c) –5 (d) 10

12. If the distance between the points (3, –5) and (x, –5) is 15 units, then the values of x are :
(a) 12, –18 (b) –12, 18 (c) 18, 5 (d) –9, –12

13. The sum of the length, breadth and height of a cuboid is 6√3cm and the length of its diagonal is
2√3cm. The total surface area of the cuboid is
(a) 48 cm2 (b) 72 cm2 (c) 96 cm2 (d) 108 cm2

14. If the difference of Mode and Median of a data is 24, then the difference of median and mean is
(a) 8 (b) 12 (c) 24 (d) 36

15. The volume of the largest right circular cone that can be carved out from a solid cube of edge 2 cm
is :
4 5 8 2
(a) cu cm (b) cu cm (c) cu cm (d) cu cm
3 3 3 3

16. Two dice are rolled simultaneously. What is the probability that 6 will come up at least once?
(a)1/6 (b) 7/36 (c) 11/36 (d) 13/36

17. If the vertices of a parallelogram PQRS taken in order are P(3, 4), Q(-2, 3) and R(-3, -2), then the
coordinates of its fourth vertex S are
(a) (-2,-1) (b) (-2,-3) (c) (2,-1) (d) (1,2)

18. If the system of equations 3x + y =1 and (2k – 1)x + (k – 1)y = 2k + 1 is inconsistent, then k =
(a) -1 (b) 0 (c) 1 (d) 2

Direction : In the question number 19 & 20 , A statement of Assertion (A) is followed by a

statement of Reason(R) . Choose the correct option
(a) Both, Assertion (A) and Reason (R) are true and Reason (R) is correct explanation of Assertion (A).
(b) Both, Assertion (A) and Reason (R) are true but Reason (R) is not correct explanation for Assertion
(A).
(c) Assertion (A) is true but Reason (R) is false.
(d) Assertion (A) is false but Reason (R) is true.

19. Assertion (A): If the graph of a polynomial touches x-axis at only one point, then the polynomial
cannot be a quadratic polynomial.
Reason (R): A polynomial of degree n(n >1) can have at most n zeroes.

20. Assertion (A): The tangents drawn at the end points of a diameter of a circle, are parallel.
Reason (R): Diameter of a circle is the longest chord.

SECTION-B
Questions 21 to 25 carry 2M each
21. If 49x + 51y = 499, 51x + 49y = 501, then find the value of x and y

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22. If sin(A + B) = 1 and cos(A – B) = √3/2, 0°< A + B ≤ 90° and A > B, then find the measures of
angles A and B.
OR
cos   sin  1  3
Find an acute angle θ when 
cos   sin  1  3

23. In the given figure below, AD/AE=AC/BD and ∠1=∠2. Show that Δ BAE~ ΔCAD .

24. Given that √3 is irrational, prove that 5 + 2√3 is irrational.

OR
Show that the number 5 х l1 х 17 + 3 х 11 is a composite number.

25. In a pack of 52 playing cards one card is lost. From the remaining cards, a card is drawn at random.
Find the probability that the drawn card is queen of heart, if the lost card is a black card.

SECTION-C
Questions 26 to 31 carry 3 marks each

26. In a teachers' workshop, the number of teachers teaching French, Hindi and English are 48, 80 and
144 respectively. Find the minimum number of rooms required if in each room the same number of
teachers are seated and all of them are of the same subject.

27. A train covered a certain distance at a uniform speed. If the train would have been 6 km/h faster, it
would have taken 4 hours less than the scheduled time. And, if the train were slower by 6 km/hr; it
would have taken 6 hours more than the scheduled time. Find the length of the journey.

tan 3  cot 3 
28. Prove that:   sec  cos ec  2sin  cos 
1  tan 2  1  cot 2 

29. Prove that a parallelogram circumscribing a circle is a rhombus

OR
In the figure XY and X'Y' are two parallel tangents to a circle with centre O and another tangent AB
with point of contact C interesting XY at A and X'Y' at B, what is the measure of ∠AOB.

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 8 
30. Find the ratio in which the point  , y  divides the line segment joining the points (1, 2) and (2, 3).
5 
Also, find the value of y.
OR
ABCD is a rectangle formed by the points A (–1, –1), B(–1, 6), C (3, 6) and D (3, –1). P, Q, R and
S are midpoints of sides AB, BC, CD and DA respectively. Show that diagonals of the quadrilateral
PQRS bisect each other.

31. Due to heavy floods in a state, thousands were rendered homeless. 50 schools collectively decided
to provide place and the canvas for 1500 tents and share the whole expenditure equally. The lower
part of each tent is cylindrical with base radius 2.8 m and height 3.5 m and the upper part is conical
with the same base radius, but of height 2.1 m. If the canvas used to make the tents costs ₹120 per
m2, find the amount shared by each school to set up the tents.

SECTION-D
Questions 32 to 35 carry 5M each

32. The sum of first and eighth terms of an A.P. is 32 and their product is 60. Find the first term and
common difference of the A.P. Hence, also find the sum of its first 20 terms.
OR
In an A.P. of 40 terms, the sum of first 9 terms is 153 and the sum of last 6 terms is 687. Determine
the first term and common difference of A.P. Also, find the sum of all the terms of the A.P.

33. Prove that if a line is drawn parallel to one side of a triangle intersecting the other two sides in
distinct points, then the other two sides are divided in the same ratio.
Using the above theorem prove that a line through the point of intersection of the diagonals and
parallel to the base of the trapezium divides the non parallel sides in the same ratio.
OR
In the given figure PA, QB and RC are each perpendicular to AC. If AP = x, BQ = y and CR = z,
1 1 1
then prove that  
x z y

34. A pole 6m high is fixed on the top of a tower. The angle of elevation of the top of the pole observed
from a point P on the ground is 600 and the angle of depression of the point P from the top of the
tower is 450. Find the height of the tower and the distance of point P from the foot of the tower.
(Use √3 = 1.73)

35. An arc of a circle of radius 21 cm subtends an angle of 600 at the centre. Find (i) the length of the
arc (ii) the area of the minor segment of the circle made by the corresponding chord.

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 SECTION-E (Case Study Based Questions)
Questions 36 to 38 carry 4M each

36. BINGO is game of chance. The host has 75 balls numbered 1 through 75. Each player has a BINGO
card with some numbers written on it. The participant cancels the number on the card when called
out a number written on the ball selected at random. Whosoever cancels all the numbers on his/her
card, says BINGO and wins the game.
The table given below, shows the data of one such game where
48 balls were used before Tara said 'BINGO'.
Numbers announced Number of times
0-15 8
15-30 9
30-45 10
45-60 12
60-75 9
Based on the above information, answer the following:
(i) Write the median class.
(ii) When first ball was picked up, what was the probability of calling out an even number?
(iii) (a) Find median of the given data.
OR
(b) Find mode of the given data.
37. A backyard is in the shape of a triangle ABC with right angle at B. AB = 7 m and BC 15 m. A
circular pit was dug inside it such that it touches the walls AC, BC and AB at P, Q and R
respectively such that AP = x m.

Based on the above information, answer the following questions:

(i) Find the length of AR in terms of x.
(ii) Write the type of quadrilateral BQOR.
(iii) (a) Find the length PC in terms of x and hence find the value of x.
OR
(b) Find x and hence find the radius r of circle.
38. A rectangular floor area can be completely tiled with 200 square tiles. If the side length of each tile
is increased by 1 unit, it would take only 128 tiles to cover the floor.

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 (i) Assuming the original length of each side of a tile be x units, make a quadratic equation from the
above information.
(ii) Write the corresponding quadratic equation in standard form.
(iii) (a) Find the value of x, the length of side of a tile by factorisation.
OR
(b) Solve the quadratic equation for x, using quadratic formula.

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PM SHRI KENDRIYA VIDYALAYA GACHIBOWLI, GPRA CAMPUS, HYD-32
SAMPLE PAPER TEST 03 FOR BOARD EXAM 2025

SUBJECT: MATHEMATICS MAX. MARKS : 80

CLASS : X DURATION : 3 HRS
General Instruction:
1. This Question Paper has 5 Sections A-E.
2. Section A has 20 MCQs carrying 1 mark each.
3. Section B has 5 questions carrying 02 marks each.
4. Section C has 6 questions carrying 03 marks each.
5. Section D has 4 questions carrying 05 marks each.
6. Section E has 3 case based integrated units of assessment (04 marks each) with sub-parts of the
values of 1, 1 and 2 marks each respectively.
7. All Questions are compulsory. However, an internal choice in 2 Qs of 5 marks, 2 Qs of 3 marks
and 2 Questions of 2 marks has been provided. An internal choice has been provided in the
2marks questions of Section E
8. Draw neat figures wherever required. Take π =22/7 wherever required if not stated.
SECTION – A
Questions 1 to 20 carry 1 mark each.
1. If the sum of zeroes of the polynomial p(x) = 2x2 – k√2 x + l is √2, then value of k is :
(a) √2 (b) 2 (c) 2√2 (d) 1/2

2. If two positive integers p and q can be expressed as p = 18 a2b4 and q = 20 a3b2, where a and b
are prime numbers, then LCM (p, q) is :
(a) 2 a2b2 (b) 180a2b2 (c) 12 a2b2 (d) 180 a3b4

3. If the roots of equation ax2 + bx + c = 0, a ≠ 0 are real and equal, then which of the following
relation is true?
(a) a = b2/c (b) b2 = ac (c) ac = b2/4 (d) c = b2/a

4. The centre of a circle is at (2, 0). If one end of a diameter is at (6, 0), then the other end is at :
(a) (0, 0) (b) (4, 0) (c) (-2, 0) (d) (-6, 0)

5. In the given figure, graphs of two linear equations are shown. The pair of these linear equations
is:

(a) consistent with unique solution.

(b) consistent with infinitely many solutions.
(c) inconsistent.
(d) inconsistent but can be made consistent by extending these lines.

6. If x tan 60°cos 60°= sin60°cot 60°, then x =

(a) cos30° (b) tan30° (c) sin30° (d) cot30°

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7. If sec θ – tan θ = m, then the value of sec θ + tan θ is :
1 1
(a) 1  (b) m2  1 (c) (d) m
m m

8. In the given figure, DE ∥ BC, AE = a units, EC =b units, DE =x units and BC = y units. Which
of the following is true?

a b ax ay x a
(a) x  (b) y  (c) x  (d) 
ay a b a b y b

9. The number of revolutions made by a circular wheel of radius 0.25m in rolling a distance of
11km is
(a) 2800 (b) 4000 (c) 5500 (d) 7000

10. ABCD is a trapezium with AD ∥ BC and AD = 4cm. If the diagonals AC and BD intersect each
other at O such that AO/OC = DO/OB =1/2, then BC =
(a) 6cm (b) 7cm (c) 8cm (d) 9cm

11. The area of the circle that can be inscribed in a square of 6cm is
(a) 36π cm2 (b) 18π cm2 (c) 12 π cm2 (d) 9π cm2

12. A solid sphere is cut into two hemispheres. The ratio of the surface areas of sphere to that of two
hemispheres taken together, is:
(a) 1 : 1 (b) 1 : 4 (c) 2 : 3 (d) 3 : 2

13. The middle most observation of every data arranged in order is called
(a) mode (b) median (c) mean (d) deviation

14. ΔABC~ΔPQR. If AM and PN are altitudes of ΔABC and ΔPQR respectively and AB2 : PQ2 = 4
: 9, then AM : PN =
(a) 3 : 2 (b) 16 : 81 (c) 4 : 9 (d) 2 : 3

15. If two tangents inclined at an angle of 60ᵒ are drawn to a circle of radius 3cm, then the length of
each tangent is equal to
(a) 3√3/2 cm (b) 3cm (c) 6cm (d) 3√3cm

16. For some data xl, x2, …….. xn with respective frequencies f1, f2, ..... fn, the value of
n

 f ( x  x) is equal to:
1
i i

(a) nx (b) 1 (c) f i (d) 0

17. Two dice are rolled together. The probability of getting sum of numbers on the two dice as 2, 3
or 5, is:
(a) 7/36 (b) 11/36 (c) 5/36 (d) 4/9

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    
18. If cos (α + β) = 0, then value of cos   is equal to:
 2 
1 1
(a) (b) (c) 0 (d) 2
2 2
DIRECTION: In the question number 19 and 20, a statement of Assertion (A) is followed by a
statement of Reason (R).
Choose the correct option
(a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of
assertion (A)
(b) Both assertion (A) and reason (R) are true and reason (R) is not the correct explanation of
assertion (A)
(c) Assertion (A) is true but reason (R) is false.
(d) Assertion (A) is false but reason (R) is true.
19. Assertion (A): If the co-ordinates of the mid-points of the sides AB and AC of ΔABC are
D(3,5) and E(-3,-3) respectively, then BC = 20 units
Reason (R) : The line joining the mid points of two sides of a triangle is parallel to the third
side and equal to half of it.
20. Assertion (A): If product of two numbers is 5780 and their HCF is 17, then their LCM is 340
Reason (R) : HCF is always a factor of LCM

SECTION – B
Questions 21 to 25 carry 2 marks each.
21. Solve the following system of linear equations: 7x – 2y = 5 and 8x + 7y= 15 and verify your
answer.
22. In the given figure, ABCD is a quadrilateral. Diagonal BD bisects ∠B and ∠D both. Prove that
(i) ∆ABD ~ ∆CBD (ii) AB = BC

23. The length of the minute hand of a clock is 6cm. Find the area swept by it when it moves from
7:05 p.m. to 7:40 p.m.
OR
In the given figure, arcs have been drawn of radius 7cm each with vertices A, B, C and D of
quadrilateral ABCD as centres. Find the area of the shaded region.

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24. Evaluate: 2 2 cos 450 sin 300  2 3 cos 300
OR
If A = 600 and B = 300, verify that: sin (A + B) = sin A cos B + cos A sin B

25. In the given figure, O is the centre of circle. Find ∠AQB, given that PA and PB are tangents to
the circle and ∠APB = 75°.

SECTION – C
Questions 13 to 22 carry 3 marks each.
26. Prove that 5 – 2√3 is an irrational number. It is given that √3 is an irrational number.

27. Three years ago, Rashmi was thrice as old as Nazma. Ten years later, Rashmi will be twice as
old as Nazma. How old are Rashmi and Nazma now?
OR
Anuj had some chocolates, and he divided them into two lots A and B. He sold the first lot at the
rate of ₹2 for 3 chocolates and the second lot at the rate of ₹1 per chocolate, and got a total of
₹400. If he had sold the first lot at the rate of ₹1 per chocolate, and the second lot at the rate of
₹4 for 5 chocolates, his total collection would have been ₹460. Find the total number of
chocolates he had.

tan  cot 
28. Prove that:   1  sec  cos ec
1  cot  1  tan 

29. In the given below left figure, AB is a diameter of the circle with centre O. AQ, BP and PQ are
tangents to the circle. Prove that ∠POQ = 900.

OR
A circle with centre O and radius 8 cm is inscribed in a quadrilateral ABCD in which P, Q, R, S
are the points of contact as shown in above right sided figure. If AD is perpendicular to DC, BC
= 30 cm and BS = 24 cm, then find the length DC.

30. Two coins are tossed simultaneously. What is the probability of getting
(i) At least one head? (ii) At most one tail? (iii) A head and a tail?

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31. If the zeroes of the polynomial x2 + px + q are double in value to the zeroes of the polynomial
2x2 – 5x – 3, then find the values of p and q.

SECTION – D
Questions 32 to 35 carry 5 marks each.

32. If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct
points, then prove that the other two sides are divided in the same ratio.

33. The difference between the outer and inner radii of a hollow right circular cylinder of length 14
cm is 1 cm. If the volume of the metal used in making the cylinder is 176 cm3, find the outer
and inner radii of the cylinder.
OR

There are two identical solid cubical boxes of side 7cm. From the top face of the first cube a
hemisphere of diameter equal to the side of the cube is scooped out. This hemisphere is inverted
and placed on the top of the second cube’s surface to form a dome. Find (i) the ratio of the total
surface area of the two new solids formed (ii) volume of each new solid formed.

34. To fill a swimming pool two pipes are used. If the pipe of larger diameter used for 4 hours and
the pipe of smaller diameter for 9 hours, only half of the pool can be filled. Find, how long it
would take for each pipe to fill the pool separately, if the pipe of smaller diameter takes 10
hours more than the pipe of larger diameter to fill the pool?

OR

In a flight of 600km, an aircraft was slowed down due to bad weather. Its average speed for the
trip was reduced by 200 km/hr from its usual speed and the time of the flight increased by 30
min. Find the scheduled duration of the flight.

35. The median of the following data is 525. Find the values of x and y, if the total frequency is 100

Class Frequency
0-100 2
100-200 5
200-300 x
300-400 12
400-500 17
500-600 20
600-700 y
700-800 9
800-900 7
900-1000 4

SECTION – E(Case Study Based Questions)

Questions 36 to 38 carry 4 marks each.

36. The school auditorium was to be constructed to accommodate at least 1500 people. The chairs
are to be placed in concentric circular arrangement in such a way that each succeeding circular
row has 10 seats more than the previous one.

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 (i) If the first circular row has 30 seats, how many seats will be there in the 10th row?
(ii) For 1500 seats in the auditorium, how many rows need to be there?
OR
If 1500 seats are to be arranged in the auditorium, how many seats are still left to be put after
10th row?
(iii) If there were 17 rows in the auditorium, how many seats will be there in the middle row?

37. We all have seen the airplanes flying in the sky but might have not thought of how they actually
reach the correct destination. Air Traffic Control (ATC) is a service provided by ground-based
air traffic controllers who direct aircraft on the ground and through a given section of controlled
airspace, and can provide advisory services to aircraft in non-controlled airspace. Actually, all
this air traffic is managed and regulated by using various concepts based on coordinate
geometry and trigonometry.

At a given instance, ATC finds that the angle of elevation of an airplane from a point on the
ground is 60°. After a flight of 30 seconds, it is observed that the angle of elevation changes to
30°. The height of the plane remains constantly as 3000√3 m. Use the above information to
answer the questions that follow-
(i) Draw a neat labelled figure to show the above situation diagrammatically.
(ii) What is the distance travelled by the plane in 30 seconds?
OR
Keeping the height constant, during the above flight, it was observed that after 15(√3 -1)
seconds, the angle of elevation changed to 45°. How much is the distance travelled in that
duration.
(iii) What is the speed of the plane in km/hr

38. A tiling or tessellation of a flat surface is the covering of a plane using one or more geometric
shapes, called tiles, with no overlaps and no gaps. Historically, tessellations were used in
ancient Rome and in Islamic art. You may find tessellation patterns on floors, walls, paintings
etc. Shown below is a tiled floor in the archaeological Museum of Seville, made using squares,
triangles and hexagons.

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 A craftsman thought of making a floor pattern after being inspired by the above design. To
ensure accuracy in his work, he made the pattern on the Cartesian plane. He used regular
octagons, squares and triangles for his floor tessellation pattern

Use the above figure to answer the questions that follow:

(i) What is the length of the line segment joining points B and F?
(ii) The centre ‘Z’of the figure will be the point of intersection of the diagonals of quadrilateral
WXOP. Then what are the coordinates of Z?
(iii) What are the coordinates of the point on y axis equidistant from A and G?
OR
What is the area of Trapezium AFGH?

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PM SHRI KENDRIYA VIDYALAYA GACHIBOWLI,GPRA CAMPUS, HYD-32
SAMPLE PAPER TEST 04 FOR BOARD EXAM 2025

SUBJECT: MATHEMATICS MAX. MARKS : 80

CLASS : X DURATION : 3 HRS
General Instruction:
1. This Question Paper has 5 Sections A-E.
2. Section A has 20 MCQs carrying 1 mark each.
3. Section B has 5 questions carrying 02 marks each.
4. Section C has 6 questions carrying 03 marks each.
5. Section D has 4 questions carrying 05 marks each.
6. Section E has 3 case based integrated units of assessment (04 marks each) with sub-parts of the
values of 1, 1 and 2 marks each respectively.
7. All Questions are compulsory. However, an internal choice in 2 Qs of 5 marks, 2 Qs of 3 marks
and 2 Questions of 2 marks has been provided. An internal choice has been provided in the 2marks
questions of Section E
8. Draw neat figures wherever required. Take π =22/7 wherever required if not stated.
SECTION – A
Questions 1 to 20 carry 1 mark each.
1. In the given figure, tangents PA and PB to the circle centred at O, from point P are perpendicular
to each other. If PA = 5 cm, then length of AB is equal to

(a) 5 cm (b) 5√2 cm (c) 2√5 cm (d) 10 cm

2. XOYZ is a rectangle with vertices X(–3, 0), O(0, 0), Y(0, 4) and Z(x, y). The length of its each
diagonal is
(a) 5 units (b) √5 units (c) x² + y² units (d) 4 units

3. Which term of the A.P. –29, –26, –23, ..., 61 is 16?

(a) 11th (b) 16th (c) 10th (d) 31st

4. If the length of an arc of a circle subtending an angle 60° at its centre is 22 cm, then the radius of
the circle is :
(a) √21 cm (b) 21 cm (c) √42 cm (d) 42 cm

5. If x = 5 is a solution of the quadratic equation 2x2 + (k – 1)x + 10 = 0, then the value of k is :

(a) 11 (b) – 11 (c) 13 (d) – 13

6. The pair of equations x = 2a and y = 3b (a, b ≠ 0) graphically represents straight lines which are :
(a) coincident (b) parallel (c) intersecting at (2a, 3b) (d) intersecting at (3b, 2a)

7. The point on x-axis which is equidistant from the points (5, – 3) and (4, 2) is :
(a) (4.5, 0) (b) (7, 0) (c) (0.5, 0) (d) (– 7, 0)
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8. The 7th term from the end of the A.P. : – 8, – 5, – 2, ..., 49 is :
(a) 67 (b) 13 (c) 31 (d) 10

9. After an examination, a teacher wants to know the marks obtained by maximum number of the
students in her class. She requires to calculate ................. of marks.
(a) median (b) mode (c) mean (d) range

10. Two positive integers m and n are expressed as m = p5q2 and n = p3q4, where p and q are prime
numbers. The LCM of m and n is :
(a) p8q6 (b) p3q2 (c) p5q4 (d) p5q2 + p3q4

 1 
11. The value of  sin 2   2  is :
 1  tan  
(a) 0 (b) 2 (c) 1 (d) – 1

12. All queens, jacks and aces are removed from a pack of 52 playing cards. The remaining cards are
well-shuffled and one card is picked up at random from it. The probability of that card to be a
king is :
(a) 1/10 (b) 1/13 (c) 3/10 (d) 3/13

1 1
13. If α and β are zeroes of the polynomial 5x² + 3x – 7, the value of  is
 
(a) −3/7 (b) 3/5 (c) 3/7 (d) −5/7
14. The perimeters of two similar triangles ABC and PQR are 56 cm and 48 cm respectively. PQ/AB
is equal to
(a) 7/8 (b) 6/7 (c) 7/6 (d) 8/7
15. In the given figure, if M and N are points on the sides OP and OS respectively of ∆OPS, such that
MN || PS, then the length of OP is :
(a) 6.8 cm (b) 17 cm (c) 15.3 cm (d) 9.6 cm

16. In the given figure, PA and PB are two tangents drawn to the circle with centre O and radius 5
cm. If ∠APB = 60°, then the length of PA is :
(a) 5/√3 cm (b) 5√3 cm (c) 10/√3 cm (d) 10 cm

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17. If value of each observation in a data is increased by 2, then median of the new data
(a) increases by 2 (b) increases by 2n (c) remains same (d) decreases by 2

18. The probability of getting a chocolate flavoured ice cream at random, in a lot of 600 ice creams is
0.055. The number of chocolate flavoured ice creams in the lot is :
(a) 33 (b) 55 (c) 11 (d) 44

DIRECTION: In the question number 19 and 20, a statement of Assertion (A) is followed by a
statement of Reason (R).
Choose the correct option
(a) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of
Assertion (A)
(b) Both assertion (A) and reason (R) are true and reason (R) is not the correct explanation of
Assertion (A)
(c) Assertion (A) is true but reason(R) is false.
(d) Assertion (A) is false but reason(R) is true.

19. Assertion (A): Two cubes each of edge length 10 cm are joined together. The total surface area
of newly formed cuboid is 1200 cm².
Reason (R): Area of each surface of a cube of side 10 cm is 100 cm².

1 2 2
20. Assertion (A): If sin A = (0° < A < 90°) , then the value of cos A is
3 3
Reason (R): For every angle θ, sin²θ + cos²θ = 1.

SECTION – B
Questions 21 to 25 carry 2 marks each.
1 1
21. (a) If cos (A + B) = and tan (A – B) = , where 0 ≤ A + B ≤ 90°, then find the value of
2 3
sec (2A – 3B).
OR
3
(b) Find the value of x such that, 3tan²60° – xsin²45° + sec²30° = 2cosec²30°
4
22. In the given figure, PAQ and PBR are tangents to the circle with centre ‘O’ at the points A and B
respectively. If T is a point on the circle such that Ð QAT = 45° and ∠TBR = 65°, then find
∠ATB.

23. (a) In what ratio is the line segment joining the points (3, –5) and (–1, 6) divided by the line y =
x?
OR
(b) A(3, 0), B(6, 4) and C(–1, 3) are vertices of a triangle ABC. Find length of its median BE.

24. Can the number (15)n, n being a natural number, end with the digit 0? Give reasons.
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25. Find the type of triangle ABC formed whose vertices are A(1, 0), B(–5, 0) and C(–2, 5).

SECTION – C
Questions 26 to 31 carry 3 marks each.
26. Prove that √5 is an irrational number.

27. (a) If a hexagon PQRSTU circumscribes a circle, prove that, PQ + RS + TU = QR + ST + UP

OR
(b) In the given figure, two concentric circles have radii 3 cm and 5 cm. Two tangents TR and TP
are drawn to the circles from an external point T such that TR touches the inner circle at R and TP
touches the outer circle at P. If TR = 4√10 cm, then find the length of TP.

 1  tan 2 A  (1  tan A)2

28. Prove that:  2  2
 1  cot A  (1  cot A)
29. The government rescued 100 people after a train accident. Their ages were recorded in the
following table. Find their mean age.
Age (in years) Number of people rescued
10 – 20 9
20 – 30 14
30 – 40 15
40 – 50 21
50 – 60 23
60 – 70 12
70 – 80 6

30. If Nidhi were 7 years younger than what she actually is, then the square of her age (in years)
would be 1 more than 5 times her actual age. What is her present age?

31. (a) If the sum of first m terms of an A.P. is same as sum of its first n terms (m ≠ n), then show that
the sum of its first (m + n) terms is zero.
OR
(b) In a A.P., the sum of the three consecutive terms is 24 and the sum of their squares is 194.
Find the numbers.

SECTION – D
Questions 32 to 35 carry 5 marks each.

32. (a) If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct
points, then prove that the other two sides are divided in the same ratio.
OR

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 (b) In the given figure, MNOP is a parallelogram and AB || MP. Prove that QC || PO.

33. From the top of a 45 m high light house, the angles of depression of two ships, on the opposite
side of it, are observed to be 30° and 60°. If the line joining the ships passes through the foot of
the light house, find the distance between the ships. (Use √3 = 1.73)

34. The perimeter of a certain sector of a circle of radius 5.6 m is 20.0 m. Find the area of the sector.

35. (a) Using graphical method, solve the following system of equations:
3x + y + 4 = 0 and 3x – y + 2 = 0
OR
(b) Tara scored 40 marks in a test, getting 3 marks for each right answer and losing 1 mark for
each wrong answer. Had 4 marks been awarded for each correct answer and 2 marks been
deducted for each wrong answer, then Tara would have scored 50 marks. Assuming that Tara
attempted all question, find the total number of questions in the test.

SECTION – E(Case Study Based Questions)

Questions 36 to 38 carry 4 marks each.

36. The word ‘circus’ has the same root as ‘circle’. In a closed circular area, various entertainment
acts including human skill and animal training are presented before the crowd.

A circus tent is cylindrical upto a height of 8 m and conical above it. The diameter of the base is
28 m and total height of tent is 18.5 m.
Based on the above, answer the following questions:
(i) Find slant height of the conical part.
(ii) Determine the floor area of the tent.
(iii) (a) Find area of the cloth used for making tent.
OR
(b) Find total volume of air inside an empty tent.

37. In a survey on holidays, 120 people were asked to state which type of transport they used on their
last holiday. The following pie chart shows the results of the survey.

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 Observe the pie chart and answer the following questions:
(i) If one person is selected at random, find the probability that he/she travelled by bus or ship.
(ii) Which is most favourite mode of transport and how many people used it?
(iii) (a) A person is selected at random. If the probability that he did not use train is 4/5, find the
number of people who used train.
OR
(b) The probability that randomly selected person used aeroplane is 7/60.
Find the revenue collected by air company at the rate of ₹ 5,000 per person.

38. A ball is thrown in the air so that t seconds after it is thrown, its height h metre above its starting
point is given by the polynomial h = 25t – 5t².

Observe the graph of the polynomial and answer the following questions:
(i) Write zeroes of the given polynomial.
(ii) Find the maximum height achieved by ball.
(iii) (a) After throwing upward, how much time did the ball take to reach to the height of 30 m?
OR
(b) Find the two different values of t when the height of the ball was 20 m.

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PM SHRI KENDRIYA VIDYALAYA GACHIBOWLI, GPRA CAMPUS, HYD-32
SAMPLE PAPER TEST 05 FOR BOARD EXAM 2025

SUBJECT: MATHEMATICS MAX. MARKS : 80

CLASS : X DURATION : 3 HRS
General Instruction:
1. This Question Paper has 5 Sections A-E.
2. Section A has 20 MCQs carrying 1 mark each.
3. Section B has 5 questions carrying 02 marks each.
4. Section C has 6 questions carrying 03 marks each.
5. Section D has 4 questions carrying 05 marks each.
6. Section E has 3 case based integrated units of assessment (04 marks each) with sub-parts of the
values of 1, 1 and 2 marks each respectively.
7. All Questions are compulsory. However, an internal choice in 2 Qs of 5 marks, 2 Qs of 3 marks and
2 Questions of 2 marks has been provided. An internal choice has been provided in the 2marks
questions of Section E
8. Draw neat figures wherever required. Take π =22/7 wherever required if not stated.
SECTION – A
Questions 1 to 20 carry 1 mark each.
1. If the length of the shadow on the ground of a pole is √3 times the height of the pole, then the angle
of elevation of the Sun is :
(a) 30° (b) 45° (c) 60° (d) 90°
2. Two dice are thrown at the same time and the product of the numbers appearing on them is noted.
The probability that the product of the numbers lies between 8 and 13 is :
(a) 7/36 (b) 5/36 (c) 2/9 (d) 1/4
3. If the HCF(2520, 6600) = 40 and LCM(2520, 6600) = 252 × k, then the value of k is
(a) 1650 (b) 1600 (c) 165 (d) 1625
4. The value of k for which the system of equations 3x – y + 8 = 0 and 6x – ky + 10 = 0 has infinitely
many solutions, is
(a) –2 (b) 2 (c) 1/2 (d) −1/2
5. If k + 7, 2k – 2 and 2k + 6 are three consecutive terms of an A.P., then the value of k is :
(a) 15 (b) 17 (c) 5 (d) 1
6. The quadratic equation x2 + x + 1 = 0 has ................. roots.
(a) real and equal (b) irrational (c) real and distinct (d) not-real
7. AB and CD are two chords of a circle intersecting at P. Choose the correct statement from the
following:

(a) ∆ADP ~ ∆CBA (b) ∆ADP ~ ∆BPC (c) ∆ADP ~ ∆BCP (d) ∆ADP ~ ∆CBP

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8. In the given figure ∆ABC is shown. DE is parallel to BC. If AD = 5 cm, DB = 2.5 cm and BC = 12
cm, then DE is equal to

(a) 10 cm (b) 6 cm (c) 8 cm (d) 7.5 cm

9. The diagonals of a rhombus ABCD intersect at O. Taking ‘O’ as the centre, an arc of radius 6 cm is
drawn intersecting OA and OD at E and F respectively. The area of the sector OEF is :
(a) 9π cm2 (b) 3π cm2 (c) 12π cm2 (d) 18π cm2
10. If tan2θ + cot2 = 2, where θ = 45° and θ° ≤ ≤ 90°, then the value of a is :
(a) 30° (b) 45° (c) 60° (d) 90°
11. If sin θ = cos θ, (0° < θ < 90°), then value of (sec θ. sin θ) is:
(a) 1/√2 (b) √2 (c) 1 (d) 0
12. Two dice are rolled together. The probability of getting the sum of the two numbers to be more
than 10, is
(a) 1/9 (b) 1/6 (c) 7/12 (d) 1/12
13. PQ is a diameter of a circle with centre O(2, – 4). If the coordinates of the point P are (– 4, 5), then
the coordinates of the point Q will be :
(a) (– 3, 4.5) (b) (– 1, 0.5) (c) (4, – 5) (d) (8, – 13)
14. The common difference of an A.P. in which a15 – a11 = 48, is
(a) 12 (b) 16 (c) –12 (d) –16
15. A cap is cylindrical in shape, surmounted by a conical top. If the volume of the cylindrical part is
equal to that of the conical part, then the ratio of the height of the cylindrical part to the height of
the conical part is :
(a) 1 : 2 (b) 1 : 3 (c) 2 : 1 (d) 3 : 1
16. A box contains cards numbered 6 to 55. A card is drawn at random from the box. The probability
that the drawn card has a number which is a perfect square, is
(a) 7/50 (b) 7/55 (c) 1/10 (d) 5/49
17. Point P divides the line segment joining the points A(4, –5) and B(1, 2) in the ratio 5 : 2. Co-
ordinates of point P are
 5 3   11   13   13 
(a)  ,  (b)  , 0  (c)  , 0  (d)  0, 
2 2  2  7   7
18. In the given figure, AT is tangent to a circle centred at O. If ∠CAT = 40°, then ∠CBA is equal to

(a) 70° (b) 50° (c) 65° (d) 40°

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Questions number 19 and 20 are Assertion and Reason based questions. Two statements are given,
one labelled as Assertion (A) and the other is labelled as Reason (R). Select the correct answer to these
questions from the codes (A), (B), (C) and (D) as given below.
(a) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the
Assertion (A).
(b) Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the
Assertion (A).
(c) Assertion (A) is true, but Reason (R) is false.
(d) Assertion (A) is false, but Reason (R) is true.

19. Assertion (A): TA and TB are two tangents drawn from an external point T to a circle with centre
‘O’. If ∠TBA = 75° then ∠ABO = 25°.

Reason (R): The tangent drawn at any point of a circle is perpendicular to the radius through the
point of contact.
20. Assertion (A): If the graph of a polynomial intersects the x-axis at exactly two points, then the
number of zeroes of that polynomial is 2.
Reason (R): The number of zeroes of a polynomial is equal to the number of points where the
graph of the polynomial intersects x-axis.

SECTION-B
Questions 21 to 25 carry 2M each
21. In the given figure, AB and CD are tangents to a circle centred at O. Is ∠BAC = ∠DCA? Justify
your answer.

22. (a) Evaluate : 2 sin²30° sec60° + tan²60°.

OR
(b) If 2 sin(A + B) = √3 and cos(A – B) = 1, then find the measures of angles A and B. 0 ≤ A, B, (A
+ B) ≤ 90°.

23. PQRS is a trapezium with PQ y SR. If M and N are two points on the non-parallel sides PS and QR
PM QN
respectively, such that MN is parallel to PQ, then show that  .
MS NR

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24. Prove that 7 – 3√5 is an irrational number, given that √5 is an irrational number.

25. (a) A chord is subtending an angle of 90° at the centre of a circle of radius 14 cm. Find the area of
the corresponding minor segment of the circle.
OR
(b) Find the area of the shaded region if length of radius of each circle is 7 cm. Each circle touches
the other two externally.

SECTION-C
Questions 26 to 31 carry 3 marks each

26. Find a quadratic polynomial whose sum of the zeroes is 8 and difference of the zeroes is 2.

27. (a) The sum of the digits of a 2-digit number is 12. Seven times the number is equal to four times
the number obtained by reversing the order of the digits. Find the number.
OR
(b) Find the values of x and y from the following pair of linear equations :
62x + 43y = 167
43x + 62y = 148

28. A school has invited 42 Mathematics teachers, 56 Physics teachers and 70 Chemistry teachers to
attend a Science workshop. Find the minimum number of tables required, if the same number of
teachers are to sit at a table and each table is occupied by teachers of the same subject.

29. In a test, the marks obtained by 100 students (out of 50) are given below:
Marks Obtained 0 – 10 10 – 20 20 – 30 30 – 40 40 – 50
Number of Student 12 23 34 25 6
Find the mean marks of the students.

1  sec   tan  1  sin 

30. Prove that: 
1  sec   tan  cos 

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31. (a) In the given figure, PQ is tangent to a circle at O and ∠BAQ = 30°, show that BP = BQ.

OR

(b) In the given figure, AB, BC, CD and DA are tangents to the circle with centre O forming a
quadrilateral ABCD. Show that ∠AOB + ∠COD = 180°

SECTION-D
Questions 32 to 35 carry 5M each

32. (a) The largest possible hemisphere is drilled out from a wooden cubical block of side 21 cm such
that the base of the hemisphere is on one of the faces of the cube. Find :
(i) the volume of wood left in the block,
(ii) the total surface area of the remaining solid.

OR

(b) A solid toy is in the form of a hemisphere surmounted by a right circular cone. Ratio of the
radius of the cone to its slant height is 3 : 5. If the volume of the toy is 240 cm3, then find the total
height of the toy.
33. Sides AB and AC and median AD to ∆ABC are respectively proportional to sides PQ and PR and
median PM of another triangle PQR. Show that ∆ABC ~ ∆PQR.

34. An age-wise list of number of literate people in a block is prepared in the following table. There
are total 100 people and their median age is 41.5 years. Information about two groups are missing,
which are denoted by x and y. Find the value of x and y.
Age (in years) 10 – 20 20 – 30 30 – 40 40 – 50 50 – 60 60 – 70 70 – 80
No. of literate people 15 x 12 20 y 8 10

35. (a) In a 2-digit number, the digit at the unit’s place is 5 less than the digit at the ten’s place. The
product of the digits is 36. Find the number.

OR

(b) A shopkeeper buys a number of books for ₹ 1,800. If he had bought 15 more books for the
same amount, then each book would have cost him ₹ 20 less. Find how many books he bought
initially.

SECTION-E (Case Study Based Questions)

Questions 36 to 38 carry 4M each

36. A school has decided to plant some endangered trees on 51st World Environment Day in the nearest
park. They have decided to plant those trees in few concentric circular rows such that each
succeeding row has 20 more trees than the previous one. The first circular row has 50 trees.

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 Based on the above given information, answer the following questions :
(i) How many trees will be planted in the 10th row ? (1)
(ii) How many more trees will be planted in the 8th row than in the 5th row ? (1)
(iii) (a) If 3200 trees are to be planted in the park, then how many rows are required ? (2)
OR
(b) If 3200 trees are to be planted in the park, then how many trees are still left to be planted after
the 11th row ?

37. Partha, a software engineer, lives in Jerusalem for his work. He lives in the most convenient area of
the city from where bank, hospital, post office and supermarket can be easily accessed. In the graph,
the bank is plotted as A(9, 5), hospital as B(– 3, – 1) and supermarket as C(5, – 5) such that A, B, C
form a triangle.

Based on the above given information, answer the following questions :

(i) Find the distance between the bank and the hospital. (1)

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 (ii) In between the bank and the supermarket, there is a post office plotted at E which is their mid-
point. Find the coordinates of E. (1)
(iii) (a) In between the hospital and the supermarket, there is a bus stop plotted as D, which is their
mid-point. If Partha wants to reach the bus stand from the bank, then how much distance does he
need to cover ? (2)
OR
(b) P and Q are two different garment shops lying between the bank and the hospital, such that BP =
PQ = QA. If the coordinates of P and Q are (1, a) and (b, 3) respectively, then find the values of ‘a’
and ‘b’. (2)

38. Due to short circuit, a fire has broken out in New Home Complex. Two buildings, namely X and Y
have mainly been affected. The fire engine has arrived and it has been stationed at a point which is
in between the two buildings. A ladder at point O is fixed in front of the fire engine.
The ladder inclined at an angle 60° to the horizontal is leaning against the wall of the terrace (top)
of the building Y. The foot of the ladder is kept fixed and after some time it is made to lean against
the terrace (top) of the opposite building X at an angle of 45° with the ground. Both the buildings
along with the foot of the ladder, fixed at ‘O’ are in a straight line.

Based on the above given information, answer the following questions :

(i) Find the length of the ladder. (1)
(ii) Find the distance of the building Y from point ‘O’, i.e. OA. (1)
(iii) (a) Find the horizontal distance between the two buildings. (2)
OR
(b) Find the height of the building X.

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PM SHRI KENDRIYA VIDYALAYA GACHIBOWLI,GPRA CAMPUS,HYD-32
SAMPLE PAPER TEST 06 FOR BOARD EXAM 2025

SUBJECT: MATHEMATICS MAX. MARKS : 80

CLASS : X DURATION : 3 HRS
General Instruction:
1. This Question Paper has 5 Sections A-E.
2. Section A has 20 MCQs carrying 1 mark each.
3. Section B has 5 questions carrying 02 marks each.
4. Section C has 6 questions carrying 03 marks each.
5. Section D has 4 questions carrying 05 marks each.
6. Section E has 3 case based integrated units of assessment (04 marks each) with sub-parts of the
values of 1, 1 and 2 marks each respectively.
7. All Questions are compulsory. However, an internal choice in 2 Qs of 5 marks, 2 Qs of 3 marks and
2 Questions of 2 marks has been provided. An internal choice has been provided in the 2marks
questions of Section E
8. Draw neat figures wherever required. Take π =22/7 wherever required if not stated.
SECTION – A
Questions 1 to 20 carry 1 mark each.

1. If the sum of the first n terms of an A.P. be 3n² + n and its common difference is 6, then its first
term is
(a) 2 (b) 3 (c) 1 (d) 4

2. The roots of the equation x2 + 3x – 10 = 0 are:

(a) 2, – 5 (b) – 2, 5 (c) 2, 5 (d) –2, – 5

3. The distance of the point (–1, 7) from x-axis is:

(a) – 1 (b) 7 (c) 6 (d) 50

32
4. If p 2  , then p is a/an
50
(a) whole number (b) integer (c) rational number (d) irrational number

5. The circumferences of two circles are in the ratio 4 : 5. What is the ratio of their radii ?
(a) 16 : 25 (b) 25 : 16 (c) 2 : 5 (d) 4 : 5

6. The empirical relation between the mode, median and mean of a distribution is:
(a) Mode = 3 Median – 2 Mean (b) Mode = 3 Mean – 2 Median
(c) Mode = 2 Median – 3 Mean (d) Mode = 2 Mean – 3 Median

7. The point of intersection of the line represented by 3x – y = 3 and y-axis is given by

(a) (0, –3) (b) (0, 3) (c) (2, 0) (d) (–2, 0)

8. If a and b are the zeroes of the polynomial x2 – 1, then the value of (ab) is
(a) 2 (b) 1 (c) – 1 (d) 0

9. If a pole 6 m high casts a shadow 2√3 m long on the ground, then sun's elevation is:
(a) 60° (b) 45° (c) 30° (d) 90°

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 cos2  1
10. 2
 2 , in simplified form is:
sin  sin 
(a) tan2θ (b) sec2θ (c) 1 (d) – 1

11. Two dice are thrown together. The probability of getting the difference of numbers on their upper
faces equals to 3 is:
(a) 1/9 (b) 2/9 (c) 1/6 (d) 1/12

12. In the given figure, ∆ABC ~ ∆QPR. If AC = 6 cm, BC = 5 cm, QR = 3 cm and PR = x; then the
value of x is:

(a) 3.6 cm (b) 2.5 cm (c) 10 cm (d) 3.2 cm

13. The distance of the point (–6, 8) from origin is:

(a) 6 (b) – 6 (c) 8 (d) 10

14. In the given figure, PA and PB are tangents from external point P to a circle with centre C and Q is
any point on the circle. Then the measure of ∠AQB is

(a) 62½° (b) 125° (c) 55° (d) 90°

15. In the given figure, PQ is a tangent to the circle with centre O. If ∠OPQ = x, ∠POQ = y, then x + y
is:

(a) 45° (b) 90° (c) 60° (d) 180°

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16. If the zeroes of the quadratic polynomial x² + (a + 1)x + b are 2 and – 3, then
(a) a = – 7, b = – 1 (b) a = 5, b = – 1 (c) a = 2, b = – 6 (d) a = 0, b = – 6

17. A card is drawn at random from a well-shuffled pack of 52 cards. The probability that the card
drawn is not an ace is:
(a) 1/13 (b) 9/13 (c) 4/13 (d) 12/13
18. In ∆ABC, PQ || BC. If PB = 6 cm, AP = 4 cm, AQ = 8 cm, find the length of AC.

(a) 12 cm (b) 20 cm (c) 6 cm (d) 14 cm

Direction : In the question number 19 & 20 , A statement of Assertion (A) is followed by a

statement of Reason(R) . Choose the correct option
(a) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion
(A).
(b) Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of
Assertion (A).
(c) Assertion (A) is true but Reason (R) is false.
(d) Assertion (A) is false but Reason (R) is true.
19. Assertion (A): The probability that a leap year has 53 Sunday is 2/7.
Reason (R): The probability that a non-leap year has 53 Sunday is 5/7.

20. Assertion (A): a, b, c are in A.P. if only if 2b = a + c.

Reason (R): The sum of first n odd natural numbers is n2.

SECTION-B
Questions 21 to 25 carry 2M each

21. Two number are in the ratio 2 : 3 and their LCM is 180. What is the HCF of these numbers?
5cos 2 600  4sec 2 300  tan 2 450
22. Evaluate:
sin 2 300  cos2 300
OR
If A and B are acute angles such that sin (A – B) = 0 and 2 cos (A + B) – 1 = 0, then find angles A
and B.

23. If one zero of the polynomial p(x) = 6x² + 37x – (k – 2) is reciprocal of the other, then find the
value of k.

24. Find the sum and product of the roots of the quadratic equation 2x² – 9x + 4 = 0.
OR
Find the discriminant of the quadratic equation 4x² – 5 = 0 and hence comment on the nature of
roots of the equation.

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25. If a fair coin is tossed twice, find the probability of getting 'atmost one head'.

SECTION-C
Questions 26 to 31 carry 3 marks each

26. Two concentric circles are of radii 5 cm and 3 cm. Find the length of the chord of the larger circle
which touches the smaller circle.

27. Find the HCF and LCM of 26, 65 and 117, using prime factorisation.
OR
Prove that √2 is an irrational number.
sin A  2sin 3 A
28. Prove that:  tan A
2 cos3 A  cos A

29. The sum of two numbers is 15. If the sum of their reciprocals is 3/10, find the two numbers.
30. How many terms are there in an A.P. whose first and fifth terms are –14 and 2, respectively and the
last term is 62.
OR
Which term of the A.P.: 65, 61, 57, 53, .................. is the first negative term?
31. Prove that the angle between the two tangents drawn from an external to circle is supplementary to
the angle subtended by the line joining the points of contact at the centre.

SECTION-D
Questions 32 to 35 carry 5M each

32. D is a point on the side BC of a triangle ABC such that ∠ADC = ∠BAC, prove that CA2 = CB. CD
OR
If AD and PM are medians of triangles ABC and PQR respectively where ∆ABC ~ ∆PQR, prove
AB AD
that  .
PQ PM

33. A straight highway leads to the foot of a tower. A man standing on the top of the 75 m high tower
observes two cars at angles of depression of 30° and 60°, which are approaching the foot of the
tower. If one car is exactly behind the other on the same side of the tower, find the distance between
the two cars. (Use √3 = 1.73)
OR
From the top of a 7 m high building, the angle of elevation of the top of a cable tower is 60° and the
angle of depression of its foot is 30°. Determine the height of the tower.

34. A solid is in the shape of a right-circular cone surmounted on a hemisphere, the radius of each of
them being 7 cm and the height of the cone is equal to its diameter. Find the volume of the solid.

35. The monthly expenditure on milk in 200 families of a Housing Society is given below:
Monthly
1000 1500 2000 2500 3000 3500 4000 4500
Expenditure
– 1500 – 2000 – 2500 – 3000 – 3500 – 4000 – 4500 – 5000
(in Rs.)
Number of
24 40 33 x 30 22 16 7
families
Find the value of x and also, find the median and mean expenditure on milk.

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 SECTION-E (Case Study Based Questions)
Questions 36 to 38 carry 4M each

36. Two schools 'P' and 'Q' decided to award prizes to their students for two games of Hockey Rs. x per
student and Cricket Rs. y per student. School 'P' decided to award a total of Rs. 9,500 for the two
games to 5 and 4 students respectively; while school 'Q' decided to award Rs. 7,370 for the two
games to 4 and 3 students respectively.

Based on the above information, answer the

following questions:
(i) Represent the following information algebraically (in terms of x and y).
(ii) (a) What is the prize amount for hockey?
(b) Prize amount on which game is more and by how much?
OR
(iii) What will be the total prize amount if there are 2 students each from two games ?

37. Jagdhish has a field which is in the shape of a right angled triangle AQC. He wants to leave a space
in the form of a square PQRS inside the field from growing wheat and the remaining for growing
vegetables (as shown in the figure). In the field, there is a pole marked as O.

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 Based on the above information, answer the following questions:
(i) Taking O as origin, coordinates of P are (–200, 0) and of Q are (200, 0). PQRS being a square,
what are the coordinates of R and S?
(ii) (a) What is the area of square PQRS ?
OR
(b) What is the length of diagonal PR in square PQRS?
(iii) If S divides CA in the ratio K : 1, what is the value of K, where point A is (200, 800) ?

38. Governing council of a local public development authority of Dehradun decided to build an
adventurous playground on the top of a hill, which will have adequate space for parking. After
survey, it was decided to build rectangular playground, with a semi-circular are allotted for parking
at one end of the playground. The length and breadth of the rectangular playground are 14 units and
7 units, respectively. There are two quadrants of radius 2 units on one side for special seats.

Based on the above information, answer the following questions:

(i) What is the total perimeter of the parking area?
(ii) (a) What is the total area of parking and the two quadrants?
OR
(b) What is the ratio of area of playground to the area of parking area?
(iii) Find the cost of fencing the playground and parking area at the rate of Rs. 2 per unit.

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PM SHRI KENDRIYA VIDYALAYA GACHIBOWLI,GPRA CAMPUS,HYD-32
SAMPLE PAPER TEST 07 FOR BOARD EXAM 2025

SUBJECT: MATHEMATICS MAX. MARKS : 80

CLASS : X DURATION : 3 HRS
General Instruction:
1. This Question Paper has 5 Sections A-E.
2. Section A has 20 MCQs carrying 1 mark each.
3. Section B has 5 questions carrying 02 marks each.
4. Section C has 6 questions carrying 03 marks each.
5. Section D has 4 questions carrying 05 marks each.
6. Section E has 3 case based integrated units of assessment (04 marks each) with sub-parts of the
values of 1, 1 and 2 marks each respectively.
7. All Questions are compulsory. However, an internal choice in 2 Qs of 5 marks, 2 Qs of 3 marks and
2 Questions of 2 marks has been provided. An internal choice has been provided in the 2marks
questions of Section E
8. Draw neat figures wherever required. Take π =22/7 wherever required if not stated.
SECTION – A
Questions 1 to 20 carry 1 mark each.

1. The distance of the point (–6, 8) from x-axis is

(a) 6 units (b) – 6 units (c) 8 units (d) 10 units

2. sec θ when expressed in terms of cot θ, is equal to:

1  cot 2  2 1  cot 2  1  cot 2 
(a) (b) 1  cot  (c) (d)
cot  cot  cot 

3. The ratio of HCF to LCM of the least composite number and the least prime number is:
(a) 1 : 2 (b) 2 : 1 (c) 1 : 1 (d) 1 : 3

4. The pair of linear equations 2x = 5y + 6 and 15y = 6x – 18 represents two lines which are:
(a) intersecting (b) parallel (c) coincident (d) either intersecting or parallel

5. If ∆PQR ~ ∆ABC; PQ = 6 cm, AB = 8 cm and the perimeter of ∆ABC is 36 cm, then the perimeter
of ∆PQR is
(a) 20.25 cm (b) 27 cm (c) 48 cm (d) 64 cm

6. The next term of the A.P.: √6 , √24, √54 is:

(a) √60 (b) √96 (c) √72 (d) √216

7. What is the area of a semi-circle of diameter 'd' ?

1 1 1 1 2
(a) d2 (b)  d 2 (c)  d 2 (d) d
16 4 8 2

8. If a, b are zeroes of the polynomial x2 – 1, then value of (a + b) is:

(a) 2 (b) 1 (c) – 1 (d) 0

9. If the quadratic equation ax2 + bx + c = 0 has two real and equal roots, then 'c' is equal to
(a) −b/2a (b) b/2a (c) −b²/4a (d) b²/4a

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10. The number of quadratic polynomials having zeroes – 5 and – 3 is
(a) 1 (b) 2 (c) 3 (d) more than 3

11. In the given figure, DE||BC. If AD = 3 cm, AB = 7 cm and EC = 3 cm, then the length of AE is
(a) 2 cm (b) 2.25 cm (c) 3.5 cm (d) 4 cm

12. In the given figure, TA is a tangent to the circle with centre O such that OT = 4 cm, ∠OTA = 30°,
then length of TA is:

(a) 2√3 cm (b) 2 cm (c) 2√2 cm (d) 3 cm

13. The volume of a right circular cone whose area of the base is 156 cm² and the vertical height is 8
cm, is:
(a) 2496 cm³ (b) 1248 cm³ (c) 1664 cm³ (d) 416 cm³

14. 3 chairs and 1 table cost Rs. 900; whereas 5 chairs and 3 tables cost Rs. 2,100. If the cost of 1 chair
is Rs. x and the cost of 1 table is Rs. y, then the situation can be represented algebraically as
(a) 3x + y = 900, 3x + 5y = 2100 (b) x + 3y = 900, 3x + 5y = 2100
(c) 3x + y = 900, 5x + 3y = 2100 (d) x + 3y = 900, 5x + 3y = 2100

15. A bag contains 5 pink, 8 blue and 7 yellow balls. One ball is drawn at random from the bag. What is
the probability of getting neither a blue nor a pink ball ?
(a) 1/4 (b) 2/5 (c) 7/20 (d) 13/20

16. A card is drawn at random from a well shuffled deck of 52 playing cards. The probability of getting
a face card is
(a) 1/2 (b) 3/13 (c) 4/13 (d) 1/13

17. If θ is an acute angle of a right angled triangle, then which of the following equation is not true?
(a) sinθ cotθ = cosθ (b) cosθ tanθ = sinθ
(c) cosec²θ – cot²θ = 1 (d) tan²θ – sec²θ = 1

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 1 1
18. If α, β are the zeroes of the polynomial p(x) = 4x² – 3x – 7, then    is equal to:
  
(a) 7/3 (b) −7/3 (c) 3/7 (d) −3/7

Direction : In the question number 19 & 20 , A statement of Assertion (A) is followed by a

statement of Reason(R) . Choose the correct option
(a) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion
(A).
(b) Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of
Assertion (A).
(c) Assertion (A) is true but Reason (R) is false.
(d) Assertion (A) is false but Reason (R) is true.
19. Assertion (A): For 0 < θ ≤ 90°, cosecθ – cotθ and cosecθ + cotθ are reciprocal of each other.
Reason (R): cosec²θ – cot²θ = 1

20. Assertion (A): If 5 + √7 is a root of a quadratic equation with rational coefficients, then its other
root is 5 − √7.
Reason (R): Surd roots of quadratic equation with rational coefficients occur in conjugate pairs.

SECTION – B
Questions 21 to 25 carry 2 marks each.

21. Show that 6n cannot end with digit 0 for any natural number 'n'.
OR
Find the HCF and LCM of 72 and 120.

22. Find the length of the shadow on the ground of a pole of height 18 m when angle of elevation θ of
the sun is such that tanθ = 6/7.

23. In the given figure, ABC is a triangle in which DE||BC. If AD = x, DB = x – 2, AE = x + 2 and EC

= x – 1, then find the value of x.

OR
Diagonals AC and BD of trapezium ABCD with AB||DC intersect each other at point O. Show that
OA/OC = OB/OD.

24. In the given figure, PA is a tangent to the circle drawn from the external point P and PBC is the
secant to the circle with BC as diameter. If ∠AOC = 130°, then find the measure of ∠APB, where O
is the centre of the circle.

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25. A line intersects y-axis and x-axis at point P and Q, respectively. If R(2, 5) is the mid-point of line
segment PQ, then find the coordinates of P and Q.

SECTION – C
Questions 26 to 31 carry 3 marks each.

26. Find the value of 'p' for which the quadratic equation px(x – 2) + 6 = 0 has two equal real roots.

OR

If α and β are roots of the quadratic equation x² – 7x + 10 = 0, find the quadratic equation whose
roots are α² and β².

1  sec A sin 2 A
27. Prove that: 
sec A 1  cos A
OR

Prove that sec A (1 – sin A) (sec A + tan A) = 1.

28. Find the ratio in which the line segment joining the points A(6, 3) and B(–2, –5) is divided by x-
axis.

29. Prove that √5 is an irrational number.

30. In the given figure, E is a point on the side CB produced of an isosceles triangle ABC with AB =
AC. If AD ⊥ BC and EF ⊥ AC, them prove that ∆ABD ~ ∆ECF.

31. In a circle of radius 21 cm, an arc subtends an angle of 60° at the centre. Find the area of the sector
formed by the arc. Also, find the length of the arc.

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 SECTION – D
Questions 32 to 35 carry 3 marks each.

32. 250 apples of a box were weighted and the distribution of masses of the apples is given in the
following table:
Mass (in grams) 80 – 100 100 – 120 120 – 140 140 – 160 160 – 180
Number of apples 20 60 70 x 60
(i) Find the value of x and the mean mass of the apples.
(ii) Find the modal mass of the apples.

33. The ratio of the 11th term to the 18th term of an A.P. is 2 : 3. Find the ratio of the 5th term to the
21st term. Also, find the ratio of the sum of first 5 terms to the sum of first 21 terms.

OR

If the sum of first 6 terms of an A.P. is 36 and that of the first 16 terms is 256, find the sum of first
10 terms.

34. Two tangents TP and TQ are drawn to a circle with centre O from an external point T (see below
left figure). Prove that ∠PTQ = 2 ∠OPQ.

OR

A circle touches the side BC of a ∆ABC at a point P and touches AB and AC when produced at Q
1
and R respectively (see above right sided figure). Show that AQ = (Perimeter of ∆ABC).
2

35. A student was asked to make a model shaped like a cylinder with two cones attached to its ends by
using a thin aluminium sheet. The diameter of the model is 3 cm and its total length is 12 cm. If
each cone has a height of 2 cm, find the volume of air contained in the model.

SECTION – E(Case Study Based Questions)

Questions 36 to 38 carry 4 marks each.

36. Aditya is a pilot in Air India. During the Covid-19 pandemic, many Indian passengers were stuck at
Dubai Airport. The government of India sent special aircraft to take them. Mr. Vinod was leading
this operation. He is flying from Dubai to New Delhi with these passengers. His airplane is
approaching point A along a straight line and at a constant altitude h. At 10:00 am, the angle of
elevation of the airplane is 30° and at 10:01 am, it is 60°.

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 (i) What is the distance d is covered by the airplane from 10:00 am to 10:01 am if the speed of the
airplane is constant and equal to 600 miles/hour?
(ii) What is the altitude h of the airplane? (round answer to 2 decimal places)

OR

Find the distance between passenger and airplane when the angle of elevation is 60°.

(iii) Find the distance between passenger and airplane when the angle of elevation is 30°.

37. "Eight Ball" is a game played on a pool table with 15 balls numbered 1 to 15 and a "cue ball" that is
solid and white. Of the 15 numbered balls, eight are solid (non-white) coloured and numbered 1 to
8 and seven are striped balls numbered 9 to 15.

The 15 numbered pool balls (no cue ball) are placed in a large bowl and mixed, then one ball is
drawn out at random.
Based on the above information, answer the following question:
(i) What is the probability that the drawn ball bears number 8?
(ii) What is probability that the drawn ball bears an even number?

OR

What is the probability that the drawn ball bears a number, which is a multiple of 3?

(iii) What is the probability that the drawn ball is a solid coloured and bears an even number?

38. A coaching institute of Mathematics conducts classes in two batches I and II and fees for rich and
poor children are different. In batch I, there are 20 poor and 5 rich children, whereas in batch II,
there are 5 poor and 25 rich children. The total monthly collection of fees from batch I is Rs. 9000
and from batch II is Rs. 26,000. Assume that each poor child pays Rs. x per month and each rich
child pays Rs. y per month.

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 Based on the above information, answer the following questions:
(i) Represent the information given above in terms of x and y.
(ii) Find the monthly fee paid by a poor child.

OR

Find the difference in the monthly fee paid by a poor child and a rich child.

(iii) If there are 10 poor and 20 rich children in batch II, what is the total monthly collection of fees
from batch II?

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PM SHRI KENDRIYA VIDYALAYA GACHIBOWLI, GPRA CAMPUS, HYD-32
SAMPLE PAPER TEST 08 FOR BOARD EXAM 2025

SUBJECT: MATHEMATICS MAX. MARKS : 80

CLASS : X DURATION : 3 HRS
General Instruction:
1. This Question Paper has 5 Sections A-E.
2. Section A has 20 MCQs carrying 1 mark each.
3. Section B has 5 questions carrying 02 marks each.
4. Section C has 6 questions carrying 03 marks each.
5. Section D has 4 questions carrying 05 marks each.
6. Section E has 3 case based integrated units of assessment (04 marks each) with sub-parts of the
values of 1, 1 and 2 marks each respectively.
7. All Questions are compulsory. However, an internal choice in 2 Qs of 5 marks, 2 Qs of 3 marks and
2 Questions of 2 marks has been provided. An internal choice has been provided in the 2marks
questions of Section E
8. Draw neat figures wherever required. Take π =22/7 wherever required if not stated.
SECTION – A
Questions 1 to 20 carry 1 mark each.

1. The pair of equations x + 2y + 5 = 0 and –3x – 6y + 1 = 0 have

(a) a unique solution (b) exactly two solutions
(c) Infinitely many solutions (d) no solution

2. If p and q are positive integers such that p = a3b2 and q = a2b, where ‘a’ and ‘b’ are prime numbers,
then the LCM ( p, q) is …..
(a) ab (b) a2b2 (c) a3b2 (d) a3b3

3. The ratio in which x-axis divides the join of (2, -3) and (5, 6) is:
(a) 1: 2 (b) 3 : 4 (c) 1: 3 (d) 1: 5

4. Find the value of k for which the equation x2 + k(2x + k − 1)+ 2 = 0 has real and equal roots.
(a) 2 (b) 3 (c) 4 (d) 5

5. In a formula racing competition, the time taken by two racing cars A and B to complete 1 round of
the track is 30 minutes and p minutes respectively. If the cars meet again at the starting point for the
first time after 90 minutes and the HCF (30, p) = 15, then the value of p is
(a)45 minutes (b)60 minutes (c)75 minutes (d)180 minutes

6. For the following distribution:

Marks Below Below Below Below Below Below
10 20 30 40 50 60
No. of Students 3 12 27 57 75 80
the modal class is
(a) 10 – 20 (b) 20 – 30 (c) 30 – 40 (d) 50 – 60

7. A medicine-capsule is in the shape of a cylinder of radius 0.25 cm with two hemispheres stuck to
each of its ends. The length of the entire capsule is 2 cm. What is the total surface area of the
capsule? (Take π as 3.14)

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 (a) 0.785 cm2 (b) 0.98125 cm2 (c) 2.7475 cm2 (d) 3.14 cm2

8. In ABC, DE || AB, If CD = 3 cm, EC = 4 cm, BE = 6 cm, then DA is equal to

(a) 7.5 cm (b) 3 cm (c) 4.5 cm (d) 6 cm

9. The 11th and 13th terms of an AP are 35 and 41 respectively, its common difference is
(a) 38 (b) 32 (c) 6 (d) 3

10. If is an acute angle and tan + cot = 2, then the value of sin3 + cos3 is
1 2
(a) 1 (b) (c) (d) 2
2 2

11. Volumes of two spheres are in the ratio 64 : 27. The ratio of their surface areas is
(a) 3 : 4 (b) 4 : 3 (c) 9 : 16 (d) 16 : 9

12. The area of the square that can be inscribed in a circle of radius 8 cm is
(a) 256 cm² (b) 128 cm² (c) 64√2 cm² (d) 64 cm²

13. Two dice are thrown at the same time and the product of numbers appearing on them is noted. The
probability that the product is a prime number is
(a) 1/3 (b) 1/6 (c) 1/5 (d) 5/6

14. In ΔABC right angled at B, if cotC = √3 , then then cosAsinC + sinAcosC =

(a) –1 (b) 0 (c) 1 (d) √3 / 2

15. In the below figure, the pair of tangents AP and AQ drawn from an external point A to a circle with
centre O are perpendicular to each other and length of each tangent is 5 cm. Then radius of the
circle is
(a) 10 cm (b) 7.5 cm (c) 5 cm (d) 2.5 cm

16. A sphere of diameter 18 cm is dropped into a cylindrical vessel of diameter 36 cm, partly filled with
water. If the sphere is completely submerged, then the water level rises (in cm) by
(a) 3 (b) 4 (c) 5 (d) 6

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17. A tangent is drawn from a point at a distance of 17 cm of circle (O, r) of radius 8 cm. The length of
tangent is
(a) 5 cm (b) 9 cm (c) 15 cm (d) 23 cm

18. If in two triangles, DEF and PQR, ∠ =∠ and ∠ =∠ , then which of the following is not true?
EF DF EF DE DE DF EF DE
(a)  (b)  (c)  (d) 
PR PQ RP PQ QR PQ RP QR

Direction : In the question number 19 & 20 , A statement of Assertion (A) is followed by a

statement of Reason(R) . Choose the correct option

19. Assertion (A): The length of the minute hand of a clock is 7 cm. Then the area swept by the
minute hand in 5 minute is 77/6 cm2.

Reason (R): The length of an arc of a sector of angle q and radius r is given by l   2 r
3600

20. Assertion (A): If x = 2 sin2θ and y = 2 cos2θ + 1 then the value of x + y = 3.

Reason (R): For any value of θ, sin2θ + cos2θ = 1

SECTION – B
Questions 21 to 25 carry 2 marks each.

21. For what value of k, the following system of equations have infinite solutions:
2x – 3y = 7, (k + 2)x – (2k + 1)y = 3 (2k – 1)?
OR
Sumit is 3 times as old as his son. Five years later, he shall be two and a half time as old as his son.
How old is Sumit at present?

22. ABCD is a trapezium in which AB || CD and its diagonals intersect each other at the point O. Using
OA OB
a similarity criterion of two triangles, show that 
OC OD

23. The probability of selecting a blue marble at random from a jar that contains only blue, black and
green marbles is 1/5. The probability of selecting a black marble at random from the same jar is 1/4.
If the jar contains 11 green marbles, find the total number of marbles in the jar.

24. From a point P, two tangents PA and PB are drawn to a circle C(0, r). If OP = 2r, then find ∠APB.
Prove that triangle APB is an equilateral triangle.

OR
Two concentric circles are of radii 8 cm and 5 cm. Find the length of the chord of the larger circle
which touches the smaller circle.

25. Find the point on y-axis which is equidistant from the points (5, – 2) and (–3, 2).

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 SECTION – C
Questions 26 to 31 carry 3 marks each.

26. Prove that the lengths of the tangents drawn from an external point to a circle are equal.

27. Prove that (sinA + cosecA)2 + (cosA + secA)2 = 7 + tan2A + cot2A

OR
If sin θ + cos θ = √3 , then prove that tan θ + cot θ = 1.

28. Daily wages of 110 workers, obtained in a survey, are tabulated below:
Daily Wages (in Rs. ) 100-120 120-140 140-160 160-180 180-200 200-220 220-240
Number of Workers 10 15 20 22 18 12 13
Compute the mean daily wages and modal daily wages of these workers.

29. The sum of the digits of a two-digit number is 9. Also 9 times this number is twice the number
obtained by reversing the order of the digits. Find the number.

30. The sum of the 5th and the 9th terms of an AP is 30. If its 25th term is three times its 8th term, find
the AP.
OR
If the ratio of the sum of first n terms of two AP’s is (7n + 1) : (4n + 27), find the ratio of their mth
terms.

31. Find the coordinates of the points which divide the line segment joining A (–2, 2) and B (2, 8) into
four equal parts.

SECTION – D
Questions 32 to 35 carry 3 marks each.

32. Ramesh made a bird-bath for his garden in the shape of a cylinder with a hemispherical depression
at one end. The height of the cylinder is 1.45 m and its radius is 30 cm. Find the total surface area
of the bird-bath.

OR
A tent is in shape of a cylinder surmounted by a conical top. If the height and diameter of the
cylindrical part are 2.1m and 4m respectively and the slant height of the top is 2.8m. Find the area
of canvas used for making the tent. Also find the cost of canvas of the tent at the rate of 500 per m2.

33. State and prove Basic Proportional Theorem.

34. A person on tour has Rs.360 for his expenses. If he extends his tour for 4 days, he has to cut down
his daily expenses by Rs.3. Find the original duration of the tour.

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35. The lower window of a house is at a height of 2 m above the ground and its upper window is 4 m
vertically above the lower window. At certain instant, the angles of elevation of a balloon from
these windows are observed to be 60° and 30°, respectively. Find the height of the balloon above
the ground.
OR
From the top of a 60 m high building, the angles of depression of the top and the bottom of a tower
are 45° and 60° respectively. Find the height of the tower. [Take √3 = 1.73]

SECTION – E(Case Study Based Questions)

Questions 36 to 38 carry 4 marks each.

36. Mohan takes a loan from a bank for his car. Mohan replays his total loan of Rs.118000 by paying
every month starting with the first instalment of Rs.1000. If he increases the instalment by Rs.100
every month.

(i) What is the first term and common difference of given question. (1)
(ii) The amount paid buy him in 30th instalment. (1)
(iii) The amount paid by him in the 30 instalments is (2)
(OR)
(iii) What amount does he still have to pay after 30th instalment? (2)

37. Aditya plantations have two rectangular fields of the same width but different lengths. They are
required to plant 168 trees in the smaller field and 462 trees in the larger field. In both fields, the
trees will be planted in the same number of rows but in different number of columns.

(i) What is the maximum number of rows in which the trees can be planted in each of the fields? (2)
(ii) If the trees are planted in the number of rows obtained in part (i), how many columns will each
field have?
(iii) If total cost of planted trees in one column is Rs. 500, then find the cost to plant the trees in
smaller field.
OR
If the total cost of planted trees in one column is Rs. 500, the find the cost to plant the trees in larger
field.

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38. Shivani took a pack of 52 cards. She kept aside all the black face cards and shuffled the remaining
cards well.

Based on the above information answer the following questions.

(i) Write the number of total possible outcomes.
(ii) She draws a card from the well-shuffled pack of remaining cards. What is the probability that
the card is a face card?
(iii) Write the probability of drawing a black card.
OR
(iii) What is the probability of getting neither a black card nor an ace card?

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PM SHRI KENDRIYA VIDYALAYA GACHIBOWLI,GPRA CAMPUS, HYD-32
SAMPLE PAPER TEST 09 FOR BOARD EXAM 2025

SUBJECT: MATHEMATICS MAX. MARKS : 80

CLASS : X DURATION : 3 HRS
General Instruction:
1. This Question Paper has 5 Sections A-E.
2. Section A has 20 MCQs carrying 1 mark each.
3. Section B has 5 questions carrying 02 marks each.
4. Section C has 6 questions carrying 03 marks each.
5. Section D has 4 questions carrying 05 marks each.
6. Section E has 3 case based integrated units of assessment (04 marks each) with sub-parts of the
values of 1, 1 and 2 marks each respectively.
7. All Questions are compulsory. However, an internal choice in 2 Qs of 5 marks, 2 Qs of 3 marks
and 2 Questions of 2 marks has been provided. An internal choice has been provided in the 2marks
questions of Section E
8. Draw neat figures wherever required. Take π =22/7 wherever required if not stated.
SECTION – A
Questions 1 to 20 carry 1 mark each.
1. The solution of the following pair of equation is:
x – 3y = 2, 3x – y = 14
(a) x = 5, y = 1 (b) x = 2, y = 3 (c) x = 1, y = 2 (d) x = 1, y = 4

2. In the given figure, ∆ABC ~ ∆QPR. If AC = 6 cm, BC = 5 cm, QR = 3 cm and PR = x; then the
value of x is:

(a) 3.6 cm (b) 2.5 cm (c) 10 cm (d) 3.2 cm

3. If 3 sin θ – cos θ = 0 and 0° < θ < 90°, find the value of θ.

(a) 30° (b) 45° (c) 60° (d) 90°

4. In the given figure, if AB = 14 cm, then the value of tan B is:

4 14 5 13
(a) (b) (c) (d)
3 3 3 3
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5. If the distance between the points (4,p) and (1,0) is 5, then value of p is
(a) 4 only (b) ±4 (c) -4 only (d) 0
6. If two positive integers a and b are written as a = x3y2 and b = xy3, where x and y are prime
numbers, then the HCF (a, b) is:
(a) xy (b) xy2 (c) x3y3 (d) x2y2

7. 108 can be expressed as a product of its primes as ……………..

(a) 23 x 32 (b) 23 x 33 (c) 22 x 32 (d) 22 x 33

8. If p and q are the zeroes of the quadratic polynomial f(x) = 2x2 – 7x + 3, find the value of p + q –
pq is
(a) 1 (b) 2 (c) 3 (d) None of these

1
9. If sin 2A = tan² 45° where A is an acute angle, then the value of A is
2
(a) 60° (b) 45° (c) 30° (d) 15°

10. If angle between two radii of a circle is 130⁰, the angle between the tangents at the ends of the
radii is :
(a) 90⁰ (b) 50⁰ (c) 70⁰ (d) 40⁰

11. The relationship between mean, median and mode for a moderately skewed distribution is
(a) mode = median – 2 mean (b) mode = 3 median – 2 mean
(c) mode = 2 median – 3 mean (d) mode = median – mean

12. The runs scored by a batsman in 35 different matches are given below:
Runs Scored 0-15 15-30 30-45 45-60 60-75 75-90
Frequency 5 7 4 8 8 3
The lower limit of the median class is
(a) 15 (b) 30 (c) 45 (d) 60

13. Two cubes each with 6 cm edge are joined end to end. The surface area of the resulting cuboid is
(a) 180 ² (b) 360 ² (c) 300 ² (d) 260 ²

14. A cone, a hemisphere and cylinder are of the same base and of the same height. The ratio of their
volumes is
(a) 1 : 2 : 3 (b) 2 : 1 : 3 (c) 3 : 1 : 2 (d) 3 : 2 : 1

15. The probability of getting a bad egg in a lot of 400 is 0.035. The number of bad eggs in the lot is
(a) 7 (b) 14 (c) 21 (d) 28

16. A 1.6 m tall girl stands at distance of 3.2 m from a lamp post and casts shadow of 4.8 m on the
ground, then the height of the lamp post is
(a) 8 m (b) 4 m (c) 6 m (d) 8/3 m

17. The area of a quadrant of a circle, whose circumference is 22 cm, is

11 2 77 77 77
(a) cm (b) cm2 (c) cm2 (d) cm2
8 8 2 4

18. If the quadratic equation x2 + 4x + k = 0 has real and equal roots, then
(a) k < 4 (b) k > 4 (c) k = 4 (d) k ≥ 4

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DIRECTION: In the question number 19 and 20, a statement of Assertion (A) is followed by a
statement of Reason (R).
Choose the correct option

19. Assertion (A): If HCF ( 90, 144) = 18, then LCM (90, 144) = 720
Reason (R): HCF (a, b) x LCM (a, b) = a x b
(a) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of
Assertion (A).
(b) Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of
Assertion (A).
(c) Assertion (A) is true but Reason (R) is false.
(d) Assertion (A) is false but Reason (R) is true.

20. Assertion (A): The point (0, 4) lies on y -axis.

Reason (R): The x co-ordinate on the point on y -axis is zero.
(a) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of
Assertion (A)
(b) Both assertion (A) and reason (R) are true and reason (R) is not the correct explanation of
Assertion (A)
(c) Assertion (A) is true but reason(R) is false.
(d) Assertion (A) is false but reason(R) is true.

SECTION – B
Questions 21 to 25 carry 2 marks each.

21. For what value of k will the following system of linear equations have no solution?
3x + y = 1; (2k – 1) x + (k – 1) y = 2k + 1

22. In figure PA and PB are tangents to the circle drawn from an external point P. CD is the third
tangent touching the circle at Q. If PA = 15 cm, find the perimeter of ΔPCD.

1
23. If tan (A + B) = 3 and tan (A – B) = ; 0° < A+B ≤ 90°; A > B, find A and B.
3
OR
If xsin θ + ycos θ = sinθ cosθ and xsinθ = ysinθ then find x2 + y2.
3 3

24. X is a point on the side BC of ∆ABC. XM and XN are drawn parallel to AB and AC respectively
meeting AB in N and AC in M. MN produced meets CB produced at T. Prove that TX2 = TB ×
TC.
25. The length of the minute hand of a clock is 14 cm. Find the area swept by the minute hand in 5
minutes.
OR
In a circle of radius 21 cm, an arc subtends an angle of 60° at the centre. Find (i) the length of the
arc (ii) area of the sector formed by the arc
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 SECTION – C
Questions 26 to 31 carry 3 marks each.
26. Solve the following linear equations:
152x – 378y = –74 and –378x + 152y = –604

OR
Yash scored 40 marks in a test, getting 3 marks for each right answer and losing 1 mark for each
wrong answer. Had 4 marks been awarded for each correct answer and 2 marks been deducted for
each incorrect answer, then Yash would have scored 50 marks. How many questions were there in
the test?

27. Prove that √5 is an irrational number.

28. Find the zeroes of the quadratic polynomial x2 – 2x – 8 and verify the relationship between the
zeroes and the coefficients of the polynomial.

29. If PQ is a tangent drawn from an external point P to a circle with centre O and QOR is a diameter
where length of QOR is 8 cm such that ∠POR = 120°, then find OP and PQ.
OR
In the figure XY and X'Y' are two parallel tangents to a circle with centre O and another tangent
AB with point of contact C interesting XY at A and X'Y' at B, what is the measure of ∠AOB.

30. Two dice are thrown at the same time. What is the probability that the sum of the two numbers
appearing on the top of the dice is
(i) 8? (ii) 7? (iii) less than or equal to 12?

p2 1
31. If sec θ + tan θ = p, prove that sin θ = .
p2 1

SECTION – D
Questions 32 to 35 carry 5 marks each.

32. A motor boat whose speed is 15 km/hr in still water goes 30 km downstream and comes back in 4
hours 30 minutes. Find the speed of the stream.
OR
Rs.6500 were divided equally among a certain number of persons. Had there been 15 more
persons, each would have got Rs.30 less. Find the original number of persons.

33. From a solid cylinder whose height is 2.4 cm and diameter 1.4 cm, a conical cavity of the same
height and same diameter is hollowed out. Find the total surface area of the remaining solid to the
nearest cm2.
OR
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 Rasheed got a playing top (lattu) as his birthday present, which surprisingly had no colour on it.
He wanted to colour it with his crayons. The top is shaped like a cone surmounted by a
hemisphere. The entire top is 5 cm in height and the diameter of the top is 3.5 cm. Find the area
he has to colour.

34. State and Prove Basic Proportionality Theorem.

35. The following frequency distribution gives the monthly consumption of 68 consumers of a
locality. Find median, mean and mode of the data and compare them.
Monthly consumption of Number of consumers
electricity (in units)
65-85 4
85-105 5
105-125 13
125-145 20
145-165 14
165-185 8
185-205 4

SECTION – E(Case Study Based Questions)

Questions 36 to 38 carry 4 marks each.
36. Lakshaman Jhula is located 5 kilometers north-east of the city of Rishikesh in the Indian state of
Uttarakhand. The bridge connects the villages of Tapovan to Jonk. Tapovan is in Tehri Garhwal
district, on the west bank of the river, while Jonk is in Pauri Garhwal district, on the east bank.
Lakshman Jhula is a pedestrian bridge also used by motorbikes. It is a landmark of Rishikesh. A
group of Class X students visited Rishikesh in Uttarakhand on a trip. They observed from a point
(P) on a river bridge that the angles of depression of opposite banks of the river are 60° and 30°
respectively. The height of the bridge is about 18 meters from the river.

Based on the above information answer the following questions.

(i) Find the distance PA. (1)
(ii) Find the distance PB (1)
(iii) Find the width AB of the river. (2)
OR
(iii) Find the height BQ if the angle of the elevation from P to Q be 30°. (2)

37. In the month of April to June 2022, the exports of passenger cars from India increased by 26% in
the corresponding quarter of 2021–22, as per a report. A car manufacturing company planned to
produce 1800 cars in 4th year and 2600 cars in 8th year. Assuming that the production increases
uniformly by a fixed number every year.
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 Based on the above information answer the following questions.
(i) Find the production in the 1st year. (1)
(ii) Find the production in the 12th year. (1)
(iii) Find the total production in first 10 years. (2)
OR
(iii) In how many years will the total production reach 31200 cars? (2)

38. In order to conduct sports day activities in your school, lines have been drawn with chalk powder
at a distance of 1 m each in a rectangular shaped ground ABCD. 100 flower pots have been
placed at the distance of 1 m from each other along AD, as shown in the following figure.
1 1
Niharika runs ( )th distance AD on the 2nd line and posts a green Flag. Preet runs ( ) th
4 5
distance AD on the eighth line and posts are red flags. Taking A as the origin AB along x-axis
and AD along y-axis, answer the following questions:
(i) Find the coordinates of the green flag. (1)
(ii) Find the distance between the two flags. (1)
(iii) If Rashmi has to post a blue flag exactly halfway between the line segment joining the two
flags, where should she post her flag? (2)
OR
(iii) If Joy has to post a flag at one fourth distance from the green flag, in the line segment joining
the green and red flags, then where should he post his flag? (2)

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PM SHRI KENDRIYA VIDYALAYA GACHIBOWLI,GPRA CAMPUS, HYD-32
SAMPLE PAPER TEST 10 FOR BOARD EXAM 2025

SUBJECT: MATHEMATICS MAX. MARKS : 80

CLASS : X DURATION : 3 HRS
General Instruction:
1. This Question Paper has 5 Sections A-E.
2. Section A has 20 MCQs carrying 1 mark each.
3. Section B has 5 questions carrying 02 marks each.
4. Section C has 6 questions carrying 03 marks each.
5. Section D has 4 questions carrying 05 marks each.
6. Section E has 3 case based integrated units of assessment (04 marks each) with sub-parts of the
values of 1, 1 and 2 marks each respectively.
7. All Questions are compulsory. However, an internal choice in 2 Qs of 5 marks, 2 Qs of 3 marks and
2 Questions of 2 marks has been provided. An internal choice has been provided in the 2marks
questions of Section E
8. Draw neat figures wherever required. Take π =22/7 wherever required if not stated.
SECTION – A
Questions 1 to 20 carry 1 mark each.

1. If the lines 3x + 2ky – 2 = 0 and 2x + 5y + 1 = 0 are parallel, then what is the value of k?
(a) 4/15 (b) 15/4 (c) 4/5 (d) 5/4

2. If the coordinates of one end of a diameter of a circle are (2, 3) and the coordinates of its centre are
(-2, 5), then the coordinates of the other end of the diameter are
(a) (0, 8) (b) (0, 4) (c) (6, -7) (d)(-6, 7)

3. A bag has 5 white marbles, 8 red marbles and 4 purple marbles. If we take a marble randomly, then
what is the probability of not getting purple marble?
(a) 0.5 (b) 0.66 (c) 0.08 (d) 0.77

4. In what ratio does the x-axis divide the join of A(2, -3) and B(5, 6)?
(a) 1 : 2 (b) 3 : 5 (c) 2 : 1 (d) 2 : 3
5. If the distance between the points A(2, -2) and B(-1, x) is equal to 5, then the value of x is:
(a) 2 (b) -2 (c) 1 (d) -1
6. The least number that is divisible by all the numbers from 1 to 10 (both inclusive) is:
(a) 10 (b) 100 (c) 504 (d) 2520
7. The mode and mean is given by 7 and 8, respectively. Then the median is:
(a) 1/13 (b) 13/3 (c) 23/3 (d) 33
8. The length of a tangent from a point A at a distance 5 cm from the centre of the circle is 4 cm. The
radius of the circle is:
(a) 3 cm (b) 5 cm (c) 7 cm (d) 10 cm
9. The midpoint of a line segment joining two points A(2, 4) and B(-2, -4) is
(a) (-2, 4) (b) (2, -4) (c) (0, 0) (d) (-2, -4)

10. A sphere of diameter 18 cm is dropped into a cylindrical vessel of diameter 36 cm, partly filled with
water. If the sphere is completely submerged then the water level rises by
(a) 4cm (b) 5 cm (c) 3 cm (d) 6 cm

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11. The angle of depression of a car, standing on the ground, from the top of a 75 m tower, is 30°. The
distance of the car from the base of the tower (in metres) is
(a) 25√3 (b) 75√3 (c) 150 (d) 50√3

12. The solution of the equations x - y = 2 and x + y = 4 is:

(a) 3 and 1 (b) 4 and 3 (c) 5 and 1 (d) -1 and -3

13. If P(E) = 0.07, then what is the probability of ‘not E’?

(a) 0.93 (b) 0.95 (c) 0.89 (d) 0.90

14. HCF of (23 x 32 x 5), (22 x 33 x 52) and (24 x 3 x 53 x 7) is

(a) 60 (b) 48 (c) 30 (d) 105

15. If the zeroes of the quadratic polynomial ax2 + bx + c, c ≠ 0 are equal, then
(a) c and b have opposite signs (b) c and a have opposite signs
(c) c and b have same signs (d) c and a have same signs

16. If one root of equation 4x2 – 2x+k-4=0 is reciprocal of the other. The value of k is:
(a) -8 (b) 8 (c) -4 (d) 4

17. If P(A) denotes the probability of an event A, then

(a) P(A) < 0 (b) P(A) > 1 (c) 0 ≤ P(A) ≤ 1 (d) –1 ≤ P(A) ≤ 1

18. In ∆ ABC, right-angled at B, AC = 25 cm, BC = 7 cm. The value of tan C is:

(a) 12/7 (b) 24/7 (c) 20/7 (d) 7/24

Direction : In the question number 19 & 20 , A statement of Assertion (A) is followed by a

statement of Reason(R) . Choose the correct option

19. Assertion (A): If two triangles are similar and have an equal area, then they are congruent.
Reason (R): Corresponding sides of two triangles are equal, then triangles are congruent.
(a) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of
Assertion (A)
(b) Both assertion (A) and reason (R) are true and reason (R) is not the correct explanation of
Assertion (A)
(c) Assertion (A) is true but reason(R) is false.
(d) Assertion (A) is false but reason(R) is true.

20. Assertion : The HCF of two numbers is 18 and their product is 3072. Then their LCM = 169.
Reason : If a, b are two positive integers, then HCF x LCM = a x b.
(a) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of
Assertion (A).
(b) Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of
Assertion (A).
(c) Assertion (A) is true but Reason (R) is false.
(d) Assertion (A) is false but Reason (R) is true.

SECTION-B
Questions 21 to 25 carry 2M each

21. Find the value of k such that the polynomial x2 – (k + 6)x + 2(2k – 1) has sum of its zeroes equal to
half of their product.

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22. If the point P(k – 1, 2) is equidistant from the points A(3, k) and B(k, 5), find the values of k.
OR
Find the ratio in which the point C(2, y) divides the line segment joining the points A(–2, 2) and
B(3, 7).

23. A card is drawn at random from a well shuffled pack of 52 cards. Find the probability of getting (i)
a red king (ii) a queen or a jack

24. Two concentric circles are of radii 6.5 cm and 2.5 cm. Find the length of the chord of the larger
circle which touches the smaller circle.
OR
From an external point P, tangents PA and PB are drawn to a circle with center O. If CD is the
tangent to the circle at a point E and PA = 14cm, find the perimeter of ∆PCD.

25. Solve for x and y: 71x + 37y = 253, 37x + 71y = 287

SECTION-C
Questions 26 to 31 carry 3 marks each

26. The angles of depression of the top and bottom of a 50 m high building from the top of a tower are
45° and 60° respectively. Find the height of the tower and the horizontal distance between the tower
and the building. (Use √3 =1.73 )

27. Prove that opposite sides of a quadrilateral circumscribing a circle subtend supplementary angles at
the centre of the circle.
OR
Prove that the tangent drawn at any point of a circle is perpendicular to the radius through the point
of contact.

28. Given that √3 is irrational, prove that (2 + √3) is an irrational number.

29. A father’s age is three times the sum of the ages of his two children. After 5 years his age will be
two times the sum of their ages. Find the present age of the father.

30. A girl of height 100 cm is walking away from the base of a lamp post at a speed of 1.9 m/s. If the
lamp is 5 m above the ground, find the length of her shadow after 4 seconds.

31. Prove that (cosec A – sin A)(sec A – cos A)(tan A + cot A) = 1

OR
cos A 1  sin A
Prove that   2sec A
1  sin A cos A

SECTION-D
Questions 32 to 35 carry 5M each

32. Out of a group of swans, 7/2 times the square root of the total number of swans are playing on the
shore of a tank. Remaining two are playing, with amorous fight, in the water. What is the total
number of swans?
OR
A plane left 30 minutes late than its scheduled time and in order to reach the destination 1500 km
away in time, it had to increase its speed by 100 km/h from the usual speed. Find its usual speed.

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33. The median of the following data is 52.5. Find the values of x and y. if the total frequency is 100
Class 0-10 10-20 20-30 30-40 40-50 50-60 60-70 70-80 80-90 90-100
Frequency 2 5 x 12 17 20 y 9 7 4

34. Prove that if a line is drawn parallel to one side of a triangle

intersecting the other two sides in distinct points, then the other two
sides are divided in the same ratio.
Using the above theorem prove that a line through the point of
intersection of the diagonals and parallel to the base of the
trapezium divides the non parallel sides in the same ratio.

35. A horse is tied to a peg at one corner of a square shaped grass field
of side 15 m by means of a 5 m long rope.
Find (i) the area of that part of the field in which the horse can
graze.
(ii) the increase in the grazing area if the rope were 10 m long instead of 5 m. (Use π = 3.14)
OR
The below figure depicts a racing track whose left and right ends are semicircular.

The distance between the two inner parallel line segments is 60 m and they are each 106 m long. If
the track is 10 m wide, find :
(i) the distance around the track along its inner edge
(ii) the area of the track.

SECTION-E (Case Study Based Questions)

Questions 36 to 38 carry 4M each

36. A pen stand made of wood is in the shape of a cuboid with four conical depressions to hold pens.
The dimensions of the cuboid are 15 cm by 10 cm by 3.5 cm. The radius of each of the depressions
is 0.5 cm and the depth is 1.4 cm.

Based on the above information, answer the following questions.

(i) Find the volume of four conical depressions in the entire stand [2]
(ii) Find the volume of wood in the entire stand [2]

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 OR
(ii) Three cubes each of side 15 cm are joined end to end. Find the total surface area of the resulting
cuboid. [2]

37. A boy 4 m tall spots a pigeon sitting on the top of a pole of height 54 m from the ground. The angle
of elevation of the pigeon from the eyes of boy at any instant is 60°. The pigeon flies away
horizontally in such a way that it remained at a constant height from the ground. After 8 seconds,
the angle of elevation of the pigeon from the same point is 45°.

Based on the above information, answer the following questions. (Take √3 =1.73 )
(i) Find the distance of first position of the pigeon from the eyes of the boy. [2]
(ii) How much distance the pigeon covers in 8 seconds? [2]
OR
0
(ii) If the elevation of sun is 30 , then find the length of the shadow cast by tower of 300ft height.

38. Lahari has to buy a scooty. She can buy scooty either making cashdown payment of Rs. 25,000 or
by making 15 monthly instalments as below.
Ist month = Rs. 3425, IInd month = Rs. 3225, Illrd month = Rs. 3025, IVth month = Rs. 2825 and
so on

(i) Find the amount of 6th instalment. [1]

(ii) Find the total amount paid in 15 instalments. [2]
OR
(ii) If Lahari pays Rs. 82625 then find the number of instalment. [2]
(iii) Lahari paid 10th and 11th instalment together find the amount paid that month. [1]

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PM SHRI KENDRIYA VIDYALAYA GACHIBOWLI, GPRA CAMPUS, HYD-32
SAMPLE PAPER TEST 01 FOR BOARD EXAM 2025

SUBJECT: SCIENCE MAX. MARKS: 80

CLASS : X DURATION: 3 HRS
General Instruction:
1. This Question Paper has 5 Sections A-E.
2. Section A has 20 MCQs carrying 1 mark each.
3. Section B has 6 questions carrying 02 marks each.
4. Section C has 7 questions carrying 03 marks each.
5. Section D has 3 questions carrying 05 marks each.
6. Section E has 3 case based integrated units of assessment (04 marks each) with sub-parts of the
values of 1, 1 and 2 marks each respectively.
7. All Questions are compulsory. However, an internal choice in 2 Qs of 5 marks, 2 Qs of 3 marks
and 2 Questions of 2 marks has been provided. An internal choice has been provided in the
2marks questions of Section E
8. Draw neat figures wherever required. Take π =22/7 wherever required if not stated.
SECTION – A
Questions 1 to 20 carry 1 mark each.
1. While studying the saponification reaction, what do you observe when you mix an equal amount
of colourless vegetable oil and 20% aqueous solution of NaOH in a beaker?
(a) The colour of the mixture has become dark brown.
(b) A brisk effervescence is taking place in the beaker.
(c) The outer surface of the beaker has become hot.
(d) The outer surface of the beaker has become cold.

2. Identify gas A in the following experiment.

(a) Nitrogen (b) Hydrogen (c) Oxygen (d) Carbon dioxide

3. Why do we store silver chloride in dark-coloured bottles?

(a) To prevent precipitation of silver chloride
(b) To prevent decomposition of silver chloride
(c) To promote decomposition of silver chloride
(d) All of these
4. Which of the following will turn phenolphthalein pink?
(a) NaOH(aq) (b) HCl(aq) (c) CH3COOH(aq) (d) H2O

5. When sodium hydrogen carbonate is added to ethanoic acid, a gas is evolved. Consider the
following statements about the gas evolved.
(i) It turns lime water milky.
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 (ii) It is evolved with a brisk effervescence.
(iii) It has a smell of burning sulphur.
(iv) It is also a by-product of respiration.
The correct statements are:
(a) (i) and (ii) only (b) (i) and (iv) only (c) (i), (iii) and (iv) (d) (i), (ii) and (iv)

6. Which option illustrates the location of centre that controls the feelings associated with hunger
(M) and the centre that allows a person to walk in a straight line (N)?

7. Identify X, Y and Z based on the basis of given information. X is a non-metal, which is an

important constituent of our food. It forms two oxides Y and Z. Y is toxic and it causes
suffocation and sometimes death. Z is responsible for global warming.
(a) X= C, Y= CO, Z=CO2 (b) X = S, Y= SO2, Z= SO3
(c) X=P, Y=P2O3, Z=P2O3 (d) X= O, Y = O2, Z = O3
8. What is the direction of magnetic field at a point A above the wire carrying current I as shown
in figure?

(a) Out of the page (b) Into the page (c) Up the page (d) Down the page

9. Choose the correct statement about heart.

(a) The upper two chambers of human heart are called ventricles.
(b) The lower two chambers of human heart are called atrium.
(c) The chambers of the heart are separated by a partition called pericardium.
(d) The pulmonary artery carries deoxygenated blood from the right ventricle to the lungs.
10. If the structure marked X in the diagram given below is blocked, then which of the processes
will not occur?

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 (a) Transpiration and respiration
(b) Transpiration, photosynthesis and respiration
(c) Respiration, transpiration and transportation
(d) Respiration and photosynthesis

11. In peas, a pure tall plant (TT) is crossed with a short plant (tt). The ratio of pure tall plants to
short plants in F2 is
(a) 1 : 3 (b) 3 : 1 (c) 1 : 1 (d) 2 : 1

12. A cylindrical conductor of length l and uniform area of cross section A has resistance R.
Another conductor of length 2l and resistance R of the same material has area of crosssection:
(a) A/2 (b) 3A/2 (c) 2A (d) 3A

13. As per Michael Faraday, the forefinger, middle finger and thumb indicate the direction of:
(a) magnetic field, force and current respectively.
(b) magnetic field, current and force respectively.
(c) current, force and magnetic field respectively.
(d) force, magnetic field and current respectively.
14. A uniform magnetic field exists in the plane of paper pointing from left to right as shown in
below Figure. In the field an electron and a proton move as shown. The electron and the proton
experience

(a) forces both pointing into the plane of paper

(b) forces both pointing out of the plane of paper
(c) forces pointing into the plane of paper and out of the plane of paper, respectively
(d) force pointing opposite and along the direction of the uniform magnetic field respectively

15. The hetero atoms present in CH3—CH2—O—CH2—CH2—Cl are

(i) Oxygen (ii) Carbon (iii) Hydrogen (iv) Chlorine
(a) (i) and (ii) (b) (ii) and (iii) (c) (iii) and (iv) (d) (i) and (iv)

16. In humans, the life processes are controlled and regulated by:
(a) reproductive and endocrine system (b) respiratory and nervous system
(c) endocrine and digestive system (d) nervous and endocrine system

DIRECTION: In the question number 17 and 20, a statement of Assertion (A) is followed by a
statement of Reason (R).
Choose the correct option
(a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of
assertion (A)
(b) Both assertion (A) and reason (R) are true and reason (R) is not the correct explanation of
assertion (A)
(c) Assertion (A) is true but reason (R) is false.
(d) Assertion (A) is false but reason (R) is true.

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17. Assertion (A): Hydrogen gas is not evolved when a metal reacts with nitric acid.
Reason (R): Nitric acid is a strong oxidising agent.

18. Assertion (A): Lipase help in emulsification of fats.

Reason (R): Lipase hydrolyses fats and oils.

19. Assertion: Strength of an electromagnet can be increased by increasing the number of turns per
unit length in solenoid coil.
Reason: Strength of an electromagnet can be increased by increasing the current flowing
through the solenoid.

20. Assertion(A): Spores are formed in sporangia.

Reason(R): Spores grow into separate individuals in moist conditions.

SECTION – B
Questions 21 to 26 carry 2 marks each.

21. Observe the given figure: What happens when the tube is heated?
(a) Write a balanced chemical equation of the reaction.
(b) Identify the brown gas X evolved.
22. Define an ecosystem. Draw a block diagram to show the flow of
energy in an ecosystem.

23. What will happen if mucus is not secreted by the gastric glands?

24. Why does carbon become stable after sharing four electrons? What type of bond is formed by
sharing?
OR
Why are covalent compounds being poor conductors of electricity? Why do covalent
compounds have low melting and boiling points?
25. A student sitting at the back of the classroom cannot read clearly the letters written on the
blackboard. What advice will a doctor give to her? Draw ray diagram for the correction of this
defect.
OR
Why do we see a rainbow in the sky only after rainfall?

26. Give two examples of decomposers. State their important role in nature.

SECTION – C
Questions 27 to 33 carry 3 marks each.
27. Can two people with brown eyes have a blue-eyed baby? Explain.

28. A chemical compound ‘X’ is used in the soap and glass industry. It is prepared from brine.
(i) Write the chemical name, common name and chemical formula of ‘X’.
(ii) Write the equation involved in its preparation.
(iii) What happens when it is treated with water containing Ca or Mg salts?

29. A piece of wire having resistance ‘R’ is cut into four equal parts.
(a) How does the resistance of each part compare with the original resistance?
(b) If the four parts are placed in parallel, how will be the resistance of the combination compare
with the resistance of the original wire?

30. An object 6 cm in size is placed at 50 cm in front of a convex lens of focal length 30 cm. At
what distance from the lens should a screen be placed in order to obtain a sharp image of the

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 object? Find the nature and size of the image. Also draw labelled ray diagram to show the image
formation in this case.

31. (i) What is an electromagnet? List any two uses.

(ii) Draw a labelled diagram to show how an electromagnet is made.
OR
With the help of a labelled diagram, explain the distribution of magnetic field due to a current
through a circular loop. Why is it that if a current carrying coil has n turns the field produced at
any point is n times as large as that produced by a single turn?
(ii) Draw a pattern of magnetic field formed around a current carrying solenoid. What happens
to the magnetic field when the current through the solenoid is reversed?

32. (a) How does food chain differ from a food web?
(b) Make food chains in (i) forest (ii) pond.

33. How is copper extracted from its sulphide ore ? Explain the various steps supported by chemical
equations. Draw labelled diagram for the electrolytic refining of copper.
OR
Write the balanced chemical equations for the following reactions and identify the type of
reaction in each case.
(i) Thermit reaction, iron (III) oxide reacts with aluminium and gives molten iron and
aluminium oxide.
(ii) Magnesium ribbon is burnt in an atmosphere of nitrogen gas to form solid magnesium
nitride.
(iii) Chlorine gas is passed in an aqueous potassium iodide solution to form potassium chloride
solution and solid iodine.
(iv) Ethanol is burnt in air to form carbon dioxide, water and releases heat.

SECTION – D
Questions 34 to 36 carry 5 marks each.
34. What are esters? How are esters prepared? Write the chemical equation for the reaction
involved. What happens when an ester reacts with sodium hydroxide? Write the chemical
equation for the reaction and also state the name and use of this reaction.
OR
What is the difference between soaps and detergents? State in brief the cleansing action of soaps
in removing an oily spot from a fabric. Why are soaps not very effective when a fabric is
washed in hard water? How is this problem resolved?

35. (i) How will you infer with the help of an experiment that the same current flows through every
part of the circuit containing three resistors R1, R2 and R3 in series connected to a battery of V
volts?
(ii) Study the following circuit and find out:

(a) Current in 12  resistor.

(b) Difference in the readings of A1 and A2, if any.
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36. What is sexual reproduction? Explain how this mode of reproduction gives rise to more viable
variations than asexual reproduction. How does this affect the evolution?
OR
(a) What are dominant and recessive traits?
(b) "Is it possible that a trait is inherited but may not be expressed in the next generation?" Give
a suitable example to justify this statement.

SECTION – E(Case Study Based Questions)

Questions 37 to 39 carry 4 marks each.
37. Case Study – 1
A student added 10 g of calcium carbonate in a rigid container, secured it tightly and started to
heat it. After some time, an increase in pressure was observed, the pressure reading was then
noted at intervals of 5 mins and plotted against time, in a graph as shown below.

(i) During which interval did maximum decomposition took place?

(ii) Marble statues are corroded or stained when they repeatedly come into contact with polluted
rain water. Identify the main reason.

(iii) What happens when calcium carbonate decompose? What could be done to increase the rate
of decomposition of CaCO3?
OR
(iii) Is decomposition of limestone endothermic? Give reason.
38. Case Study - 2
Dispersion of light occurs when white light is separated into its different constituent colors
because of refraction and Snell's law.
From Snell's law it can be seen that the angle of refraction of light in a prism depends on the
refractive index of the prism material.

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 Color l(nm) Freq. (Hz)
Red 760–647 4.3 × 1014
Orange 647-585 4.3 × 1014
Yellow 585-575 5.2 × 1014
Green 575-491 5.6 × 1014
Blue 491-424 6.6 × 1014

Since the refractive index varies with wavelength, the angle that the light is refracted by will
also vary with wavelength, causing an angular separation of the colors known as angular
dispersion.
For visible light, refraction indices n of most transparent materials (e.g., air, glasses) decrease
with increasing wavelength l:
Colour Wavelength Crown Flint
(nm) glass glass
Violet 396.9 1.533 1.663
Blue 486.1 1.523 1.639
Yellow 589.3 1.517 1.627
Red 656.3 1.515 1.622

Most often seen in recently made puddles on the sides of roads, the oil refracts light much the
same way a rainbow does. Simply put, the thin layer of oil floating on top of the water refracts
the light which then bounces back up off the water underneath, splitting the light rays creating a
pool of rainbow colours.
(a) Which ray is least deviated by a prism?
(b) Which colour of light which has the minimum velocity in the glass prism?
(c) Which optical phenomenon is involved in formation of rainbow?
OR
(c) What is the angle of deviation (d) of a prism?

39. Case Study – 3

Sahil performed an experiment to study the inheritance pattern of genes. He crossed tall pea
plants (TT) with short pea plants (tt) and obtained all tall plants in F1 generation.
(i) What will be set of genes present in the F1 generation?
(ii) Give reason why only tall plants are observed in F1 progeny.
(iii) When F1 plants were self-pollinated, a total of 800 plants were produced. How many of
these would be tall, medium height or short plants? Give the genotype of F2 generation.
OR
(iii) When F1 plants were cross - pollinated with plants having tt genes, a total of 800 plants
were produced. How many of these would be tall, medium height or short plants? Give the
genotype of F2 generation.

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 SAMPLE PAPER TEST 02 FOR BOARD EXAM 2025

SUBJECT: SCIENCE MAX. MARKS: 80

CLASS : X DURATION: 3 HRS
General Instruction:
1. This Question Paper has 5 Sections A-E.
2. Section A has 20 MCQs carrying 1 mark each.
3. Section B has 5 questions carrying 02 marks each.
4. Section C has 6 questions carrying 03 marks each.
5. Section D has 4 questions carrying 05 marks each.
6. Section E has 3 case based integrated units of assessment (04 marks each) with sub-parts of the
values of 1, 1 and 2 marks each respectively.
7. All Questions are compulsory. However, an internal choice in 2 Qs of 5 marks, 2 Qs of 3 marks
and 2 Questions of 2 marks has been provided. An internal choice has been provided in the
2marks questions of Section E
8. Draw neat figures wherever required. Take π =22/7 wherever required if not stated.
SECTION – A
Questions 1 to 20 carry 1 mark each.
1. A sample of soil is mixed with water and allowed to settle. The clear supernatant solution turns
the pH paper yellowish-orange. Which of the following would change the colour of this pH
paper to greenish-blue?
(a) Lemon juice (b) Vinegar (c) Common salt (d) An antacid

2. Generally metals react with acids to give salt and hydrogen gas. Which of the following acids
does not give hydrogen gas on reacting with metals (except Mn and Mg)?
(a) H2SO4 (b) HCl (c) HNO3 (d) All of these
3. Identify the unsaturated compounds from the following
(i) Propane (ii) Propene (iii) Propyne (iv) Chloropropane
(a) (i) and (ii) (b) (ii) and (iv) (c) (iii) and (iv) (d) (ii) and (iii)
4. Which one among the following is not removed as a waste product from the body of a plant?
(a) Resins and Gums (b) Urea (c) Dry Leaves (d) Excess Water
5. Which of the following statement is incorrect?
(a) For every hormone there is a gene.
(b) For every protein there is a gene.
(c) For production of every enzyme there is a gene.
(d) For every molecule of fat there is a gene.
6. The diagram shows the reaction between metal and dilute acid.

What is the reason for different behaviour of Mg in test tube B?

(a) Mg is lighter element than dil. HCl
(b) Mg reacts with dil. HCl to produce H2 gas which helps in floating
(c) Mg reacts with dil. HCl to produce N2 gas which helps in floating
(d) Mg reacts with dil. HCl to produce CO2 gas which helps in floating

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7. A student adds an equal amount of copper sulphate solution in two beakers. He adds zinc in
beaker P and silver in beaker Q. The student observes that the color of the solution in beaker P
changes while no change is observed in beaker Q. Which option arranges the metals in
increasing order of reactivity?
(a) Copper-silver-zinc (b) Zinc-copper-silver (c) Silver-copper-zinc (d) Silver-zinc-copper
8. Mohan was confused and did not know how to draw the correct figure for geotropism. So, he
has drawn three figures, as shown below.

Which appears more accurate and why?

(a) (I), (II) (b) (I) only (c) (II), (III) (d) (II) only
9. Select the mismatched pair
(a) Adrenaline: Pituitary gland (b) Testosterone: Testes
(c) Estrogen : Ovary (d) Thyroxin: Thyroid gland
10. A student carries out an experiment and plots the V - I graph of three samples of nichrome wire
with resistances R1, R2 and R3 respectively as shown in figure. Which of the following is true?

(a) R1 = R2 = R3 (b) R1 > R2 > R3 (c) R3 > R2 > R1 (d) R2 > R3 > R1
11. Four students plotted the sketch of the patterns of magnetic field lines representing the magnetic
field around a current carrying straight wire as shown in figures P, Q, R and S. Which one of the
following sketches is correct?

(a) P (b) Q (c) R (d) S

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12. Offspring formed by asexual method of reproduction have greater similarity among themselves
because
(i) asexual reproduction involves only one parent
(ii) asexual reproduction does not involve gametes
(iii) asexual reproduction occurs before sexual reproduction
(iv) asexual reproduction occurs after sexual reproduction
(a) (i) and (ii) (b) (i) and (iii)
(c) (ii) and (iv) (d) (iii) and (iv)

13. What is the effective resistance between points P and Q in the circuit shown below?

(a) 0.15 Ω (b) 0.66 Ω (c) 1.5 Ω (d) 1.75 Ω

14. In the given diagram, when the magnet is pushed into the solenoid, the pointer of the
galvanometer deflects slightly to the left.

Which of the following would produce a deflection of the pointer towards the right?
(a) Move the solenoid towards the magnet.
(b) Move the solenoid away from the magnet.
(c) Move the magnet faster into the solenoid.
(d) By placing the magnet above the coil.

15. What happens when a solution of an acid is mixed with a solution of a base in a test tube?
(i) The temperature of the solution increases
(ii) The temperature of the solution decreases
(iii) The temperature of the solution remains the same
(iv) Salt formation takes place
(a) (i) only (b) (i) and (iii) (c) (ii) and (iii) (d) (i) and (iv)
16. Which of the following reactions is a neutralisation reaction?
(a) 4Na + O2 → 2Na2O
(b) Fe + 2HCl → FeCl2 + H2
(c) MgO + H2O → Mg(OH)2
(d) HNO3 + NaOH → NaNO3 + H2O
DIRECTION: In the question number 17 and 20, a statement of Assertion (A) is followed by a
statement of Reason (R).
Choose the correct option
(a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of
assertion (A)
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 (b) Both assertion (A) and reason (R) are true and reason (R) is not the correct explanation of
assertion (A)
(c) Assertion (A) is true but reason (R) is false.
(d) Assertion (A) is false but reason (R) is true.

17. Assertion: The chemical name of bleaching powder is calcium oxychloride.

Reason: Bleaching powder is used as an oxidising agent in chemical industries.

18. Assertion (A) : Acquired traits cannot be passed from one generation to next generation.
Reason (R) : Inaccuracy during DNA copying of acquired trait is minimum.

19. Assertion (a): The opening and closing of the pore is a function of the guard cells.
Reason (R): Stomatal pores are the site for exchange of gases by diffusion.

20. Assertion (A) : The compass placed near the current-carrying wire remains stationary.
Reason (R) : The current flowing through a wire gives rise to a magnetic field.

SECTION – B
Questions 21 to 25 carry 2 marks each.

21. DDT was sprayed in a lake to regulate breeding of mosquitoes. How would it affect the trophic
levels in the following food chain associated with a lake? Justify your answer.

22. List in tabular form three distinguishing features between cerebrum and cerebellum.

23. Define the term power of accommodation. Write the modification in the curvature of the eye
lens which enables us to see the nearby objects clearly? Give relation between power and focal
length.
OR
Why is the sun visible to us 2 minutes before actual sunrise and 2 minutes after actual sunset?

24. What changes are observed in the uterus subsequent to implantation of young embryo?

25. Why do fire flies glow at night?

OR
A dilute ferrous sulphate solution was gradually added to the beaker containing acidified
potassium permanganate solution. The light purple colour of the solution fades and finally
disappears. Write the correct explanation for this observation.
26. Answer the following:
(i) Which hormone is responsible for the changes noticed in females at puberty?
(ii) Dwarfism results due to deficiency of which hormone?
(iii) Blood sugar level rises due to deficiency of which hormone?
(iv) Iodine is necessary for the synthesis of which hormone?

SECTION – C
Questions 27 to 33 carry 3 marks each.
27. 1 g of copper powder was taken in a China dish and heated. What change takes place on
heating? When hydrogen gas is passed over this heated substance, a visible change is seen in it.
Give the chemical equations of reactions, the name and the color of the products formed in each
case.
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28. State the events occurring during the process of photosynthesis. Is it essential that these steps
take place one after the other immediately?
OR
Bile juice does not have any digestive enzyme but still plays a significant role in the process of
digestion. Justify the statement.

29. Based on the group valency of elements, write the molecular formula of the following
compounds giving justification for each:
(a) Oxides of first group elements.
(b) Halides of the elements of group 13.
(c) Compounds formed when an element A of group 2 combines with an element B of group 17.

30. A student holding a mirror in his hand, directed the reflecting surface of the mirror towards the
Sun. He then directed the reflected light on to a sheet of paper held close to the mirror.
(a) What should he do to burn the paper?
(b) Which type of mirror does he have?
(c) Will he be able to determine the approximate value of focal length of this mirror from this
activity? Give reason and draw ray diagram to justify your answer in this case.

31. (a) Determine whether the P and Q-marked poles in the following diagram represent the North
or South pole. Why did you choose that response?

(b) Imagine that you are sitting in a chamber with your back to one wall. An electron beam,
moving horizontally from back wall towards the front wall, is deflected by a strong magnetic
field to your right side. What is the direction of magnetic field?
OR
State the rule to determine the direction of a (a) magnetic field produced around a straight
conductor-carrying current and (b) force experienced by a current-carrying straight conductor
placed in a magnetic field which is perpendicular to it.
32. Plastic cups were used to serve tea in trains in early days—these could be returned to the
vendors, cleaned and reused. Later, Kulhads were used instead of plastic cups. Now, paper cups
are used for serving tea. What are the reasons for the shift from Plastic to Kulhads and then
finally to paper cups?

33. A lens produces a magnification of –0.5. Is this a converging or diverging lens? If the focal
length of the lens is 6 cm, draw a ray diagram showing the image formation in this case.

SECTION – D
Questions 34 to 36 carry 5 marks each.

34. Explain Mendel’s experiment with peas on inheritance of characters considering only one
visible contrasting character.
OR
In the following crosses write the characteristics of the progeny.
Cross Progeny
(i) RR YY × RR YY ___________________________
Round, yellow and round, yellow
(ii) Rr Yy × Rr Yy ___________________________
Round, yellow and round, yellow
(iii) rr yy × rr yy ___________________________

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 Wrinkled, green and wrinkled, green
(iv) RR YY × rr yy ___________________________
Round, yellow and wrinkled, green

35. What is a homologous series of carbon compounds? List its any two characteristics. Write the
name and formula of the next higher homologous of HCOOH.

OR

A compound C (molecular formula, C2H4O2) reacts with Na-metal to form a compound R and
evolves a gas which burns with a pop sound. Compound C on treatment with an alcohol A in
presence of an acid forms a sweet smelling compound S (molecular formula C3H6O2). On
addition of NaOH to C, it also gives R and water. S on treatment with NaOH solution gives
back R and A.
Identify C, R, A, S and write down the reactions involved.

36. If, in Figure Rl = 10 Ohms, R2 = 40 Ohms, R, = 30

Ohms, R4 = 20 Ohms, RA = 60 Ohms and a 12 volt
battery is connected to the arrangement, calculate:
(a) the total resistance and (b) the total current
flowing in the circuit.

SECTION – E(Case Study Based Questions)

Questions 37 to 39 carry 4 marks each.
37. Case Study - 1
Sohan went door to door posing as a goldsmith. He promised to bring back the glitter of old and
dull gold ornaments. An unsuspecting lady gave a set of gold bangles to him, which he dipped
in a particular solution. The bangles sparkled like new but their weight was reduced drastically.

The lady was sad but after a futile argument, the man beat a hasty retreat.
(a) What is used for dissociation of gold? [1]
(b) Why the weight of the bangle was reduced drastically? [1]
(c) Aqua-regia is a strong oxidising agent. (True or False). [2]

OR

(c) What is the other name of the solution (in Latin) used by that man posing as the goldsmith?
Why is it so called?

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38. Case Study – 2
Light spectrum is the many different wavelengths of energy produced by light source. Light is
measured in nanometers (nm). Each nanometer represents a wavelength of light or band of light
energy. Visible light is the part of spectrum from 380 nm to 780 nm.

Isaac Newton was the first to use a glass prism to obtain the spectrum of sunlight. He tried to
split the colours of the spectrum of white light further by using another similar prism. He then
placed a second identical prism in an inverted position with respect to the first prism. This
allowed all the colours of the spectrum to pass through second prism. He found a beam of white
light emerging from the other side of the second prism. This observation gave Newton the idea
that the sunlight is made up of seven colours.
(i) (a) What is the range of wavelength of visible light spectrum?
(b) What do you understand by light spectrum?
(ii) Explain the process of refraction when critical angle between an equilateral prism and air is
45 degree, if the incident ray is perpendicular to the refracting surface?
OR
(ii) (a) Why do different rays deviate differently in the prism?
(b) How will you use two identical prisms so that a narrow beam of white light incident on one
prism emerges out of the second prism as white light?
39. Case Study – 3
The growing size of the human population is a cause of concern for all people. The rate of birth
and death in a given population will determine its size. The human population growth year wise
is shown in the below figure. Reproduction is the process by which organisms increase their
population. The process of sexual maturation for reproduction is gradual and takes place while
general body growth is still going on. Some degree of sexual maturation does not necessarily
mean that the mind or body is ready for sexual act or for having and bringing up children.
Various contraceptive devices are being used by human beings to control the size of population.

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 (a) List two common signs of sexual maturation in boys and girls.
(b) What is the result of reckless female foeticide?
(c) Which contraceptive method changes the hormonal balance of the body? Give an example of it
OR
Write two factors that determine the size of a population.

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 SAMPLE PAPER TEST 03 FOR BOARD EXAM 2025

SUBJECT: SCIENCE MAX. MARKS: 80

CLASS : X DURATION: 3 HRS
General Instruction:
1. This Question Paper has 5 Sections A-E.
2. Section A has 20 MCQs carrying 1 mark each.
3. Section B has 5 questions carrying 02 marks each.
4. Section C has 6 questions carrying 03 marks each.
5. Section D has 4 questions carrying 05 marks each.
6. Section E has 3 case based integrated units of assessment (04 marks each) with sub-parts of the
values of 1, 1 and 2 marks each respectively.
7. All Questions are compulsory. However, an internal choice in 2 Qs of 5 marks, 2 Qs of 3 marks
and 2 Questions of 2 marks has been provided. An internal choice has been provided in the
2marks questions of Section E
8. Draw neat figures wherever required. Take π =22/7 wherever required if not stated.
SECTION – A
Questions 1 to 20 carry 1 mark each.
1. A scientist in a chemistry lab wants to make salt of pH 5.5 using acid and base. The table shows
the acid and base present in the lab.
1 HCl
2 NaOH
3 H2CO3
4 NH4OH
5 CH3COOH
Which of the acid and base he should use for the reaction?
(a) CH3COOH and NaOH (b) HCl and NaOH (c) HCl and NH4OH (d) H2CO3 and NaOH

2. Which of the following are correct structural isomers of butane?

(a) (i) and (iii) (b) (ii) and (iv) (c) (i) and (ii) (d) (iii) and (iv)

3. Biomagnification refers to the increase in the :

(a) body weight of an organism.
(b) growth of phytoplanktons.
(c) the amount of harmful chemicals in the successive trophic levels of a food chain.
(d) number of plants and animals in an area.

4. When aqueous solutions of barium chloride and sodium sulphate react together, an insoluble
substance along with aqueous solution of sodium chloride is formed. This reaction is an
example of a :
(a) combination reaction (b) decomposition reaction
(c) displacement reaction (d) double displacement reaction

5. A doctor advised a person to take an injection of insulin because :

(a) his heart was beating slowly.
(b) his blood pressure was low.
(c) he was looking short in height.
(d) his pancreas was not secreting the required hormone in proper amounts.
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6. The movement of sunflowers is in response to a stimulus such as :
(a) gravity (b) chemicals (c) day or night (d) water

7. The acid present in nettle sting is :

(a) Acetic acid (b) Methanoic acid (c) Tartaric acid (d) Citric acid

8. Study the diagram given alongside and identify the gas formed in the reaction.

(a) Carbon dioxide which extinguishes the burning candle.

(b) Oxygen due to which the candle burns more brightly.
(c) Sulphur dioxide which produces a suffocating smell.
(d) Hydrogen which while burning produces a popping sound.

9. Electrical impulse travels in a neuron from

(a) Dendrite → axon → axonal end → cell body
(b) Cell body → dendrite → axon → axonal end
(c) Dendrite → cell body → axon → axonal end
(d) Axonal end → axon → cell body → dendrite

10. In plants, waste products like resins and gums are stored in :
(a) leaves that fall off (b) old xylem (c) phloem (d) cellular vacuoles

11. When a 4V battery is connected across an unknown resistor there is a current of 100 mA in the
circuit. The value of the resistance of the resistor is:
(a) 4 Ω (b) 40 Ω (c) 400 Ω (d) 0.4 Ω

12. The diagram shown below depicts pollination. Choose the options that will show a maximum
variation in the offspring.

(a) A, B and C (b) B and D (c) B, C and D (d) A and C

13. The path of a ray of light coming from air passing through a rectangular glass slab is traced by
four students shown as A, B, C and D in the figure. Which one of them is correct?
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14. In the given food chain, suppose the amount of energy at the fourth trophic level is 5 kJ, what
will be the energy available at the producer level?
Grass → Grasshopper → Frog → Snake → Hawk
(a) 5 kJ (b) 50 kJ (c) 500 kJ (d) 5000 kJ

15. The name of the compound ‘A’ formed in the following reaction is :
NaCl + NH3 + H2O + CO2 → ‘A’ + NH4Cl
(a) Sodium carbonate (b) Ammonium carbonate
(c) Sodium hydrogen carbonate (d) Ammonium hydrogen carbonate

16. Select the correct statement from the following about the reaction :
CuO + H2 → Cu + H2O
(a) CuO is getting oxidised and H2 is getting reduced.
(b) H2 is getting oxidised and CuO is getting reduced.
(c) CuO is a reducing agent.
(d) H2 is an oxidising agent.

DIRECTION: In the question number 17 and 20, a statement of Assertion (A) is followed by a
statement of Reason (R).
Choose the correct option
(a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of
assertion (A)
(b) Both assertion (A) and reason (R) are true and reason (R) is not the correct explanation of
assertion (A)
(c) Assertion (A) is true but reason (R) is false.
(d) Assertion (A) is false but reason (R) is true.

17. Assertion (A) : The energy of charged particle moving in a uniform magnetic field does not
change.
Reason (R) : Work done by magnetic field on the charge is zero.

18. Assertion (A): Ozone (O3) is a molecule formed by the three atoms of oxygen.
Reason (R): Ozone shields the surface of the Earth from ultraviolet (UV) radiation from the
Sun.

19. Assertion (A): Soaps do not form lather (foam) with hard water.
Reason (R): Hard water has calcium and magnesium salts dissolved in it which on reacting
with soap form scum.

20. Assertion (A): Chemical co-ordination is seen in both plants and animals.
Reason (R): Plant hormones control directional growth, whereas in animals, growth is never
seen in one direction only.

SECTION – B
Questions 21 to 25 carry 2 marks each.

21. Define the terms ductility and malleability. Name an element which exhibits both of these
properties giving justification for your answer.

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22. ‘Variations are beneficial to the species but not necessarily for the individual’. Justify.

23. Draw a labelled ray diagram to show the formation of image due to a concave mirror when an
object is placed between its pole and principal focus.

24. (a) Draw a ray diagram to explain the term angle of deviation.
OR
(b) Name the muscles present in the human eye which enable it to focus on objects at varied
distances (i.e., distant as well as nearby objects). Explain how it happens.

25. “A vegetarian food habit helps in getting more energy.” Justify the statement.

26. (a) In the diagram given below, name the labelled parts X and Y. Mention one function for each.

OR
(b) Name the parts of the nervous system which are involved in the following activities :
(i) Maintaining body posture
(ii) Salivation
(iii) Hunger
(iv) Answering a question

SECTION – C
Questions 27 to 33 carry 3 marks each.
27. An element A burns with golden flame in air. It reacts with another element B, atomic number
17 to give a product C. An aqueous solution of product C on electrolysis gives a compound D
and liberates hydrogen. Identify A, B, C and D. Also write down the equations for the reactions
involved.

28. (a) Identify the acid and the base from which sodium chloride is obtained. Which type of salt is
it? When is it called rock salt? How is rock salt formed?
OR
(b) (i) Identify the acid and the base from which the following salts are obtained :
(I) Sodium chloride
(II) Ammonium sulphate
(ii) Write the nature, acidic/basic/neutral, of each of the above mentioned salts, giving reason
for your answer.
29. A cross was carried out between pure breed tall pea plant with pure dwarf pea plant and F1
progeny was obtained. Later, F1, progeny was selfed to obtain F2 progeny. Answer the following
questions:
(a) What is the phenotype of the F1 progeny and why?
(b) Give the phenotypic ratio of the F2 progeny.
(c) Why is F2 progeny different from the F1 progeny?
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30. Study the following circuit and answer the questions that follows:

(a) State the type of combination of two resistors in the circuit.

(b) How much current is flowing through (i) 10 Ohms and (ii) 15 Ohms resistor?
(c) What is the ammeter reading?

31. (a) Name a part of the flower which (i) persists even after a fruit is formed,
(ii) attracts insects for pollination, (iii) produces pollen grains and
(iv) changes into seed after fertilisation.
(b) After pollination, how does a male germ cell reach the ovary ? Mention the significance of
this event.

32. (a) State (i) right-hand thumb rule, and (ii)

Fleming’s left-hand rule.
(b) Using Fleming’s left-hand rule determine the
direction of force experienced by a proton, which
enters vertically downwards in a uniform magnetic
field acting horizontally from west to east as
shown in the diagram.

33. Rakesh performed the experiment to study the dispersion of light by a glass prism and drew the
following figure.
(a) The colour at position marked 3 and 5 are similar to the colour of the sky and the colour of
gold metal respectively. Is the above statement made by the student correct or incorrect? Justify.
(b) Which of the above shown positions correspond approximately to the colour of:
(i) a solution of potassium permanganate?
(ii) danger or stop signal lights?

SECTION – D
Questions 34 to 36 carry 5 marks each.

34. (a) (i) Label the endocrine glands given in figure below:

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 (ii) A hot object has been touched by you. Draw a diagram that shows the steps that result in a
response, such as a hasty hand pullback.
(iii) How are involuntary actions and reflex actions different from each other?
OR
(b) (i) Study the diagram below showing schematic representation of transport and exchange of
gases in human heart and name the parts labelled as A, B and C. Mention the function of each
part.
(ii) Explain how separation of right and left side of the heart is useful for birds.

35. (a) (i) Write the relation between the electrical resistivity ‘r’ and the resistance ‘R’ of a
cylindrical conductor of length ‘l’ and area of cross-section ‘A’. Use this relationship to
determine the SI unit of ‘r’.
(ii) Find the electrical resistivity of the material of a wire of length 120 cm and diameter 0·4
mm. The resistance of this wire is 3 W.
OR
(b) (i) What is meant by heating effect of electric current ? Derive an expression for the amount
of heat produced in a conductor of resistance R through which a current I flows for a time t.
(ii) Calculate the amount of heat produced in a conductor of resistance 10 W through which a
current of 2 A flows for 100 seconds.

36. (a) Write electronic configurations of two elements X (At. no. 12) and Y (At. no. 17). Show the
formation of ionic compound when X and Y combine with each other. Write the name and
formula of the compound formed. State what would happen if electric current is passed through
the aqueous solution of this compound. Name the ion that will reach at (i) cathode, and (ii)
anode.
OR
(b) (i) Write the name of two metals of moderate reactivity. Which one of the two is more
reactive ? How can this fact be demonstrated experimentally in a school laboratory?
(ii) Some metals of moderate reactivity are also found in the Earth’s crust in the form of their
carbonates. Name the processes involved in the extraction of metal from them, giving chemical
equations for the reactions that occur.

SECTION – E(Case Study Based Questions)

Questions 37 to 39 carry 4 marks each.
37. Have you ever wondered how water reaches the top of tall trees, or for that matter how and why
substances move from one cell to the other? Plants need to move molecules over very long
distances, much more than animals do; they also do not have a circulatory system in place.

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 Water taken up by the roots has to reach all parts of the plant, up to the very tip of the growing
stem. The photosynthates or food synthesised by the leaves have also to be moved to all parts
including the root tips embedded deep inside the soil. Movement across short distances, say
within the cell, across the membranes and from cell to cell within the tissue has also to take
place. Over small distances substances move by diffusion and by cytoplasmic streaming
supplemented by active transport. Transport over longer distances proceeds through the vascular
system (the xylem and the phloem) and is called translocation.

The table below gives the results of an experiment carried out to study the factors affecting the
rate of transpiration:

Amount of water transpired in 1 Hour (ml)

Normal With Fan With Heater With Lamp
Arrowhead 3.6 7.5 6.6 4
Coleus 0.9 6 3.9 3
Devil's Ivy 2.9 4.6 4.1 3
Dieffenbachia 4.1 7.7 6 3.9
English Ivy 1.8 5.1 3.2 2.1
Geranium 1.2 4.7 5.8 2.4
Rubber Plant 4.9 8.4 6.8 4.3
Weeping Fig 3.3 6.1 4.9 2.5
Zebra Plant 4.2 7.6 6.1 3.2

(a) What do we call the absorption and upward movement of minerals from roots to leaves.
(b) Root pressure is involved in transpiration. Is this statement true?
(c) Effect of root pressure in transport of water is more important at night. Justify.

OR
(c) What is the function of phloem?

38. We know that the characteristics of image formed by a concave mirror depend on the position of
the object with respect to the mirror.
When an object is placed between F and infinity, the image formed is real and inverted. But
when the object is placed between F and mirror it cannot be obtained on the screen. The image
formed in this case is virtual, erect and magnified. Such image may be seen by looking in the
mirror directly.

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 When the object is moved from focus towards infinity, the image moves from infinity towards
focus and its size decreases.
When object is placed at 2F image of the same size is formed at 2F, itself.
(i) What will be the nature of image if an object is placed 10 cm in front of a concave mirror of
focal length 20 cm?
(ii) What is the minimum distance between the object and its real image for concave mirror?
(iii) A candle flame 3 cm high is placed at a distance of 3 m from a wall. How far from the wall
must a concave mirror be placed in order that it may form an image of the flame 9 cm high on
the wall?
OR
(iii) Draw a ray diagram when an object is placed near a concave mirror at a distance of one-
fourth the radius of curvature of the concave mirror?
39. Ethanol (commonly known as alcohol) is an important carbon compound widely used in
industries, hospitals, etc. Because it is a very good solvent, it is used in medicines such as cough
syrups, tincture iodine and many tonics. As it is a cleaner fuel, ethanol is used as an additive in
petrol in most of the developed countries of the world.

(a) Write the structure of ethanol. (1)

(b) Name the products formed when ethanol burns in sufficient air (oxygen). (1)
(c) (i) State what happens when 5% solution of alkaline potassium permanganate is added to
warm ethanol. Draw the structure of the product formed and state the role of 5% solution of
alkaline potassium permanganate in the reaction. (2)
OR
(c) (ii) State what happens when ethanol is heated with excess conc. H2SO4 at 443 K. Draw the
structure of the product formed and state the role of conc. H2SO4 in the reaction.

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 SAMPLE PAPER TEST 04 FOR BOARD EXAM 2025

SUBJECT: SCIENCE MAX. MARKS: 80

CLASS : X DURATION: 3 HRS
General Instruction:
1. This Question Paper has 5 Sections A-E.
2. Section A has 20 MCQs carrying 1 mark each.
3. Section B has 5 questions carrying 02 marks each.
4. Section C has 6 questions carrying 03 marks each.
5. Section D has 4 questions carrying 05 marks each.
6. Section E has 3 case based integrated units of assessment (04 marks each) with sub-parts of the
values of 1, 1 and 2 marks each respectively.
7. All Questions are compulsory. However, an internal choice in 2 Qs of 5 marks, 2 Qs of 3 marks
and 2 Questions of 2 marks has been provided. An internal choice has been provided in the
2marks questions of Section E
8. Draw neat figures wherever required. Take π =22/7 wherever required if not stated.
SECTION – A
Questions 1 to 20 carry 1 mark each.
1. Consider the following reactions I and II
I. Mg + 2HCl → MgCl2 + H2
II. NaOH + HCl → NaCl + H2O
The correct statement about these equations is
(a) I is displacement reaction, II is decomposition reaction.
(b) I is displacement reaction, II is double displacement reaction.
(c) Both I and II are displacement reactions.
(d) Both I and II are double displacement reactions.

2. Identify in which of the following, reaction will take place.

3. A solution turns the colour of turmeric to reddish brown. If the same solution is poured on
universal indicator, the colour would change to
(a) violet (b) blue (c) red (d) green

4. Which of the following statements about transmission of nerve impulse is incorrect?

(a) Nerve impulse travels from dendritic end towards axonal end
(b) At the dendritic end electrical impulses bring about the release of some chemicals which
generate an electrical impulse at the axonal end of another neuron
(c) The chemicals released from the axonal end of one neuron cross the synapse and generate a
similar electrical impulse in a dendrite of another neuron
(d) A neuron transmits electrical impulses not only to another neuron but also to muscle and
gland cells

5. A child is standing in front of a magic mirror. She finds the image of her head bigger, the
middle portion of her body of the same size and that of the legs smaller. The following is the
order of combinations for the magic mirror from the top.

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 (a) Plane, convex and concave (b) Convex, concave and plane
(c) Concave, plane and convex (d) Convex, plane and concave

6. The image shows the transport of gases in body through heart and lungs.

Which option correctly shows the transport of oxygen to the cell?

(a) Lungs → pulmonary vein → left atrium → left ventricle → aorta → body cells.
(b) Lungs → pulmonary artery → right atrium → right ventricle → vena cava → body cells.
(c) Lungs → pulmonary artery → left atrium → left ventricle → vena cava → body cells.
(d) Lungs → pulmonary vein → right atrium → right ventricle → aorta → body cells.

7. A cell, a resistor, a key and ammeter are arranged as shown in circuit diagrams.

The current recorded in the ammeter will be

(a) maximum in (i) (b) maximum in (ii) (c) maximum in (iii) (d) same in all three circuits

8. Study the following diagrams:

The diagrams showing correct path of the ray after refraction from the convex lens are
(a) I, II and III (b) II, III and IV (c) III, IV and I (d) I, II and IV

9. A student was asked to write a stepwise procedure to demonstrate that carbon dioxide is
necessary for photosynthesis. He wrote the following steps. The wrongly worded step is:

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 (a) Both potted plants are kept in dark room for at least three days.
(b) Bottom of the bell jars is sealed to make them air tight.
(c) Both potted plants are kept in sunlight after the starch test.
(d) A leaf from both the plants is taken to test the presence of starch.

10. The resistance whose V – I graph is given below is

(a) 5/3 Ω (b) 3/5 Ω (c) 5/2 Ω (d) 2/5 Ω

11. In the human respiratory system, the path taken by air when we breathe in is :
(a) Nostrils → Larynx → Trachea → Pharynx → Alveoli
(b) Nostrils → Trachea → Larynx → Pharynx → Alveoli
(c) Nostrils → Pharynx → Larynx → Trachea → Alveoli
(d) Nostrils → Larynx → Pharynx → Trachea → Alveoli

12. Which features make alveoli suitable for the exchange of gases?

(a) They have a very thin wall

(b) They form a very large surface area
(c) They are covered with blood capillaries
(d) All of these

13. If a person is suffering from acidity after overeating, you should suggest him/her to take:
(a) lemon-juice (b) vinegar (c) baking soda solution (d) All of these
14. When we connect too many electrical appliances to a single socket in a circuit having a fixed
value of current rating :
(a) the total resistance of the circuit increases.
(b) the current drawn from the source decreases.
(c) the current increases beyond the rated value.
(d) each appliance starts drawing more and more current from the source.
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15. Consider the following statements :
I. Every step in a food chain is called a trophic level.
II. Decomposers convert complex inorganic matter in dead remains of organisms into simple
substances that go into the soil.
III. In a food chain, energy level increases from lower trophic level to higher trophic level.
IV. Linkages between various food chains constitute a food web.
The correct statements is/are:
(a) I only (b) I and IV (c) I, II and IV (d) II and IV

16. Disposable plastic plates should not be used because:

(a) they are made of materials with light weight
(b) they are made of toxic materials
(c) they are made of biodegradable materials
(d) they are made of non-biodegradable materials

DIRECTION: In the question number 17 and 20, a statement of Assertion (A) is followed by a
statement of Reason (R).
Choose the correct option
(a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of
assertion (A)
(b) Both assertion (A) and reason (R) are true and reason (R) is not the correct explanation of
assertion (A)
(c) Assertion (A) is true but reason (R) is false.
(d) Assertion (A) is false but reason (R) is true.

17. Assertion (A): Acquired trait cannot be passed on from one generation to next generation.
Reason (R): Inaccuracy during DNA copying of acquired trait is minimum.

18. Assertion (A): A compass needle is placed near a current carrying wire. The deflection of the
compass needle decreases when the magnitude of an electric current in the wire is increased.
Reason (R): Strength of a magnetic field at a point near the conductor increases on increasing
the current.

19. Assertion (A) : A convex mirror is used as a rear view driver's mirror.
Reason (R) : Convex mirrors have a wider field of view as they are curved outwards. They also
give an erect, although diminished image.

20. Assertion (A): In an open circuit, the current passes from one terminal of the electric cell to
another.
Reason (R): Generally, the metal disc of a cell acts as a positive terminal.

SECTION – B
Questions 21 to 26 carry 2 marks each.

21. Identify the type of chemical reaction and write balanced chemical equation for each of the
following:
(a) On heating green ferrous sulphate crystals, reddish brown solid is left and gases have smell
of burning sulphur.
(b) Iron nails when dipped in blue copper sulphate solution, becomes brownish in colour and
blue colour of copper sulphate turns to light green.
OR
A white salt on heating decomposes to give brown fumes and a residue is left behind.
(a) Name the salt.
(b) Write the equation for the decomposition reaction.

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22. (a) How do organisms create an exact copy of themselves?
(b) What is importance of chromosomal difference between sperms and egg of human beings?

23. (a) Draw a ray diagram to show the formation of a rainbow in the sky. Mark on the diagram
three points A, B and C as given below :
A – where dispersion of light occurs
B – where internal reflection of dispersed light occurs
C – where refraction of dispersed light occurs
OR
Write about power of accommodation of human eye. Explain why the image distance in the eye
does not change when we change the distance of an object from the eye?

24. “All plants give out oxygen during day and carbon dioxide during night”. Do you agree with
this statement? Give reason.
25. Give one example of an organic compound present in biogas. Draw electron dot structure of this
compound.
26. Ibrahim applied sodium hydroxide to the lustrous, divalent element M. In the reaction mixture,
he saw bubbles beginning to form. When hydrochloric acid was used to treat this element, he
recorded the same findings. Tell him how to recognise the gas that was produced. For both
reactions, write chemical equations.

SECTION – C
Questions 27 to 33 carry 3 marks each.
27. On adding a few drops of universal indicator to three unknown colourless solutions (P), (Q) and
(R) taken separately in three test tubes shown in the following diagram, a student observed the
changes in colour as green in (P), red in (Q) and violet in (R).
(a) Write the decreasing order of their pH.
(b) In which of the test tube solution is acidic in nature?

28. Write balanced equations for the reaction of:

(a) aluminium when heated in air. Write the name of the product.
(b) iron with steam. Name the product obtained.
(c) calcium with water. Why does calcium start floating in water?

29. (a) Draw diagrams of convex mirror and concave mirror showing Principal Axis, Pole, Focus,
Centre of curvature, Radius of curvature.
(b) Explain with the help of a diagram, why a pencil partly immersed in water appears to be
bent at the water surface.
OR
Refractive indices of media A, B, C and D are given:
Media: A B C D
Refractive Index: 133 144 152 165
In which of these four media is the speed of light () Minimum and (ji) Maximum?
Give reasons. Find the refractive index of medium A with respect to medium B.
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30. A plant having blue coloured flowers (BB) is crossed with a plant having white coloured
flowers (bb) :
(a) Name the term used for the trait, which is observed in F1 generation. Give its gene
combination.
(b) If the plants obtained in F1 generation are self-pollinated, write the percentage of (i) plants
with flowers of blue colour, and (ii) plants with flowers of white colour in F2 generation. What
did the reappearance of plants with white coloured flowers in F2 generation indicate ?

31. How do carbohydrates, proteins and fats get digested in human beings?
OR
What are the adaptations of leaf for photosynthesis?

32. (a) In the given food chain, which trophic level will have the maximum concentration of
chemicals? Name the phenomenon involved in it and explain it.

(b) Which chemicals are responsible to reduce the amount of ozone in the atmosphere and
where are they used? Give example.

33. In the given circuit when key is closed, determine the following :

(i) Total resistance offered by the three resistors

(ii) Reading of the ammeter
(iii) Reading of the voltmeter

SECTION – D
Questions 34 to 36 carry 5 marks each.

34. (a) State any two reasons for carbon forming a large number of compounds. Why does carbon
form compounds mainly by covalent bonding?
(b) Identify the compound which contains aldehyde as its functional group and write its
structural formulae.
C3H7OH, C3H7Cl, C2H5CHO, CH3COCH3
OR
(a) Define the term isomer.
(b) Two compounds have same molecular formula C3H6O. Write the names of the functional
group and their formulae.
(c) Write the structural formula of Benzene.

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35. What is a solenoid? Draw the pattern of magnetic field lines of (i) a current carrying solenoid
and (ii) a bar magnet. List two distinguishing features between the two fields.
OR
With the help of a labelled circuit diagram illustrating the pattern of field lines of the magnetic
field around a current-carrying straight long conducting wire. How is the right-hand thumb rule
useful to find the direction of the magnetic field associated with a current-carrying conductor?

36. (i) Study the diagram below of alimentary canal of man and name the parts marked as A, B and
C. Write the name of the enzyme present in each labelled part.
(ii) Explain how digested food reaches each and every cell of the body and is utilised.

SECTION – E(Case Study Based Questions)

Questions 37 to 39 carry 4 marks each.
37. In our laboratories we use compound microscopes to see the magnified image of a microscopic
object. A compound microscope is made up of two lenses. The lens nearest to the object to be
viewed, called objective lens, forms real, inverted and magnified image of the object. This
image serves as an object for the second lens called eyepiece. The eyepiece forms virtual, erect
and magnified image of its object. Thus, the resultant image formed by a microscope is virtual,
inverted and magnified with respect to the microscopic object viewed.

(a) The image of an object formed by a convex lens of focal length 2 cm is real, inverted and
magnified. What is the range of object distance in this case ? (1)
(b) The image of an object formed by a convex lens of focal length 6 cm is virtual, erect and
magnified. What is the range of object distance in this case ? (1)

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 (c) (i) An object is placed at a distance of 12 cm from the optical centre of a convex lens of
focal length 18 cm. Draw a labelled ray diagram to show the formation of image in this case. (2)
OR
(c) (ii) The image formed by a convex lens is real, inverted and of the same size as the object. If
the distance between the objects and the image is 60 cm, determine the focal length of the lens.
Give justification for your answer.

38. Taj Mahal, the great wonder of the

world, is made of white marble which is
composed of calcium carbonate. About
60 years ago it was discovered that this
monument is being eaten away by acid
rain. The Archeological survey of India,
that looks after this building of historical
importance is of the opinion that the
atmospheric pollution due to vehicular
traffic and industries, mainly Mathura
Refinery may be a major cause of acid
rain in and around the monument.
Normal rain is slightly acidic because it absorbs some CO2 from the atmospheric air. Acid rain
is more acidic than normal rain because it also has absorbed oxides of nitrogen and sulphur.

(a) What happens when marble is heated? Write the chemical reaction. What type of reaction is
it. Name the product formed in this reaction which is used in the manufacture of cement. How
will you test the gas evolved in this reaction.
(b) (i) Write down observations which help us to determine whether a chemical reaction has
taken place or not.
(ii) Which gases are spoiling Taj Mahal in Agra? What is the major source of this gas?
OR
(b) A solution of a substance ‘X’ is used for white washing.
(i) Name the substance ‘X’ and write its formula.
(ii) Write the reaction of substance ‘X’ with water.
(iii) Write the reaction of product formed in reaction (ii) with CO2.

39. The original organism at the top will give rise to

two individuals, similar body design, but with
subtle difference. Each of them, in turn, will
give rise to two individuals in the next
generation. Each of the four individuals at the
bottom row will be different from each other.
While some of these differences will be unique,
other will be inherited from there respective
parents, who were different from each other. It
means diversity is created over succeeding
generations.
(a) If a trait ‘A’ exists in 20% of a population of
an asexually reproducing species and a trait ‘B’ exists in 70% of the same population. Which
trait is likely to have arise earlier?
(b) What name is given to the structures of cell which are called hereditary vehicles?
(c) In the above figure, you can see only minor variations, what is the cause of these variations?
How does the creation of variations in a species promote survival?
OR
(c) What are variations? Write its importance also.

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 SAMPLE PAPER TEST 05 FOR BOARD EXAM 2025

SUBJECT: SCIENCE MAX. MARKS: 80

CLASS : X DURATION: 3 HRS
General Instruction:
1. This Question Paper has 5 Sections A-E.
2. Section A has 20 MCQs carrying 1 mark each.
3. Section B has 5 questions carrying 02 marks each.
4. Section C has 6 questions carrying 03 marks each.
5. Section D has 4 questions carrying 05 marks each.
6. Section E has 3 case based integrated units of assessment (04 marks each) with sub-parts of the
values of 1, 1 and 2 marks each respectively.
7. All Questions are compulsory. However, an internal choice in 2 Qs of 5 marks, 2 Qs of 3 marks
and 2 Questions of 2 marks has been provided. An internal choice has been provided in the
2marks questions of Section E
8. Draw neat figures wherever required. Take π =22/7 wherever required if not stated.
SECTION – A
Questions 1 to 20 carry 1 mark each.
1. Identify correctly the labelled parts Q, R and S in figure given below:

(a) Q-Bronchus, R-Bronchiole, S-Trachea (b) Q-Bronchiole, R-Trachea, S-Bronchus

(c) Q-Trachea, R-Bronchus, S-Alveolus (d) Q-Trachea, R-Bronchus, S-Bronchiole

2. Which of the following occurs during oxygen shortage in muscle cells?

(a) Only X (b) Only Y (c) Only Z (d) Any of them - X, Y or Z

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3. A few drops of turmeric solution are added to a colourless liquid. If the liquid becomes red, the
liquid may be :
(a) Hydrochloric acid (b) Distilled water (c) Ammonium hydroxide (d) Lemon juice

4. Which of the following is oxidation reaction?

(a) Zn → Zn2+ + 2e– (b) Zn2+ + 2e– → Zn(s)
(c) Fe3+ + e– → Fe2+ (d) Ag+ + e– → Ag(s)

5. In the following case(s) the combination reaction occurs in :


I. CuO + H2  
II. ZnO + C  
III. Na + O2  
IV. CH4 + O2  
(a) Only III (b) Only IV (c) II and III (d) I, III and IV

6. A hydrocarbon which contains two C – C single bonds and one C ≡ C triple bond is :
(a) Ethyne (b) Propyne (c) Butyne (d) Benzene

7. While cooking, if the bottom of the vessel is getting blackened on the outside, it means that
(a) the food is not cooked completely
(b) the fuel is not burning completely
(c) the fuel is wet
(d) the fuel is burning completely

8. Anand took four colourless solutions P, Q, R and S, and performed the following tests. What is
the definite conclusion that Anand can reach?
Solution P Solution Q Solution R Solution S
With methyl No change in Turns red No change in No change in
orange colour colour colour
With No change in No change in No change in Turns pink
phenolphthalein colour colour colour
With red litmus No change in No change in No change in Turns litmus
colour colour colour blue
With blue litmus No change in Turns litmus red No change in No change in
colour colour colour
(a) Both P and S are salt solutions. (b) Both Q and S are basic solutions.
(c) Both Q and R are salt solutions. (d) Both P and R are neutral solutions.

9. Which of the following is/are natural indicator(s)?

(a) Hydrangea (b) Petunia (c) Geranium (d) All of these

10. The image formed by a concave mirror of focal length 50 cm is real and of magnification – 1. In
this case the distance between the object from its own image is :
(a) 50 cm (b) 100 cm (c) 200 cm (d) Zero

11. Which of the following diagram indicating an uniform magnetic field?

12. Four cells each of emf 1.5V and the internal resistance 0.5 Ω are connected in series but one cell
is wrongly connected as shown in figure.

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 The net voltage and net internal resistance between A and B is
(a) 6 V, 2 Ω (b) 4.5 V, 1.5 Ω (c) 3V, 1 Ω (d) 3V, 2 Ω

13. Overloading is due to

(a) Insulation of wire is damaged (b) fault in the appliances
(c) accidental hike in supply voltage (d) All of the above

14. Differences shown by the individuals of a species forms basis of

(a) heredity (b) variation (c) mutation (d) crossing over

15. The leaves of Mimosa are sensitive to

(a) light (b) smell (c) touch (d) heat

16. Identify part A from given options in the figure.

(a) Anther of stamen (b) Style (c) Ovule (d) Ovary

DIRECTION: In the question number 17 and 20, a statement of Assertion (A) is followed by a
statement of Reason (R).
Choose the correct option
(a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of
assertion (A)
(b) Both assertion (A) and reason (R) are true and reason (R) is not the correct explanation of
assertion (A)
(c) Assertion (A) is true but reason (R) is false.
(d) Assertion (A) is false but reason (R) is true.
Ans: (b) Both assertion (A) and reason (R) are true and reason (R) is not the correct explanation
of assertion (A)

17. Assertion(A): The sex of a child in human beings will be determined by the type of
chromosome he/she inherits from the father.
Reason(R): A child who inherits ‘X’ chromosome from his father would be a girl (XX), while a
child who inherits a ‘Y’ chromosome from the father would be a boy (XY).

18. Assertion (A): A white coloured powder is used by doctors for supporting fractured bone. It is
called as plaster of paris.
Reason (R): It is also called as gypsum.

19. Assertion (A): Human heart does not allow mixing of oxygen rich blood with carbon dioxide
rich blood.
Reason (R): Human heart has different chambers

20. Assertion (A): The commercial unit of electric energy is kilowatt hour (kWh).
Reason (R): 1 kWh = 106 joule (J)

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 SECTION – B
Questions 21 to 26 carry 2 marks each.

21. Identify the substances oxidised and the substances reduced in the following reactions.
(i) ZnO(s) + C(s) → Zn + CO(g)
(ii) 4Na(s) + O2(g) → 2Na2O(s)
OR
Which among the following changes are exothermic or endothermic in nature?
(i) Decomposition of ferrous sulphate
(ii) Dilution of sulphuric acid
(iii) Dissolution of sodium hydroxide in water
(iv) Dissolution of ammonium chloride in water

22. (a) Explain any three directional movements in plants.

(b) How brain and spinal cord are protected in human?

23. List two ways due to which variations arise in a population. State the importance of variation.

24. A piece of wire of resistance 25 Ω is drawn out so that its length is increased to twice of its
original length. Calculate the resistance and ratio of resistivity of the old wire and new stretched
wire.
OR
In the given circuit, find:
(a) Total resistance of the network of resistors
(b) Current through ammeter A

25. (a) In the following food chain, 100 J of energy is available to the lion. How much energy was
available to the producer?

(b) In the following food chain, plants provide 500 J of energy to rats. How much energy will be
available to hawks from snakes?

26. Write the name and one function of each of the parts A and B shown in the following diagram.

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 SECTION – C
Questions 27 to 33 carry 3 marks each.
27. What is meant by the term pH of a solution ? The pH of rain water collected from two cities ‘A’
and ‘B’ was found to be 6·1 and 5·3 respectively. The water of which city is more acidic ?
Justify your answer. State with reason what would happen to the aquatic life of a pond in which
the rain water of city ‘B’ flows.
28. (a) Write a chemical equation for the reaction in which change in colour is observed when a
metal is kept immersed in a salt solution of another metal.
(b) When hydrogen gas is passed over heated copper(II) oxide, copper and steam are formed.
Write the balanced chemical equation with physical states for this reaction. State what kind of
chemical reaction is this.
29. Draw a ray diagram to show the refraction of a ray of light through a triangular glass prism and
mark on it (i) angle of incidence (i), (ii) angle of emergence (e), and (iii) angle of deviation (D).
What would happen, if instead of a ray, a beam of white light falls on the prism ? Give reason
for the phenomenon that occurs in this case.
30. (a) What is cornea?
(b) What part of eye controls the amount of light entering the eye?
(c) Why does the sky appear dark instead of blue to an astronaut?
31. (a) On what factors does the magnetic field produced by a current–carrying circular coil (or
wire) depend?
(b) A magnetic needle deflects when it’s brought near a current carrying conductor. Why?
(c) A magnet is hung using a string. How will you identify the poles?
32. Draw a diagram of human excretory system and label kidney, ureter, aorta, vena cava, urethra
and urinary bladder on it.
33. You have been selected to talk on “ozone layer and its protection” in the school assembly on
‘Environment Day’.
(a) Why should ozone layer be protected to save the environment?
(b) List any two ways that you would stress in your talk to bring in awareness amongst your
fellow friends that would also help in protection of ozone layer as well as the environment.
OR
What is meant by food chain? “The number of trophic levels in a food chain is limited.” Give
reason to justify this statement.

SECTION – D
Questions 34 to 36 carry 5 marks each.

34. A metal carbonate X on reacting with an acid gives a gas which when passed through a solution
Y gives the carbonate back. On the other hand, a gas G that is obtained at anode during

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 electrolysis of brine is passed on dry Y, it gives a compound Z, used for disinfecting drinking
water. Identify X, Y, G and Z.
OR
An organic compound A on heating with concentrated H2SO4 forms a compound B which on
addition of one mole of hydrogen in presence of Ni forms a compound C. One mole of
compound C on combustion forms two moles of CO2 and 3 moles of H2O. Identify the
compounds A, B and C and write the chemical equations of the reactions involved.

35. (a) A student suffering from myopia is not able to see distinctly the objects placed beyond 5 m.
List two possible reasons due to which this defect of vision may have arisen. With the help of
ray diagrams, explain:
(i) why the student is unable to see distinctly the objects placed beyond 5 m from his eyes.
(ii) the type of the corrective lens used to restore proper vision and how this defect is corrected
by the use of this lens.
(b) If, in this case, the numerical value of the focal length of the corrective lens is 5 m, find the
power of the lens as per the New Cartesian Sign Convention.

OR

(a) Draw a ray diagram to show the formation of image by a convex lens when an object is
placed in front of the lens between its optical centre and principal focus.
(b) In the above ray diagram mark the objectdistance (u) and the image-distance (v) with their
proper signs (+ve or –ve as per the New Cartesian Sign Convention) and state how these
distances are related to the focal length (f) of the convex lens in this case.
(c) Find power of a convex lens which forms a real, and inverted image of magnification –1 of
an object placed at a distance of 20 cm from its optical centre.

36. (a) Differentiate between the following:

(i) Pollen tube and style
(ii) Fission in Amoeba and Plasmodium
(iii) Fragmentation and regeneration
(b) Mention two reasons for the appearance of variations among the progeny formed by sexual
reproduction.
OR

(a) Write the functions of each of the following parts in a human female reproductive system:
(i) Ovary (ii) Uterus
(iii) Fallopian tube
(b) Write the structure and functions of placenta in a human female.

SECTION – E(Case Study Based Questions)

Questions 37 to 39 carry 4 marks each.
37. The ability of carbon atoms to form chains leads to the existence of a series of compounds that
have same functional group (and hence similar chemical properties) and only differ from each
other by the presence of an additional carbon atom and its two associated hydrogen atoms in the
molecule (which causes the physical properties to change in a regular manner). A series of
compounds related in this way is said to form an homologous series.
The point about chemical properties is best illustrated by the sections that follow, on different
homologous series. The changes in physical properties are a result of the changes that occur in
the strength of van der Waals’ forces with increasing molar mass and in some cases a change in
molecular polarity. The simplest illustration of the effect of chain length on physical properties
is the, variation of the boiling point of the alkanes with the number of carbon atoms in the chain,
as illustrated in figure.

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 (i) All the members of a homologous series have similar chemical properties. Why?
(ii) In the graph shown, which has the higher boiling point and why?
Hydrocarbon with 3 carbon atoms or hydrocarbon with 6 carbon atoms
(iii) (a) What is the boiling point of heptane as shown in the graph?
(b) Why the curve is initially steep and flattens at the end?
OR
(iii) (a) Write the molecular formula of the 2nd and the 3rd member of the homologous series
whose first member is methane.
(b) Write the next homologue of each of the following: I. C2H4 II. C4H6

38. Plantation drives are often carried out especially during monsoon season for the protection of
our environment. Such programmes need a lot of saplings for tree plantation. Plants are
propagated by sexual or asexual means in fields and nurseries. Over the years horticulturists
have developed asexual methods that use vegetative parts of the plants to multiply. Many plants
can reproduce by this method naturally as well as by artificial means.

(a) Which specific part of the plant is used for sexual and asexual means of propagation to
produce a new plant ? (1)
(b) Give one example of (i) a flower, and (ii) a fruit grown by vegetative propagation. (1)
(c) (i) List two advantages of growing plants by vegetative propagation. (2)
OR
(c) (ii) Describe an activity to show how potatoes reproduce asexually.
39. An insulated copper wire wound on a cylindrical cardboard tube such that its length is greater
than its diameter is called a solenoid. When an electric current is passed through the solenoid, it
produces a magnetic field around it. The magnetic field produced by a current-carrying solenoid
is similar to the magnetic field produced by a bar magnet. The field lines inside the solenoid are
in the form of parallel straight lines. The strong magnetic field produced inside a current
carrying solenoid can be used to magnetise a piece of magnetic material like soft iron, when
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 placed inside the solenoid. The strength of magnetic field produced by a current carrying
solenoid is directly proportional to the number of turns and strength of current in the solenoid.
(a) What do the field lines inside the solenoid indicate?
(b) Which rule is used to determine the north-south polarities of an electromagnet?
(c) The pattern of magnetic field lines around a current-carrying solenoid and a bar magnet is
shown below. Observe them carefully, compare and find out if there is any similarity and
dissimilarities between them.

OR
(c) Distinguish between an electromagnet and a permanent magnet.

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 SAMPLE PAPER TEST 01 FOR BOARD EXAM 2025

SUBJECT: SOCIAL SCIENCE MAX. MARKS : 80

CLASS : X DURATION : 3 HRS
General Instruction:
1. Question paper comprises five Sections – A, B, C, D and E. There are 37 questions in the
question paper. All questions are compulsory.
2. Section A – From question 1 to 20 are MCQs of 1 mark each.
3. Section B – Question no. 21 to 24 are Very Short Answer Type Questions, carrying 2 marks
each. Answer to each question should not exceed 40 words.
4. Section C contains Q.25to Q.29 are Short Answer Type Questions, carrying 3 marks each.
Answer to each question should not exceed 60 words
5. Section D – Question no. 30 to 33 are long answer type questions, carrying 5 marks each.
Answer to each question should not exceed 120 words.
6. Section-E - Questions no from 34 to 36 are case based questions with three sub questions and
are of 4 marks each
7. Section F – Question no. 37 is map based, carrying 5 marks with two parts, 37a from History (2
marks) and 37b from Geography (3 marks).
8. There is no overall choice in the question paper. However, an internal choice has been provided
in few questions. Only one of the choices in such questions have to be attempted.
9. In addition to this, separate instructions are given with each section and question, wherever
necessary.
SECTION – A
Questions 1 to 20 carry 1 mark each.
1. Consider the statements given below and choose the correct answer.
Statement I: By the 1870s, caricatures and cartoons were being published in Indian journals and
newspapers, commenting on social and political issues.
Statement II: Some caricatures praised the educated Indians’ fascination with Western tastes and
clothes, while others were looking forward to social change.
(a) Statement (I) is correct and (II) is incorrect.
(b) Statement (I) is incorrect and (II) is correct.
(c) Both (I) & (II) are incorrect.
(d) Both (I) & (II) are correct
2. Choose the correctly matched pair.
(a) Ferrous – Natural Gas
(b) Non– Ferrous – Nickel
(c) Non– Metallic Minerals – Limestone
(d) Energy Minerals – Cobalt

3. Match list I and II and select the correct answer using the codes below in the lists:
List I List II
(A) Reserved Forests (I) North Eastern States
(B) Protected Forests (II) Andhra Pradesh
(C) Unclassed Forests (III) Haryana
Options:
(a) (A)-(I), (B)-(II), (C)-(III) (b) (A)-(III), (B)-(II), (C)-(I)
(c) (A)-(I), (B)-(III), (C)-(II) (d) (A)-(II), (B)-(III), (C)-(I) 1

4. Arrange the following events in the correct chronological order leading up to the Civil
Disobedience Movement:
(I) Boycott of the Simon Commission
(II) Poorna Swaraj resolution passed
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 (III) Letter with 11 demands sent to Viceroy Irwin
(IV) Salt March
Options:
(a) (IV), (III), (II), (I) (b) (II), (I), (III), (IV)
(c) (I), (IV), (III), (II) (d) (I), (II), (III), (IV) 1

5. Identify the soil with the help of following information.

• It develops in areas with high temperature.
• It is the result of intense leaching due to heavy rain.
• Humus content is low.
Soil:
(a) Arid soil (b) Yellow soil (c) Laterite soil (d) Black soil

6. Which of the following term refers to the belief in and advocacy for the social, political and
economic equality of women?
(a) Patriarchy (b) Matriarchy (c) Socialist (d) Feminist

7. Read the given statements:

• India has no official religion.
• All the communities have freedom to profess and practice any religion in India.
Which one of the following constitutional term is used for the above statements?
(a) Republic (b) Secular (c) Sovereign (d) Socialist

8. Match the Column I with Column II and choose the correct option:
Column I (List) Column II (Jurisdiction Sphere)
I. Union list subjects A. State Governments alone make laws on it.
II. State list subjects B. For uniformity Central Government legislates on it.
III. Concurrent subjects C. Subjects under Jurisdiction of Centre and State
Governments.
IV. Residuary subjects D. Central Government legislates on new subjects.
I. II. III. IV.
(a) A B C D
(b) C D A B
(c) D C B A
(d) B A C D

9. Look at the given picture carefully and infer the income of the bank.

Choose the correct option from the following.

(a) The difference between the amount deposited and borrowed by the bank to Reserve Bank of
India.
(b) The difference of amount of interest between what is charged from borrowers and what is
paid to depositors.
(c) The difference of interest rate between what is charged from borrowers and what is charged
from depositor.

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 (d) The difference between the amount deposited by the depositor and borrowed by the
borrower.

10. From which of the following countries Giuseppe Garibaldi belonged to?
(a) Austria (b) Italy (c) Greece (d) Spain

11. Arrange the following events in chronological order and choose the correct option from the
following:
I. Treaty of Constantinople
II. Defeat of Napoleon
III. Unification of Italy
IV. Unification of Germany
Options:
(a) I, II, IV and III (b) II, III, I and IV (c) II, I, IV and III (d) IV, I, III and II

12. Suppose, the monthly income of the family members is as follows respectively:
• Mother– ₹ 50,000/-
• Father– ₹ 40,000/-
• Son– ₹ 20,000/-
• Daughter– ₹ 20,000/-
The average income of the family would be:
(a) ₹ 32,000/- (b) ₹ 30,000/- (c) ₹ 32,500/- (d) ₹ 33,000/-

13. Which one of the following indices is given priority by the World Bank with respect to
development?
(a) Infant Mortality Rate (b) Equality
(c) Body Mass Index (d) Per Capita Income

14. Choose the correct option to fill the blank.

Removing barriers or restrictions on business and trade set by the government is called as
___________ .
(a) Disinvestment (b) Special Economic Zones
(c) Liberalisation (d) Foreign Direct Investment

15. Which of the following is the true meaning of ‘Equal treatment of women’ as a necessary
ingredient of a democratic society?
(a) Women are always treated with respect and dignity.
(b) It is now easier for women to legally wage struggle for their rights.
(c) Most societies across the world are now women dominated.
(d) Women are now treated as equals in the political arena.

16. Why do lenders often require collateral before lending loan? Choose the most suitable option
from the following.
(a) To lower interest rates for borrowers.
(b) To establish personal relations.
(c) To increase their profit margins.
(d) To mitigate the risk of loan default.

17. Which of the following was the primary objective of Belgium to form the separate government
in Brussels?
(a) Promoting cultural events (b) Managing international relations
(c) Enforcing local laws (d) Ensuring linguistic accommodation

18. Which one of the following countries has two-party system?

(a) China (b) United Kingdom (c) India (d) Pakistan

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19. What role do checks and balances play in a democratic country? Choose the most suitable
option from the following.
(a) To establish a direct form of government without representatives.
(b) To create a separation of powers to prevent from authoritarianism.
(c) To prevent any change to the Constitution.
(d) To ensure absolute power for one branch of government.

20. Which one of the following is an example of organised sector activities?

(a) A farmer irrigating his field.
(b) A handloom weaver working in her house.
(c) A headload worker carrying cement.
(d) A teacher taking classes in a government school.

SECTION – B
Questions 21 to 24 carry 2 marks each.
21. ‘The silk routes are a good example of vibrant pre -modern trade and cultural links between
distant parts of the world.’ Substantiate the statement with illustrations.

22. India with vast population and diversity represents a classic example of power sharing that
exemplifies the very spirit of democracy. Justify the statement.

23. "Local Government is an effective way to uphold the democratic principle of decentralization."
Justify this statement with valid points.

24. (A) Suggest any two measures for the conservation of the forest.
OR
(B) Suggest any two measures for the conservation of wildlife.

SECTION – C
Questions 25 to 29 carry 3 marks each.
25. Define agricultural term used for cultivation of fruits and vegetables? Write its features with
reference to India.

26. Analyse the role of political parties in a democracy.

27. (A) Describe any three causes that led to the Non- Cooperation Movement.
OR
(B) Describe any three causes of ‘Civil Disobedience Movement.’

28. How is the issue of sustainability important for development? Explain.

29. How is credit essential for economic activities? Explain with examples.

SECTION – D
Questions 30 to 33 carry 5 marks each.
30. (A) Analyse the measures adopted to prevent soil erosion caused due to natural forces.
OR
(B) ‘"Mohan recently bought a farm and wants to grow crops such as sugarcane, cotton, and
jowar. He is unfamiliar with the local soil types and climatic conditions.” Help him identify the
appropriate soil type and its properties for successful farming.

31. (A) Political parties are a necessary condition for a democracy.’ Analyse the statement with
relevant points.

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 OR
(B) "Political parties today face several challenges that impact their democratic functioning."
Justify this statement.

32. (A) ‘Globalisation is the process of rapid integration or interconnection between countries.’
Explain the statement with examples.
OR
(B) ‘Improvement in technology has stimulated the globalisation process.’ Explain the statement
with examples.

33. (A) How did the ideology of ‘liberalism’ affect the Europe in early nineteenth century? Explain.
OR
(B) Explain the process of formation of ‘United Kingdom of Great Britain’.

SECTION – E (Case Study Based Questions)

Questions 34 to 36 carry 4 marks each.
34. Case Study – 1
Read the source given below and answer the question that follows:
Emboldened with this success, Gandhi ji in 1919 decided to launch a nationwide Satyagraha
against the proposed Rowlatt Act (1919). This Act had been hurriedly passed through the
Imperial Legislative Council despite the united opposition of the Indian members. It gave the
government enormous powers to repress political activities, and allowed detention of political
prisoners without trial for two years. Mahatma Gandhi wanted non-violent civil disobedience
against such unjust laws, which would start with a hartal on 6 April.

(i) Why did the British introduce the Rowlatt Act? (1)
(ii) Examine the effect of this Act on Indians. (2)
(iii) How did Mahatma Gandhi respond to the Rowlatt Act? Provide one reason for his reaction.
(1)
35. Case Study – 3
Read the given extract and answer following questions
HUMAN DEVELOPMENT REPORT
Once it is realised that even though the level of income is important, yet it is an inadequate
measure of the level of development, we begin to think of other criterion. There could be a long
list of such criterion but then it would not be so useful. What we need is a small number of the
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 most important things. Health and education indicators, such as the ones we used in comparison
of Kerala and Punjab, are among them. Over the past decade or so, health and education
indicators have come to be widely used along with income as a measure of development. For
instance, Human Development Report published by UNDP compares countries based on the
educational levels of the people, their health status and per capita income. It would be
interesting to look at certain relevant data regarding India and its neighbours from Human
Development Report 2006.
(i) On what basis the UNDP compares countries on Human Development? (1)
(ii) Explain Human development briefly. (2)
(iii) Mention other aspects that should be considered in measuring human development. (1)

36. Case Study – 2

Read the given extract and answer following questions.
FLOODS

Basic Safety Precautions to be Taken:

• Listen to radio/TV for the latest weather bulletins and flood warnings. Pass on the information
to others.
• Make a family emergency kit which should include; a portable radio/transistor, torch, spare
batteries, a first aid box along with essential medicines, ORS, dry food items, drinking water,
matchboxes, candles and other essential items.
• Keep hurricane lamp, ropes, rubber tubes, umbrella and bamboo stick in your house. These
could be useful.
• Keep your cash, jewellery, valuables, important documents, etc. in a safe place.
• If there is a flood, move along with your family members and cattle to safe areas like relief
camps, evacuation centres, elevated grounds where you can take shelter.
• Turn off power and gas connections before leaving your house.
During floods:
• Don’t enter into flood waters; it could be dangerous.
• Don’t allow children to play in or near flood waters.
• Stay away from sewerage line, gutters, drains, culverts etc.
• Be careful of snakes; snakebites are common during floods.
• Stay away from electric poles and fallen powerlines to avoid electrocution.
• Don’t use wet electrical appliances-get them checked before use.
• Eat freshly cooked and dry food. Always keep your food covered.
• Use boiled and filtered drinking water.
• Keep all drains, gutters near your house clean.
• Stagnation of water can breed vector/waterborne diseases. In case of sickness, seek medical
assistance.
• Use bleaching powder and lime to disinfect the surroundings.
(i) Mention any two essential items that should be included in a ‘family emergency kit’. (1)
(ii) Why are the items of family emergency kit important during flood situation? (1)
(iii) In case of a flood, what are the recommended actions to ensure the safety of your family
and belongings? Describe any two. (2)
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 SECTION – F (Map Skill Questions) – 2 + 3 = 5
37. (a) Two places A and B have been marked on the given outline map of India. Identify them and
write their correct names on the lines drawn near them.
(A) The place where the Peasant Satyagraha took place.
(B) Indian National congress session was held at this place in Sept. 1920.

(b) On the same outline map of India locate and label any three of the following with suitable
symbols.
(i) A software Technology Park in Maharashtra.
(ii) A coal mine in Jharkhand.
(iii) The tallest dam in India.
(iv) A seaport located in West Bengal.

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PM SHRI KENDRIYA VIDYALAYA GACHIBOWLI, GPRA CAMPUS, HYD-32
SAMPLE PAPER TEST 02 FOR BOARD EXAM 2025

SUBJECT: SOCIAL SCIENCE MAX. MARKS : 80

CLASS : X DURATION : 3 HRS
General Instruction:
1. Question paper comprises five Sections – A, B, C, D and E. There are 37 questions in the
question paper. All questions are compulsory.
2. Section A – From question 1 to 20 are MCQs of 1 mark each.
3. Section B – Question no. 21 to 24 are Very Short Answer Type Questions, carrying 2 marks
each. Answer to each question should not exceed 40 words.
4. Section C contains Q.25to Q.29 are Short Answer Type Questions, carrying 3 marks each.
Answer to each question should not exceed 60 words
5. Section D – Question no. 30 to 33 are long answer type questions, carrying 5 marks each.
Answer to each question should not exceed 120 words.
6. Section-E - Questions no from 34 to 36 are case based questions with three sub questions and
are of 4 marks each
7. Section F – Question no. 37 is map based, carrying 5 marks with two parts, 37a from History (2
marks) and 37b from Geography (3 marks).
8. There is no overall choice in the question paper. However, an internal choice has been provided
in few questions. Only one of the choices in such questions have to be attempted.
9. In addition to this, separate instructions are given with each section and question, wherever
necessary.

SECTION – A
Questions 1 to 20 carry 1 mark each.
1. Read the data given below and answer the question.
Infant mortality rate per Literacy rate%
State
1000 live births (2018) (2017-18)
A 30 82
B 7 94
As per the data given above, why state B has a low infant mortality rate?
(a) It has high per capita income.
(b) It has better infrastructure than state A
(c) It has good teachers and schools.
(d) It has health care and education for all.

2. Read the given statements and choose the correct option with regard to Rabi cropping season
from the following:
I. Rabi crops are sown in winter.
II. Sown from October to December and harvested from April to June.
III. Important crops are Maize, Cotton, Jute.
IV. Punjab, Haryana, Uttar Pradesh are important for the production of wheat.
Options:
(a) I, III and IV (b) II, III and IV (c) I, II and IV (d) I, II and III

3. Conservation of forest is a key to the survival of human mankind. Some of the practices
undertaken in India in this direction is Joint Forest Management. Identify the correct
information related to Joint Forest Management.
(I) It involves local communities in the management and restoration of degraded forests.
(II) The programme has been in formal existence since 1980.
(III) Jharkhand passed the first resolution for Joint Forest Management.

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 (IV) The members of local village communities are entitled to intermediary benefits like non
timber forest producers.
Options:
(a) (I) and (II) only (b) (II) and (III) only (c) (I) and (IV) only (d) (III) and (IV) only 1

4. Why did nationalists in late-nineteenthcentury India focus on recording and preserving folklore?
(a) To create new forms of artistic expression that reflected modern India.
(b) To restore a sense of pride in traditional culture and national identity
(c) To use folklore as a tool for economic development and modernization.
(d) To promote a uniform culture that could be adopted across all Indian regions

5. Interpret the following pie diagram and choose the correct option for the following question?

What is the significance of 43 percent land under plains?

(a) It provides facilities for agriculture and industry.
(b) It provides facilities for tourism.
(c) It ensures perennial flow of some river.
(d) It possesses rich reserves of minerals, fossil fuels and forests.

6. Mr. X has taken credit to make candles during the festive season. Choose the correct options
that defines the importance of credit from the given options:
(I) it plays a vital and positive role in meeting his target and accelerating his income
(II) the credit helps him to meet the ongoing expenses of production
(III) the credit helps him complete the production on time
(IV) it helps him in exercising restraint and get into the habit of taking more credit
(a) Only (IV) (b) (III) and (IV) (c) (I), (II) and (III) (d) Only (II)

7. The North-eastern States of India like Nagaland, Mizoram, Arunachal Pradesh enjoys special
status in the Constitution of India because:
(a) the area has lush green forests.
(b) literacy rates are very high.
(c) due to their social and historical circumstances.
(d) as the people speak lot of different languages

8. Napoleon in the given picture is depicted as a postman. What do each letter falling from his bag
represent?

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 (a) Number of wars he fought (b) Letters he posted to the monarchs
(c) Territories lost by him (d) Areas conquered by him 1

9. The people of Belgium have successfully dealt with their country’s power sharing problem and
is leading a happy and peaceful life. Which route to federation have they opted for?
(a) Coming Together (b) Cooperative Federation
(c) Holding Together (d) Competitive Federation

10. Match list I with list II and select the correct answer using the codes below in the lists:
List I List II
(A) Ethnic (I) Either only one or two level government
(B) Majoritrianism (II) A violent conflict opposing groups within a
country
(C) Civil war (III) Belief that the majority community should
be able to rule a country
(D) Unitary system (IV) A social division based on culture
(a) (A)-(IV), (B)-(I), (C)-(III), (D)-(II)
(b) (A)-(II), (B)-(IV), (C)-(I), (D)-(III)
(c) (A)-(Iii), (B)-(I), (C)-(II), (D)-(IV)
(d) (A)-(IV), (B)-(III), (C)-(II), (D)-(I) 1

11. Which of the following statements about Federalism in the Indian Constitution are correct?
(I) India is declared as a Union of States.
(II) Power-sharing between the Union and State governments is a basic feature.
(III) The power-sharing arrangement is easy to change.
(IV) Changes in power-sharing require a 1/3rd majority in both houses of Parliament.
Options:
(a) (I) and (II) (b) (II) and (III) (c) (I) and (III) (d) (II) and (IV) 1

12. Which one of the following pairs regarding Indian nationalism is correctly matched?
Leaders Contribution
(a) Sardar Patel : Hindustan Socialist Republican Army
(b) Bhagat Singh : Swaraj Party
(c) C.R. Das : Bardoli Satyagraha
(d) Jawahar Lal Nehru : Oudh Kisan Sabha

13. In Indian Economy, the three sectors (Primary, Secondary and Tertiary) are interdependent.
However, the share of employment in the primary sector remains high. Most appropriate
explanation for this could be:
(I) Government policies preferentially treat the primary sector.
(II) Indian economy is largely agrarian and majority of population is dependent on agriculture.
(III) Inadequate service sector jobs force people to continue working in primary sectors.
(IV) Primary sector provides raw material for the secondary and tertiary sector.
Choose the correct option:
(a) Only (I) and (II) are true
(b) Only (II) and (III) are true
(c) Only (III) and (IV) are true
(d) All are true 1

14. Two statements are given below. They are Assertion (A) and Reason (R). Read both the
statements and choose the correct option.
Assertion (A): The most serious source of nationalist tension in Europe after 1871 was Balkan.
Reason (R): A large part of the Balkan was under the control of Ottoman Empire.
Options:
(a) Both, (A) and (R) are true and (R) is the correct explanation of (A).

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 (b) Both (A) and (R) are true but (R) is not the correct explanation of (A).
(c) (A) is true but (R) is false.
(d) (A) is false but (R) is true.
15. The frequent stories of ............... remind us that no system is entirely without shortcomings,
even democracies. Identify the issue being referred to from the options given.
Clues:
(a) poverty (b) black marketing (c) terrorism (d) corruption

16. Which of the following factors significantly contribute to the process of globalisation? Select
the correct options.
(I) Expansion of Multinational Corporations (MNCs).
(II) Advancements in information and communication technology.
(III) Nationalisation and trade barriers.
(IV) Cross-border movement of people for jobs and education.
Options:
(a) Statements (I) and (II) are appropriate.
(b) Statements (I), (II) and (III) are appropriate.
(c) Statements (II), (III) and (IV) are appropriate
(d) Only statement (III) is appropriate

17. The result of greater foreign investment and greater foreign trade has been ............... across
countries. Find the correct option from below.
(a) greater bifurcation of production and markets
(b) greater segregation of production and markets
(c) greater differentiation of production and markets
(d) greater integration of production and markets

18. Which of the following are developmental goals of a prosperous farmer? Choose the correct
option from the given options.
I. Better wages
II. Higher support prices for crops
III. Assured high family income
IV. More days for work
Options:
(a) Only I and II are correct.
(b) Only II and IV are correct.
(c) Only II and III are correct.
(d) Only I and IV are correct.

19. Consider the statements given below and choose the correct answer.
Statement I: A communal mindset can lead to efforts to secure political influence for a specific
religious group.
Statement II: Members of the majority community may seek to create a separate political entity
as a response to such dynamics.
(a) Statement (I) is correct and (II) is incorrect.
(b) Statement (I) is incorrect and (II) is correct
(c) Both (I) & (II) are incorrect
(d) Both (I) & (II) are correct 1

20. Which of the following is the main factor that led to the rise of multiple political parties at the
same level in India?
(a) A federal political system
(b) Varied economic conditions
(c) Linguistic and regional diversity
(d) Low levels of literacy and political awareness
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 SECTION – B
Questions 21 to 24 carry 2 marks each.
21. “The Silk Route was a good example of vibrant pre - modern trade and the cultural link between
distant parts of the world”. Explain the statement with any two examples.
OR
"New crops can significantly impact survival and well-being." Provide evidence to support this
statement.

22. Why is power sharing desirable? Explain.

23. Differentiate between Public and Private Sector.
24. “Agriculture and industry are not exclusive of each other. They move hand in hand”. Justify
your answer with examples

SECTION – C
Questions 25 to 29 carry 3 marks each.
25. Over the forty years between 1973-74 and 2013-14, while production in all the three sectors has
increased, it has increased the most in the tertiary sector. As a result, in the year 2013-14, the
tertiary sector has emerged as the largest producing sector in India replacing the primary sector.
Why do you think tertiary sector has become so popular in India? Support your answer giving
any 3 reasons
26. Women empowerment has greatly improved their status in society over the years. Give any
three examples to prove the statement.
27. ‘Manufacturing industries are considered the backbone of economic development.’ Justify the
statement.
28. ‘By the seventeenth century, as urban culture bloomed in China, the uses of print diversified’.
Explain the statement by giving suitable examples.

29. (a) Mr.Y from a city in India visits a rural area and finds five people working in a small
agricultural farm. More than two people are not required to work in the farm and removing the
other three will not affect production. How can one solve this problem of underemployment in
rural areas? Explain.
OR
(b) Sunil and Raman did their graduation from the same college. Sunil got employed in an
unorganised sector and was not satisfied whereas Raman got employed in an organised sector
and was happy and satisfied. Identify three reasons for Sunil’s dissatisfaction as compared to
Raman.

SECTION – D
Questions 30 to 33 carry 5 marks each.
30. (a) Miss X wants to start a savoury food store in her village. She wants to supplement her
income to raise the standard of living of her family. How, do you think, self-help groups can
help, support your answer with reasons?
OR
(b) Money by providing the crucial intermediate step eliminates the need for double coincidence
of wants. Justify the statement highlighting the significance of the modern form of money in
India.

31. (A) How is energy a basic requirement for economic development? Explain.
OR
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 (B) How are conventional sources of energy different from non-conventional sources? Explain.

32. (A) How are democratic governments better than other forms of government? Explain.
OR
(B) How do democracies lead to peaceful and harmonious life among citizens? Explain.

33. (a) ‘Romanticism, a cultural movement sought to develop a particular form of nationalist
sentiment.’ Justify the statement with suitable arguments.
OR
(b) ‘The Treaty of Vienna depicted the spirit of conservatism.’ Substantiate the statement with
key features of the treaty.

SECTION – E (Case Study Based Questions)

Questions 34 to 36 carry 4 marks each.
34. Case Study – 1
Read the source given below and answer the question that follows:
Printed Words
This is how Mercier describes the impact of the printed word and the power of reading in
one of his books:
‘Anyone who had seen me reading would have compared me to a man dying of thirst who was
gulping down some fresh, pure water.... Lighting my lamp with extraordinary caution, I threw
myself hungrily into the reading. An easy eloquence, effortless and animated, carried me from
one page to the next without my noticing it. A clock struck off the hours in the silence of the
shadows and I heard nothing. My lamp began to run out of oil and produced only a pale light,
but still I read on. I could not even take out time to raise the wick for fear of interrupting my
pleasure. How those new ideas rushed into my brain! How my intelligence adopted them!’
(i) How does the passage reflect the immersive nature of reading of Mercier? (1)
(ii) Why did Mercier describe himself as a virtual writer? (1)
(iii) How did reading influence Mercier’s intellectual capacity and his engagement with new
concepts? Explain in any two points. (2)

35. Case Study – 2

Read the given extract and answer following questions.
Given the abundance and renewability of water, it is difficult to imagine that we may suffer
from water scarcity. The moment we speak of water shortages; we immediately associate it with
regions having low rainfall or those that are drought prone. We instantaneously visualise the
deserts of Rajasthan and women balancing many ‘matkas’ (earthen pots) used for collecting and
storing water and travelling long distances to get water. True, the availability of water resources
varies over space and time, mainly due to the variations in seasonal and annual precipitation, but
water scarcity in most cases is caused by over-exploitation, excessive use and unequal access to
water among different social groups.
(i) Give any one reason that could contribute to water scarcity in the future? (1)
(ii) Why a resident of Rajasthan would choose to install a submersible water pump? (2)
(iii) Why is water conservation crucial? Discuss any one key for effective water management
and conservation. (1)
36. Case Study – 3
Read the given extract and answer following questions
LOCAL GOVERNMENT
This new system of local government is the largest experiment in democracy conducted
anywhere in the world. There are now about 36 lakh elected representatives in the panchayats
and municipalities etc.. all over the country. This number is bigger than the population of many
countries in the world. Constitutional status for local government has helped to deepen
democracy in our country. It has also increased women’s representation and voice in our
democracy. At the same time, there are many difficulties. While elections are held regularly and
enthusiastically, gram sabhas are not held regularly. Most state governments have not
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 transferred significant powers to the local governments. Nor have they given adequate
resources. We are thus still a long way from realising the ideal of selfgovernment.
(i) Analyse the significance of the elected representatives in the Panchayats. (1)
(ii) In what way has the representation of women in democracy influenced by Constitutional
status for local government? (1)
(iii) What has been the impact of granting Constitutional status to local government on the
democratic landscape of the country? Analyse any two impacts. (2)

SECTION – F (Map Skill Questions) – 2 + 3 = 5

37. (i) Two places ‘A’ and ‘B’ have been marked on the given Political outline map of India.
Identify them with the help of the following information and write their correct names on the
lines drawn near them:
(a) The place where Mahatma Gandhi broke the salt law. (1)
(b) The place where Session of Indian National Congress was held in 1927. (1)
(ii) On the same Political outline map of India. locate and label any three of the following with
suitable symbols: (3×1=3)
(a) Hirakud – Dam (1)
(b) Mumbai – Software Technology Park (1)
(c) Raja Sansi – International Airport (1)
(d) Naraura – Nuclear Power Plant (1)

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 SAMPLE PAPER TEST 03 FOR BOARD EXAM 2025

SUBJECT: SOCIAL SCIENCE MAX. MARKS : 80

CLASS : X DURATION : 3 HRS
General Instruction:
1. Question paper comprises five Sections – A, B, C, D and E. There are 37 questions in the
question paper. All questions are compulsory.
2. Section A – From question 1 to 20 are MCQs of 1 mark each.
3. Section B – Question no. 21 to 24 are Very Short Answer Type Questions, carrying 2 marks
each. Answer to each question should not exceed 40 words.
4. Section C contains Q.25to Q.29 are Short Answer Type Questions, carrying 3 marks each.
Answer to each question should not exceed 60 words
5. Section D – Question no. 30 to 33 are long answer type questions, carrying 5 marks each.
Answer to each question should not exceed 120 words.
6. Section-E - Questions no from 34 to 36 are case based questions with three sub questions and
are of 4 marks each
7. Section F – Question no. 37 is map based, carrying 5 marks with two parts, 37a from History (2
marks) and 37b from Geography (3 marks).
8. There is no overall choice in the question paper. However, an internal choice has been provided
in few questions. Only one of the choices in such questions have to be attempted.
9. In addition to this, separate instructions are given with each section and question, wherever
necessary.
SECTION – A
Questions 1 to 20 carry 1 mark each.
1. Arrange the following events in chronological order and choose the correct option.
I. Treaty of Constantinople
II. Hamburg granted autonomy to Hungary
III. Balkan Conflict
IV. Napoleonic Civil Code
Options :
(a) IV, II, I & III (b) III, II, IV & I (c) IV, I, II & III (d) I, IV, III & II

2. Choose the correct option to fill in the blank.

The Vernacular Press Act was passed in ______________ on the lines of the Irish Press Act.
(a) 1878 (b) 1968 (c) 1887 (d) 1778

3. The German philosopher ‘Johann Gottfried’ belonged to which one of the following schools of
thought ?
(a) Socialist (b) Liberalist (c) Romanticist (d) Marxist

4. Choose the correct pair regarding the sectors of economy.

(a) Primary Mining
(b) Secondary Flower cultivation
(c) Tertiary Fishing
(d) Secondary Bee-keeping

5. Which one of the following states has the highest Human Development Index ?
(a) Punjab (b) Gujarat (c) Rajasthan (d) Kerala

6. Choose the correct option regarding the Axis powers in the Second World War.
(a) Germany, Italy and China (b) Britain, France and Germany
(c) Germany, France and Italy (d) Germany, Japan and Italy

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7. Read the following characteristics of a soil and identify the soil from the given options.
● It is widely spread and important soil.
● Northern plains are made of it.
● It consists of sand, silt and clay.
Options:
(a) Yellow soil (b) Black soil (c) Laterite soil (d) Alluvial soil

8. Match Column-I with Column-II and choose the correct option : 1

Column-I (Crop) Column-II (Type)
I. Wheat a. Millet Crop
II. Ragi b. Beverage Crop
III. Tea c. Food Crop
IV. Maize d. Food & Fodder Crop
Options :
I II III IV
(a) d a c b
(b) c d b a
(c) c a b d
(d) d b a c

9. Which one of the following is a non-conventional source of energy ?

(a) Natural gas (b) Petroleum (c) Coal (d) Geothermal energy

10. Two statements are given below. They are Assertion (A) and Reason (R). Read both the
statements and choose the correct option.
Assertion (A): Power sharing is the spirit of democracy.
Reason (R): A legitimate government is one where all the groups connect with the government
through their participation.
Options:
(a) Both (A) and (R) are true and (R) is the correct explanation of (A).
(b) Both (A) and (R) are true, but (R) is not the correct explanation of (A).
(c) (A) is true, but (R) is false.
(d) (A) is false, but (R) is true.

11. Two statements are given below. They are Assertion (A) and Reason (R). Read both the
statements and choose the correct option.
Assertion (A): We need to protect forests and wildlife.
Reason (R): Conservation maintains ecological diversity.
Options:
(a) (A) is true, but (R) is false.
(b) (A) is false, but (R) is true.
(c) Both (A) and (R) are true and (R) is the correct explanation of (A).
(d) Both (A) and (R) are true, but (R) is not the correct explanation of (A).

12. Choose the correct option regarding the Concurrent List of legislative rights in India.
(a) Currency, Irrigation, Adoption and Computer Software
(b) Defense, Foreign Affairs, Banking and Communication
(c) Police, Business, Commerce and Agriculture
(d) Education, Forest, Marriage and Adoption

13. Which one of the following orders has been passed by the Supreme Court to reform political
parties in India ?
(a) It is mandatory for all parties to hold organizational elections.
(b) It is mandatory for all parties to file income tax returns.
(c) It is mandatory for all the candidates to give details of criminal cases on affidavit.

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 (d) Issuing orders to regulate the internal working of parties.

14. Assume there are four families in a locality. If the incomes of these four families in a week
are ₹ 2,000, ₹ 5,000, ₹ 3,000 and ₹ 6,000, then the weekly average income of the locality
will be –
(a) ₹ 4,000 (b) ₹ 5,000 (c) ₹ 2,000 (d) ₹ 1,000

15. Which one of the following sources meets the needs of loan of rural households in India to the
maximum extent ?
(a) Commercial Bank (b) Cooperative Societies (c) Moneylender (d) Businessman

16. Look at the given image. The work done in the image comes under which one of the following
sectors?

(a) Organized sector

(b) Unorganized sector
(c) Primary sector
(d) Public sector

17. Choose the correct option regarding ‘Body Mass Index’ (BMI) from the following.
(a) Assessment of Blood Pressure
(b) Assessment of Blood Sugar Level
(c) Assessment of Body Composition
(d) Assessment of under Nutrition

18. Read the following statements about power sharing arrangement in Belgium and choose the
correct option.
I. Brussels has a separate govt. with equal representation.
II. Dutch & French speaking ministers are equal in Central Govt.
III. Community Govt. is elected by People belonging to one language.
IV. Series of majoritarian measures adopted in Belgium.
Options :
(a) I, II and IV (b) I, III and lV (c) II, III and IV (d) I, II and III

19. Refer to the following countries with federal political system and choose the correct option :
I. United States of America II. China III. Japan IV. India
Options:
(a) Only I and II are correct. (b) Only II and III are correct.
(c) Only III and IV are correct. (d) Only I and IV are correct.

20. Which one of the following is a fundamental principle of democracy ?

(a) Rule of single individual
(b) Rule with hereditary norms
(c) Rule of people with freedom
(d) Rule of military chiefs

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 SECTION – B
Questions 21 to 24 carry 2 marks each.
21. Analyse the role of Information and Communication Technology in making globalization
possible.

22. (a) Differentiate between Primitive Subsistence and Commercial Farming.

23. How is horizontal power sharing different from vertical? Explain.

24. (a) How did the Silk Route connect the world ? Explain with any two examples.
OR
(b) How did our foods facilitate cultural exchanges between distant countries? Explain with any
two examples.

SECTION – C
Questions 25 to 29 carry 3 marks each.
25. "People can have different developmental goals." Explain the statement with examples.

26. How is planning a widely accepted strategy for judicious use of resources? Explain with
examples.

27. Why should Indian farmers practice crop rotation ? Explain any three reasons.

28. Explain any three responsibilities carried out by the political parties in a democracy.

29. (a) Analyse the economic impacts of the Non-Cooperation Movement.

OR
(b) "In India, the growth of modern nationalism was intimately connected to the anti-colonial
movement." Analyse the statement.

SECTION – D
Questions 30 to 33 carry 5 marks each.
30. (a) "Promotion of energy conservation is important plank of sustainable energy." Explain the
statement with examples.
OR
(b) Energy is required for all kinds of activities." Explain this statement with examples.

31. (a) Democracy is a better form of govt. than dictatorship. Analyse.

OR
(b) Democracy accommodates social diversities. Analyse.

32. (a) Explain the rising importance of the tertiary sector in India.
OR
(b) Explain the difference between organized and unorganized sectors.

33. (a) "The 1830s were years of great economic hardship in Europe." Support the statement with
examples.
OR

(b) "Culture played an important role in creating the ideas of a nation in Europe during the early
nineteenth century." Explain the statement with examples.

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 SECTION – E (Case Study Based Questions)
Questions 34 to 36 carry 4 marks each.

34. Read the source given below and answer the question that follows:
Print and Censorship
The power of the printed word is most often seen in the way governments seek to regulate and
suppress print. The colonial government kept continuous track of all books and newspapers
published in India and passed numerous laws to control the press.
During the First World War, under the Defense of India Rules, 22 newspapers had to furnish
securities. Of these, 18 shut down rather than comply with government orders. The Sedition
Committee Report under Rowlatt in 1919 further strengthened controls that led to imposition of
penalties on various newspapers. At the outbreak of the Second World War, the Defense of
India Act was passed, allowing censoring of reports of war-related topics. All reports about the
Quit India Movement came under its purview. In August 1942, about 90 newspapers were
suppressed.

(a) What method did the colonial government employ to keep track of Indian newspapers ? (1)
(b) How did the colonial government's laws affect the press ? (1)
(c) Analyse the impact of 'Sedition Committee' on Newspapers. (2)
35. Read the given extract and answer following questions
Linguistic diversity of India
How many languages do we have in India ? The
answer depends on how one counts it. The latest
information that we have is from the Census of India
held in 2011. This census recorded more than 1300
distinct languages which people mentioned as their
mother tongues. These languages were grouped
together under some major languages. For example,
langu ages like Bhojpuri, Magadhi, Bund elkhandi,
Chhattisgarhi, Rajasthani and many others were
grouped together under 'Hindi'- Even after this
grouping, the Census found 121 major languages. Of
these, 22 languages are now included in the Eighth
Schedule of the Indian Constitution and are therefore
called 'Scheduled Languages'- Others are called
'Non-Scheduled Languages'. In terms of languages,
India is perhaps the most diverse country in the
world.

(a) How many languages were recorded as mother tongues in the 2011 Census of India ? (1)
(b) How were the languages grouped together in the Census report ? (1)
(c) How does the inclusion of languages in the Eighth Schedule of the Indian Constitution
contribute to linguistic diversity ? Explain. (2)

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36. Read the given extract and answer following questions
Sustainability of Development
Recent evidence suggests that the groundwater is under serious threat of overuse in many parts
of the country. About 300 districts have reported a water level decline of over 4 metres during
the past 20 years. Nearly one-third of the country is overusing their groundwater reserves. In
another 25 years, 60 per cent of the country would be doing the same if the present way of using
this resource continues. Groundwater overuse is particularly found in the agriculturally
prosperous regions of Punjab and Western U.P., hard rock plateau areas of central and south
India, some coastal areas and the rapidly growing urban settlements.
(a) Explain the meaning of Sustainability of Development. (1)
(b) Describe the serious threat caused by overuse of underground water. (1)
(c) Mention any two suggestions for the farmers to reduce the overuse of the groundwater in
agriculture. (2)
SECTION – F (Map Skill Questions) – 2 + 3 = 5
37. (a) Two places A and B have been marked on the given political outline map of India. Identify
them with the help of the following information and write their correct names on the lines drawn
near them (2 x 1 = 2)
(i) The place where Gandhiji broke Salt Law.
(ii) The place where the Indian National Congress Session was held in 1920.
(b) On the same political outline map of India, locate and label any three of the following with
suitable symbols (3 x 1 = 3)
(i) Salal — Dam
(ii) Kalpakkam — Nuclear Power Plant
(iii) Bengaluru — Software Technology Park
(iv) Mormugao — Major Sea Port

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 SAMPLE PAPER TEST 04 FOR BOARD EXAM 2025

SUBJECT: SOCIAL SCIENCE MAX. MARKS : 80

CLASS : X DURATION : 3 HRS
General Instruction:
1. Question paper comprises five Sections – A, B, C, D and E. There are 37 questions in the
question paper. All questions are compulsory.
2. Section A – From question 1 to 20 are MCQs of 1 mark each.
3. Section B – Question no. 21 to 24 are Very Short Answer Type Questions, carrying 2 marks
each. Answer to each question should not exceed 40 words.
4. Section C contains Q.25to Q.29 are Short Answer Type Questions, carrying 3 marks each.
Answer to each question should not exceed 60 words
5. Section D – Question no. 30 to 33 are long answer type questions, carrying 5 marks each.
Answer to each question should not exceed 120 words.
6. Section-E - Questions no from 34 to 36 are case based questions with three sub questions and
are of 4 marks each
7. Section F – Question no. 37 is map based, carrying 5 marks with two parts, 37a from History (2
marks) and 37b from Geography (3 marks).
8. There is no overall choice in the question paper. However, an internal choice has been provided
in few questions. Only one of the choices in such questions have to be attempted.
9. In addition to this, separate instructions are given with each section and question, wherever
necessary.
SECTION – A
Questions 1 to 20 carry 1 mark each.
1. Choose the correct option from the following regarding nineteenth century liberalism :
(a) Monarchy, social hierarchy and property must be maintained.
(b) The abolition of state-imposed restrictions on the movement of goods and capital.
(c) Criticised the glorification of reason and science.
(d) Not tolerating dissent and imposing censorship.

2. Arrange the following events in chronological order and choose the correct option
I. Establishment of Depressed Classes Association
II. Gandhi-Irwin Pact
III. Formation of the Indian Chambers of Commerce and Industry (FICCI)
IV. Second Round Table Conference in London
Options:
(a) I, II, III, IV (b) II, I, III, IV (c) III, I, II, IV (d) IV, I, II, III

3. Which one of the following countries has 'one-party system' ?

(a) United States of America (b) United Kingdom (c) India (d) China

4. Which one of the following is the majority community in Sri Lanka ?

(a) Sinhalas (b) Indian Tamils (c) Sri Lankan Tamils (d) Christians

5. Which one of the following pairs is correctly matched ?

List-I (Author) List-II (Book)
(a) Jyotiba Phule Amar Jiban
(b) Sudarshan Chakra Sachhi Kavitayen
(c) Rash Sundari Debi Gulamgiri
(d) Kashi Baba Chotte aur Bade Sawal

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6. Which one of the following languages is included in Eighth Schedule in Indian
Constitution ?
(a) Hariyanavi (b) Rajasthani (c) Garhwali (d) Odia

7. Choose the correct option to fill the blank.

Non Metallic Mineral : Mica
Energy Mineral : …………
(a) Natural Gas (b) Bauxite (c) Manganese (d) Platinum

8. In which one of the following states prominently prevalent for rainwater harvesting ?
(a) Tamil Nadu (b) Rajasthan (c) Bihar (d) Jharkhand

9. Read the following features of plantation agriculture and choose the correct option :
I. A single crop is grown on a large area.
II. It is capital intensive farming.
III. It is practised in areas of high population pressure on land.
IV. Food grain crops are the major crops of this type of farming.
Options:
(a) Only I and II are correct. (b) Only II and III are correct.
(c) Only III and IV are correct. (d) Only I and IV are correct.

10. Read the following statements and choose the correct term mentioned in the Indian Constitution
from the given options :
● There is no official religion for the Indian State.
● There is freedom to profess, practise and propagate any religion in India.
Options :
(a) Republic (b) Sovereign (c) Socialist (d) Secular

11. Which one of the following pairs is correctly matched ?

(Subject List in the Indian Constitution) (Subject)
(a) Union List Subjects Communication
(b) State List Subjects Education
(c) Concurrent List Subjects Adoption
(d) Residuary Subjects Marriages

12. Vertical division of power is :

(a) Power is shared among different organs of government.
(b) Power is shared among different social groups.
(c) Power is shared among different pressure groups.
(d) Power is shared among different levels of governments.
13. Two statements are given below. They are Assertion (A) and Reason (R).
Read both the statements and choose the correct option.
Assertion (A): ‘The Act of Union 1707’ between England and Scotland resulted in the
formation of ‘United Kingdom of Great Britain’.
Reason (R): England wanted to impose its influence on Scotland.
Options :
(a) Both (A) and (R) are true and (R) is the correct explaination of (A).
(b) Both (A) and (R) are true but (R) is not the correct explaination of (A).
(c) (A) is true but (R) is false.
(d) (A) is false but (R) is true.
14. Choose the correct option to fill the blank.
Literacy Rate measures the proportion of literate population in the _____ years and above age
group.
(a) 10 (b) 7 (c) 5 (d) 8

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15. Which one of the following is the main source of a
(a) Money obtained from Reserve Bank
(b) Money received from demand deposit
(c) Money obtained as interest on loan from the borrower
(d) Money received from the property of a defaulting borrower

16. Which one of the following pairs is correctly matched ?

(Sector of the Economy) (Example)
(a) Primary Sector Tailor
(b) Secondary Sector Fisherman
(c) Tertiary Sector Astronaut
(d) Primary Sector Courier

17. Study the given picture. The work being done in the picture comes under which of the following
sectors of the economy ?

(a) Primary (b) Secondary (c) Tertiary (d) Quaternary

18. Match the following aspects of globalization with their descriptions and choose the correct
option.
List-I (Global Aspect) List-II (Description)
I. Technological Advancement a. Interaction of ideas, values and traditions
II. Liberalization of Trade b. Companies operating in many countries
III. Cultural Exchange c. Innovation in manufacturing, communication
and information
IV. Multinational Corporations d. The removal of restriction on trade
Options :
I II III IV
(a) a b c d
(b) c d a b
(c) d c b a
(d) b a d c

19. Choose the correct option to fill in the blank.

World Trade Organisation was started at the initiative of the ________ countries.
(a) Developed (b) Developing (c) Non-aligned (d) Communist

20. Which of the following is the primary purpose of loan activities offered by banks ?
(a) To compete with other financial institutions
(b) To generate profits for the primary sector only
(c) To increase income of MNCs
(d) To support economic growth

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 SECTION – B
Questions 21 to 24 carry 2 marks each.
21. Why are constitutional provisions necessary for the success of federalism? Explain.

22. How can a nation achieve a balance between economic growth and environment sustainability?
Explain by giving any two arguments.

23. “Conservative regimes set up in Europe in 1815 were autocratic.” Support the statement by
giving any two arguments.

24. “In sedimentary rocks a number of minerals occur in beds or layers.” Support the statement with
example.
OR
(b) Differentiate between Rabi and Kharif cropping seasons.

SECTION – C
Questions 25 to 29 carry 3 marks each.
25. Explain any three challenges before Indian political parties in the present time.

26. Examine the significance of credit in economic development of the country.

27. 'Tertiary sector has a pivotal role in the economy of the country." Support your answer with
day-to-day examples.

28. (a) How was the 'Silk Route' an example of vibrant pre-modern trade ? Explain.
OR
(b) How did food promote long-distance cultural contacts in the pre-modern world ? Explain.

29. 'India's prosperity lies in expanding and diversifying its manufacturing industries." Justify the
statement.

SECTION – D
Questions 30 to 33 carry 5 marks each.
30. (a) Explain the significance of industries in the Indian economy.
OR
(b) How are industries responsible for air pollution ? Suggest any three measures to control it.

31. (a) How is democracy better than any other form of government ? Explain with examples.
OR
(b) How does democracy accommodate social diversities ? Explain with examples.

32. (a) 'Rapid improvement in technology has been one major factor that has stimulated the
globalisation process." Explain the statement with examples.
OR
(b) 'Foreign trade and foreign investment policies are the aspects of liberalisation and
globalisation." Explain the statement with examples.

33. (a) "The Gandhian idea of Satyagraha, emphasized the power of truth and struggle against
injustice." Explain the statement with examples.
OR
(b) How did people belonging to different communities, regions and language groups develop a
sense of collective belonging in the late — nineteenth century India ? Explain with examples.

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 SECTION – E (Case Study Based Questions)
Questions 34 to 36 carry 4 marks each.
34. Read the given extract and answer following questions.
Project Tiger
Tiger is one of the key wildlife species in the faunal web. In 1973, the authorities realized that
the tiger population had dwindled to 1,827 from an estimated 55,000 at the turn of the 20th
century. The major threats to tiger population are numerous, such as poaching for trade,
shrinking habitat, depletion of prey base species, growing human population, etc. The trade of
tiger skins and the use of their bones in traditional medicines, especially in the Asian countries
left the tiger population on the verge of extinction. Since India and Nepal provide habitat to
about two-thirds of the surviving tiger population in the world, these two nations become prime
targets for poaching and illegal trading.
"Project Tiger", one of the well publicised wildlife campaigns in the world, was launched in
1973. Tiger conservation has been viewed not only as an effort to save an endangered species
but with equal importance as a means of preserving biotypes of sizeable magnitude. Corbett
National Park in Uttarakhand, Sunderbans National Park in West Bengal, Bandhavgarh National
Park in Madhya Pradesh, Sariska Wildlife Sanctuary in Rajasthan, Manas Tiger Reserve in
Assam and Periyar Tiger Reserve in Kerala are some examples of the tiger reserves in India.
(a) Why was Project Tiger' considered a significant step for Tiger Conservation ? (1)
(b) What role did India play in the global tiger population ? (1)
(c) Mention any two major threats to the wildlife species. (2)

35. Read the source given below and answer the question that follows:
Jikji
The Jikji of Korea is among the world's oldest existing books printed with movable metal type.
It contains the essential features of Zen Buddhism. About 150 monks of India, China and Korea
are mentioned in the book. It was printed in late 14th century. While the first volume of the
book is unavailable, the second one is available in the National Library of France. This work
marked an important technical change in the print culture. That is why it was inscribed on the
UNESCO Memory of the World Register in 2001.
(a) Mention the significance of the Jikji in the history of printing (1)
(b) Why was the Jikji inscribed on the UNESCO Memory of the World Register in 2001 ? (1)
(c) How does the Jikji contribute to the understanding of Zen Buddhism ? (2)
36. Read the given extract and answer following questions.
Social and Religious Diversity
The Census of India records the religion of each and every Indian after every ten years. The
person who fills the Census form visits every household and records the religion of each
member of that household exactly the way each person describes it. If someone says she has 'no
religion' or that he is an 'atheist', this is exactly how it is recorded. Thus we have reliable
information on the proportion of different religious communities in the country and how it has
changed over the years. The record shows the population proportion of six major religious
communities in the country. Since Independence, the total population of each community has
increased substantially.
(a) At what interval is census conducted in India ? (1)
(b) Why are Indian census data considered reliable ? (1)
(c) How is the census an important tool to understand the social diversity in India ? (2)

SECTION – F (Map Skill Questions) – 2 + 3 = 5

37. (a) Two places A and B have been marked on the given political outline map of India. Identify
them with the help of the following information and write their correct names on the lines drawn
near them :
A. The place where Gandhiji organized Satyagraha to help the peasants. (1)
B. The place where the session of the Indian National Congress was held in 1927. (1)

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 (b) On the same political outline map of India, locate and label any three of the following with
suitable symbols : (3 x 1 = 3)
(i) Leading Coffee-producing State
(ii) Durg : Major iron-ore mines
(iii) Kochi : Major sea port
(iv) Rajiv Gandhi International Airport

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 SAMPLE PAPER TEST 05 FOR BOARD EXAM 2024

SUBJECT: SOCIAL SCIENCE MAX. MARKS : 80

CLASS : X DURATION : 3 HRS
General Instruction:
1. Question paper comprises five Sections – A, B, C, D and E. There are 37 questions in the
question paper. All questions are compulsory.
2. Section A – From question 1 to 20 are MCQs of 1 mark each.
3. Section B – Question no. 21 to 24 are Very Short Answer Type Questions, carrying 2 marks
each. Answer to each question should not exceed 40 words.
4. Section C contains Q.25to Q.29 are Short Answer Type Questions, carrying 3 marks each.
Answer to each question should not exceed 60 words
5. Section D – Question no. 30 to 33 are long answer type questions, carrying 5 marks each.
Answer to each question should not exceed 120 words.
6. Section-E - Questions no from 34 to 36 are case based questions with three sub questions and
are of 4 marks each
7. Section F – Question no. 37 is map based, carrying 5 marks with two parts, 37a from History (2
marks) and 37b from Geography (3 marks).
8. There is no overall choice in the question paper. However, an internal choice has been provided
in few questions. Only one of the choices in such questions have to be attempted.
9. In addition to this, separate instructions are given with each section and question, wherever
necessary.
SECTION – A
Questions 1 to 20 carry 1 mark each.
1. Which of the following options best explains this cartoon?

(a) Problem of two party system (b) A car with two steering
(c) Problem of a coalition government (d) None of these

2. Identify the characteristics of Cavour among the following and choose the correct option:
(i) He was an Italian statesman.
(ii) He spoke French much better than Italian.
(iii) He was a tactful diplomat.
(iv) He belonged to a Royal family.
(a) Only (i) and (ii) are correct. (b) Only (i), (ii) and (iii) are correct.
(c) Only (ii), (iii) and (iv) are correct. (d) Only (i), (ii) and (iv) are correct.
3. There are two statements marked as Assertion (A) and Reason (R). Mark your answer as per the
codes provided below.
Assertion (A): When the power is taken away from the Central and the State governments and
given to local governments it is called decentralisation.
Reason (R): One-third seats are reserved for women in local government bodies.
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 (a) Both A and R are correct and R is the correct explanation of A.
(b) Both A and R are correct but R is not the correct explanation of A.
(c) A is correct but R is incorrect.
(d) A is incorrect but R is correct.
4. The democracy in France was destroyed by ________.
(a) Napolean Bonaparte (c) Giuseppe Garibaldi
(b) Giuseppe Mazzini (d) Otto von Bismarck

5. Match the column I with column II and select the correct option.
Column I Column II
(A) SAIL (i) Heavy Industries
(B) Ship building (ii) Bauxite
(C) Textile (iii) Public Sector
(D) Aluminium (iv) Agro Based
A B C D
(a) (iii) (i) (iv) (ii)
(b) (iii) (ii) (iv) (i)
(c) (iv) (ii) (iii) (i)
(d) (iii) (ii) (i) (iv)

6. What led to tensions between the Dutch-speaking and French-speaking communities?

(a) Both the communities demanded special powers.
(b) The minority French-speaking community was richer and more powerful than the majority
Dutch speaking community.
(c) The majority Dutch-speaking community was richer and more powerful than the minority
French speaking community.
(d) Both the communities were equal in socio-economic ladder and this was resented by the
French speaking community.

7. Which of the following authorities of India issues currency notes on behalf of the Central
Government?
(a) State Bank of India (b) Reserve Bank of India (c) Bank of Baroda (d) Punjab National Bank

8. The products received by exploiting natural resources come under which one of the following
sectors?
(a) Quaternary (b) Tertiary (c) Secondary (d) Primary

9. Why is it that while there has been a change in the share of three sectors in GDP, a similar shift
has not taken place in employment?
(a) It is because not enough jobs were created in the secondary and tertiary sectors.
(b) The secondary and tertiary sectors have to develop more.
(c) People in India are more attached to land and want to continue in agriculture.
(d) People are not interested in working in the secondary and tertiary sectors.

10. Fill in the blanks choosing the correct options given below:
While taking loan, a borrower looks for easy terms of credit. This means (i) interest rate, (ii)
condition for repayment, (iii) collateral and documentation requirements.
(a) (i)–low, (ii)–tough, (iii)–more (b) (i)–high, (ii)–easy, (iii)–less
(c) (i)–low, (ii)–easy, (iii)–less (d) (i)–low, (ii)–tough, (iii)–less
11. Which of the following is true about globalisation?
(a) Globalisation is purely an economic phenomenon.
(b) Globalisation emerged only because of the availability of improved communications.
(c) Globalisation is the same thing as westernisation.
(d) Globalisation is a multi-dimensional concept.
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12. This soil ranges from red to brown in colour and is generally sandy in texture and saline in
nature. Identify the soil.
(a) Laterite soil (c) Black soil (b) Arid soil (d) Alluvial soil

13. Two statements are given below as Assertion (A) and Reason (R). Read the statements and
choose the most appropriate option:
Assertion (A): Transparency means openness, communication and accountability of the
government.
Reason (R): Transparency is considered missing in democratic government.
(a) Both A and R are true and R is the correct explanation of A.
(b) Both A and R are true but R is not the correct explanation of A.
(c) A is true but R is false.
(d) A is false but R is true.

14. Which among the following countries is/are examples of multi-party system?
(i) India (ii) China (iii) United States of America (iv) Cuba (v) The United Kingdom
(a) (i) only (b) (i), (ii) and (v) only (c) (i), (ii), (iii) and (iv) only (d) (ii), (iii), (iv) and (v) only

15. Read the given statements and choose the correct option.
Statement I: The name “silk routes” points to the importance of East-bound Chinese silk
cargoes.
Statement II: Until the eighteenth century, China and India were among the world’s richest
countries.
(a) Both statements I and II are true.
(b) Both statements I and II are false.
(c) Statement I is true but statement II is false.
(d) Statement II is true but statement I is false.

16. Identify the sector to which A and B belong and choose the correct option.
Place of work Nature of No. of working
employment
Office, clinic in market places with A 15
formal license
Working in small workshops usually B 50
not registered with the government
(a) A - Unorganised, B - Organised (b) A - Service sector, B - Secondary sector
(c) A - Organised, B - Unorganised (d) A - Secondary, B - Primary sector

17. Read the following data and information carefully and select the most appropriate answer from
the given options:
Table for Comparison of three countries
Countries Monthly income of citizens in 2007 (in Rupees)
I II III IV V
Country A 9500 10500 9800 10000 10200
Country B 500 500 500 500 48000
Country C 5000 1000 15000 4000 25000
Rita is an employee of a multinational company who gets transferred to different countries after
every three years of service. She has been given an opportunity to choose any one out of the
three countries mentioned in the table above as her next job location. She calculates average
income of all these countries as per the given data and chooses to be transferred to Country A.
Identify the reason for which Rita has chosen country A.
(a) Most of its citizens are rich and stable
(b) It has most equitable distribution of income
(c) National income of its citizens is higher
(d) Average income of its citizens is lower

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18. The first printing press came to India with which one of the following?
(a) Portuguese Missionaries (b) Catholic Priests
(c) Dutch protestants (d) East India Company

19. In which of the following states, Tungabhadra Dam is located?

(a) Tamil Nadu (b) Kerala (c) Andhra Pradesh (d) Karnataka

20. The Kheda Satyagraha was launched by Gandhiji to support_______.

(a) The mill workers (b) The peasants (c) The women workers (d) Rowlatt Act

SECTION – B
Questions 21 to 24 carry 2 marks each.
21. Why did Mahatma Gandhi decide to call off the Civil Disobedience Movement in 1931?
OR
Mention any two causes that led to the Civil Disobedience Movement.

22. What are leguminous crops?

23. Why did the Indian Government remove barriers to a large extent on foreign trade and foreign
investment after independence?

24. In which list of the Indian constitution does education come? Why?

SECTION – C
Questions 25 to 29 carry 3 marks each.
25. When is democracy considered successful? Explain.

26. Why did Gandhiji decide to launch a nationwide Satyagraha against the proposed Rowlatt Act
in 1919? Explain any three reasons.

27. Disguised unemployment does not help in productivity of a country, why? Explain with the help
of an example.
OR
What constitutes the unorganised sector in urban areas? Why do workers in this sector need
protection?

28. Suggest any three measures to enhance the participation of woman in politics.

29. Describe any three characteristics of the Durg-Bastar-Chandrapur Iron-ore belt in India.

SECTION – D
Questions 30 to 33 carry 5 marks each.
30. Describe the various strategies adopted by printers and publishers in the 19th century to sell
their products.
OR
“The Bengal Gazette was a commercial paper open to all, but influenced by none.” Justify the
claim of James Augustus Hickey.

31. Why do we need to conserve our forests and wildlife? What kind of steps have the government
taken to protect forest and wildlife resources?
OR
Explain Joint Forest Management?

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32. What is a Gram Sabha? Describe any four functions of a Gram Sabha.
OR
What is the meaning of decentralisation? Explain any four provisions that have been made
towards decentralisation in India after the Constitutional Amendment in 1992.

33. Is per capita income the true measure of development? Elaborate.

OR
What is Human Development Index? Which organisation measures the HDI? Explain the three
major indicators of the HDI.

SECTION – E (Case Study Based Questions)

Questions 34 to 36 carry 4 marks each.
34. Case Study – 1
Read the source given below and answer the question that follows:
The availability of resources is a necessary condition for the development of any region, but
mere availability of resources in the absence of corresponding changes in technology and
institutions may hinder development. There are many regions in our country that are rich in
resources but these are included in economically backward regions. On the contrary there are
some regions which have a poor resource base but they are economically developed. The
history of colonization reveals that rich resources in colonies were the main attractions for the
foreign invaders. It was primarily the higher level of technological development of the
colonizing countries that helped them to exploit resources of other regions and establish their
supremacy over the colonies. Therefore, resources can contribute to development only when
they are accompanied by appropriate technological development and institutional changes. India
has experienced all this in different phases of colonization. Therefore, in India, development, in
general, and resource development in particular does not only involve the availability of
resources, but also the technology, quality of human resources and the historical experiences of
the people.
(i) What is a necessary condition for the development of any region?
(ii) What helped the colonial countries to exploit resources of their colonies?
(iii) Why are some resource rich regions included in economically backward regions?

35. Case Study – 2

Read the given extract and answer following questions.
The Independence Day Pledge, 26 January, 1930 `We believe that it is the inalienable right of
the Indian people, as of any other people, to have freedom and to enjoy the fruits of their toil
and have the necessities of life, so that they may have full opportunities of growth. We believe
also that if any government deprives a people of these rights and oppresses them, the people
have a further right to alter it or to abolish it. The British Government in India has not only
deprived the Indian people of their freedom but has based itself on the exploitation of the
masses, and has ruined India economically, politically, culturally and spiritually. We believe,
therefore, that India must sever the British connection and attain Puma Swaraj or Complete
Independence:
(i) Who was the president of the Lahore Session of Congress held in December 1929? (1)
(ii) Why was Puma Swaraj considered essential by the people of India? (1)
(iii) Explain the significance of the Lahore Session of Congress (1929). (2)

36. Case Study – 3

Read the source given below and answer the question that follows:
Source A - Mode of Occurrence of Minerals
Minerals are usually found in "ores". The term ore is used to describe an accumulation of any
mineral mixed with other elements. The mineral content of the ore must be in sufficient
concentration to make its extraction commercially viable.
Source B - Conventional Source of Energy
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 In India, coal is the most abundantly available fossil fuel. It provides a substantial part of the
nation's energy needs. It is used for power generation, to supply energy to industry as well as for
domestic needs. India is highly dependent on coal for meeting its commercial energy
requirements
Source C - Non-Conventional Source of Energy
The growing consumption of energy has resulted in the country becoming increasingly
dependent on fossil fuels such as coal, oil and gas. Increasing use of fossil fuels also causes
serious environmental problems. Hence there is a pressing need to use renewable energy sources
like solar energy, wind, tide biomass and energy from waste material.
(i) Where are mineral usually found? (1)
(ii) What is the most abundantly available fossil fuel in India? (1)
(iii) Describe any two non-conventional sources of energy. (2)

SECTION – F (Map Skill Questions) – 2 + 3 = 5

37. (a) Two features ‘A’ and ‘B’ are marked on the given political map of India. Identify these
features with the help of the following information and write their correct names on the lines
marked on the map:
(I) Name the place where the Indigo farmers organized Satyagraha.
(II) Name the place where Gandhiji violated Salt Law.
(b) Identify any 3 iron ore mines in the same political map of India mark as (i), (ii), (iii), (iv)
and (v) and write their correct names.

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