KVS(DR)/2024/NA

KENDRIYA VIDYALAYA SANGATHAN, DELHI REGION

CLASS X PRE BOARD I SESSION 2024-25
MATHEMATICS STANDARD (Code No.041)
MAX. MARKS : 80 TIME : 3:00 hours

General Instructions:
1. This Question Paper has 5 Sections A, B, C, D and E.
2. Section A has 20 MCQs carrying 1 mark each
3. Section B has 5 questions carrying 2 marks each.
4. Section C has 6 questions carrying 3 marks each.
5. Section D has 4 questions carrying 5 marks each.
6. Section E has 3 case based integrated units of assessment (4 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 Questions of 5 marks, 2
Questions of 3 marks and 2 Questions of 2 marks has been provided. An internal choice has
been provided in the 2 marks questions of Section E
8. Draw neat figures wherever required. Take π =22/7 wherever required if not stated.
SECTION A

Section A consists of 20 questions of 1 mark each.

The greatest number which divides both 30 and 80, leaving remainder 2 and 3
Q.1 respectively, is
1
(a) 10 (b) 7 (c) 11 (d) 14
1 1
If α, β are the zeroes of the polynomial p(x)= 4x2 -3x-7, then α + β is equal to
Q.2
(a)
−7
(b)
7 3
(c) 7 (d)
−3 1
3 3 7
If the lines given by 3x + 2ky = 2 and 2x + 5y + 1 = 0 are parallel, then the value of k is
Q.3 −5 2 15 3
(a) 4 (b) 5 (c) 4 (d) 2 1
Which of the following equations has two distinct real roots?
Q.4 9 1
(a) 2x2 – 3√2 x + 4 =0 (b) x2 + x-5= 0 (c) x2 +3 x +2√2 = 0 (d) 5x2 – 3x + 1 = 0
In a two digit natural number, tens digit is the square of units digit and the sum of its 1
Q.5 digits is 12, then the number is
(a) 42 (b) 39 (c) 93 (d)24
Two A.P.s have the same common difference. The first term of one of these is -1 and that
Q.6 of the other is -8. Then the difference between their 4th terms is 1
(a) 1 (b) -9 (c) 7 (d)-8

In ΔABC, DE‖AC, AE = a units, EC = b units DE = x units BC=y units, then 1

Q.7 𝑎+𝑏 𝑎𝑥 𝑎𝑦 𝑥 𝑎
(a) x = ay (b) y = a+b (c) x = a+b (d) 𝑦 = b

In ΔLMN, ∠L = 50° and ∠N = 60°, If ΔLMN ~ ΔPQR, then find ∠Q

Q.8
(a) 40° (b) 50° (c) 70° (d)120° 1
The common difference of an A.P. whose nth term is given by an= 3n+7, is
Q.9
(a) 7 (b) 3 (c) 3n (d)1 1
The ratio of the 11th term to 17th term of an A.P. is 3:4. The ratio of the sum of the first 5
Q.10 terms to that of first 21 terms of the A.P. will be 1
(a) 5 : 21 (b) 25 : 189 (c) 45 : 121 (d) 25 :198
Q.11 If cos θ + sin θ = √2 cos θ, then cos θ – sin θ is equal to
1
(a) 2 𝑠𝑖𝑛θ (b) √2𝑠𝑖𝑛θ (c) 2𝑠𝑖𝑛θ (d)
1
𝑠𝑖𝑛θ 1
√ 2

1 1
Q.12 Given that sin α = 2 and cos β = 2, then the value of (β – α) is
1
(a) 0° (b) 30° (c) 60° (d) 90°

In the given figure, PA and PB are tangents to the circle with

Q.13 centre O. If ∠APB = 50°, then ∠OAB will be – 1
(a) 100° (b) 30° (c) 90° (d) 25°

If the perimeter and the area of a circle are numerically equal, then the radius of the
Q.14 circle is 1
(a) 2 units (b) π units (c) r units (d) 6 units
Anishka melted 11 chocolate cubes in a cylindrical
cup as shown in the figure. If the length of the side of
each cube is k cm and the radius of the cup is r cm,
which of these represents the height of the melted
Q.15 22 1
chocolate in the cup? (Take π = 7 )
7𝑘 3 7𝑘 3 7𝑘 2 7𝑘 2
(a) cm (b)2𝑟 2 cm (c) cm (d) 2𝑟 2
4𝑟 4𝑟
cm
For the following distribution :
Marks Below 10 Below 20 Below 30 Below 40 Below 50 Below 60
No. of 3 12 27 57 75 80
Q.16 1
students
The modal class is
(a) 10-20 (b)20-30 (c) 30-40 (d) 50-60
Two coins are tossed. What is the probability of getting at most one head
Q.17 3 1 1 3 1
(a)4 (b) 4 (c) 2 (d)8
A dice is rolled twice. The probability that 5 will not come up either time is
Q.18 11 1 13 25 1
(a)36 (b) 3 (c) 36 (d)36

In questions 19 and 20 choose the correct options given below :

(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.
Assertion (A) : If the volume of two spheres are in the ratio 27: 8 then their surface
areas are in the ratio 3:2
Q.19 1
4
Reason (R) : Volume of the sphere = 3π𝑟 3 and its surface area is equal to 4π𝑟 2 .
Assertion (A) : If the value of mode and mean is 60 and 66 respectively, then the value
of median is 64.
Q.20 1
Reason (R) : Mode = 3median + 2 mode
 SECTION B

Section B consists of 5 questions of 2 mark each.

Explain why 7 × 6 × 5 × 4 × 3 × 2 × 1 + 5 is a composite number.
21
2

A street light bulb is fixed on a pole 6 m above the

level of the
street. If a woman of height 1.5m casts a shadow of
3m, what
is the length of the shadow of the pole?

22 2
OR

In the given figure, ∠ M= ∠ Q = 460. Find the value of x

in terms of a,b and c.

5𝑐𝑜𝑠 2600 +4𝑠𝑒𝑐 2 300 −𝑡𝑎𝑛 2 450

Evaluate 𝑠𝑖𝑛 2 300 +𝑐𝑜𝑠 2 300
23 OR 2
If sin A= cos A, find the value of 2tan2A+ sin2 A - 1

A circle is touching the side BC of a Δ ABC at the point P and

24 touching AB and AC produced at points Q and R respectively.
1 2
Prove that AQ = 2(Perimeter of Δ ABC)

A number X is selected at random from the numbers 1, 2, 3 and 4. Another number Y is

25 selected at random from the numbers 1, 4, 9 and 6. Find the probability that the product 2
of X and Y is less than 16.
SECTION C

Section C consists of 6 questions of 3 mark each.

26 Prove that 5 − √3 is irrational.

3
11 2
Find the zeroes of the quadratic polynomial 7y2 – y
- 3 and verify the relationship
27 3
3
between the zeroes and the coefficients.
At present Asha’s age (in years) is 2 more than the square of her daughter Nisha’s age.
When Nisha grows to her mother’s present age, Asha’s age would be one year less than
10 times the present age of Nisha. Find the present ages of both Asha and Nisha
28 OR 3
A train travels at a certain average speed for a distance of 63 km and then travels a
distance of 72 km at an average speed of 6 km/h more than its original speed. If it takes
3 hours to complete the total journey, what is its original average speed?
29 Prove that
sinθ−cosθ+1
= secθ + tanθ 3
sinθ+cosθ−1

30 Equal circles with centers O and O' touch each other

at X. OO' produced to meet a circle with Centre O', at
A. AC is a tangent to the circle whose Centre is O. O' D 3
𝐷𝑂′
is perpendicular to AC. Find the value of 𝐶𝑂

A round table cover has six equal designs as

shown in Fig. If the radius of the cover is
28 cm, find the cost of making the designs at the
rate of ₹ 0.35 per cm2. (Use √3 = 1.7)

OR
31 3

In the given figure, two concentric circles with

centre O have radii 21 cm and 42 cm. If ∠AOB = 600,
find the area of the shaded region. ( Use π = 22/7 )

SECTION D

Section D consists of 4 questions of 5 mark each.

Solve the following pair of equations, graphically:
2x + y = 6 ; 2x – y + 2 = 0
Find the ratio of the areas of the two triangles formed by the lines representing these
equations with the x-axis and the lines with the y-axis.
5
OR
32
Ankita travels 14 km to her home partly by rickshaw and partly by bus. She takes half an
hour if she travels 2 km by rickshaw, and the remaining distance by bus. On the other
hand, if she travels 4 km by rickshaw and the remaining distance by bus, she takes 9
minutes longer. Find the speed of the rickshaw and of the bus.

a) Prove that, if a line is drawn parallel to one side of a

triangle to intersect the other two sides in distinct
points, the other two sides are divided in the same
33 5
ratio. Using the above result, do the following:
b) In the given Fig. DE || BC and BD = CE. Prove that
ΔABC is an isosceles triangle.
 The mean of the following frequency distribution is 62.8 and the sum of all the
frequencies is 50. Compute the missing frequencies f1 and f2.
Classes 0-20 20-40 40-60 60-80 80-100 100-120 5
34 Frequenc 5 f1 10 f2 7 8
y

The angle of elevation of a cloud from a point 60 m above the surface of the water of a
lake
is 30° and the angle of depression of its reflection in water of lake is 600 find the height
of the cloud from the surface of water.

OR

A 1.2 m tall girl spots a balloon moving with the wind

5
in a
35 horizontal line at a height of 88.2 m from the ground.
The angle of elevation of the balloon from the eyes of
the girl
at any instant is 60°. After some time, the angle of elevation
reduces to 30°. Find the distance travelled by the balloon
during the interval

SECTION E

Section E consists of 3 questions of 4 mark each.

In a potato race, a bucket is placed at the starting point, which is 5 m from the first
potato, and the other potatoes are placed 3 m apart in a straight line. There are ten
potatoes in the line. A competitor starts from the bucket, picks up the nearest potato,
runs back with it, drops it in the bucket, runs back to pick up the next potato, runs to the
bucket to drop it in, and she continues in the same way until all the potatoes are in the
bucket.

(1+1
36
+2)

(i)Calculate the total distance for first potato.

(ii)Calculate the total distance for second potato.
(iii) What is the total distance the competitor has to run?
OR
What is the total distance the competitor has to run if number of potatoes is to be done 8
only.
 A garden is in the shape of rectangle. Gardener grew
sapling of Ashoka tree on the boundary of garden at
the distance of 1 meter from each other. He want to
decorate the garden with rose plants. He choose
triangular region inside the park to grow rose plants.
On the above situation, gardener took help from the
students of class 10th. They made a chart for it which
looks as the given figure.
(1+1
37 (i)If A is taken as origin, What are the coordinates of
+2)
the vertices of triangle PQR ?
(ii) If A is taken as origin, what are the co-ordinates of
mid-point of PQ?
(iii) If C is taken as origin, what are the co-ordinates
of point P?
OR
If D is taken as origin, what are the co-ordinates of
point Q?
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 up to a height of 8 m and
conical above it. The diameter of the base is 28 m and
(1+1
38 total height of tent is 18.5 m. Based on the above
+2)
information, answer the following questions:
(1) Find slant height of the conical part.
(2) Determine the floor area of the tent.
(3) (a) Find area of the cloth used for making tent.
OR
(b) Find total volume of air inside an empty tent.