GYAN ASHRAM SCHOOL

TERM -1 PAPER (2024-2025)

Class 10 - Mathematics
Time Allowed: 3 hours SET-A Maximum Marks: 80
General Instructions:
1. This Question paper contains - four sections A, B, C, D. Each section is compulsory.
However, there are internal choices in some questions.
2. Section A has 18 MCQ’s .
3. Section B has 2 Assertion and Reasoning -type questions of 1 marks each.
4. Section C has 5 Very short type questions , 6 Short Answer (SA)-type questions and 4 Long type
Questions of 2 ,3
marks and 5 marks each.
5. Section D has 3 source based/case based/passage based/integrated units of assessment (4
marks each) with sub parts.
Section A
1. The least positive integer divisible by 20 and 24 is [1]

a) 480 b) 240

c) 360 d) 120

2. HCF of two numbers is 113, their LCM is 56952. If one number is 904, the second number is [1]

a) 7791 b) 7911

c) 7719 d) 7119

2 α2 β2 [1]
3. If α and β are the zeroes of the polynomial x - 6x + 8, then the value of β
+ α
is

a) 8 b) 6

c) 12 d) 9

2
4. If one of the zeroes of the quadratic polynomial (k – 1) x + kx + 1 is –3, then the value of k is [1]

a) −2 b) −4
3 3

c) 4 d) 2
3 3

5. The area of the triangle formed by y = x, x = 6 and y = 0 is [1]

a) 18 sq. units b) 72 sq. units

c) 36 sq. units d) 9 sq. units

6. The value of k for which the pair of equations kx = y + 2 and 6x = 2y + 3 has infinitely many solutions, [1]
 a) is k = 4 b) is k = -3

c) is k = 3 d) does not exist

7. If the common difference of an A.P. is 5, then the value of a20 - a13 is [1]

a) 35 b) 25

c) 40 d) 30

8. How many three-digit numbers are divisible by 9? [1]

a) 100 b) 90

c) 96 d) 86

– [1]
9. If three points (0,0), (3, √3) and (3, λ ) form an equilateral triangle, then λ =

a) -4 b) None of these

c) -3 d) 2

10. The midpoint of segment AB is P(0,4). If the coordinates of B are (-2,3),then the coordinates of A are [1]

a) (-2 -5) b) (2, 9)

c) (-2, 11) d) (2, 5)

11.
√3 o o [1]
If cos A = 2
, 0 < A < 90 , then A is equal to

o
a) 30 b) 1
o
c) √3 d) 60
2

12. Find the value of sin230o + 4cot245o - sec260o [1]

a) 0 b) 1

c) 1 d) 4
4

13. If 7 tan θ = 4 then

(7 sin θ−3 cos θ)
=? [1]
(7 sin θ+3 cos θ)

a) 3 b) 1
7 7

c) 5 d) 5
14 7

14. The mean and median of a statistical data are 21 and 23 respectively. The mode of the data is: [1]

a) 27 b) 23

c) 22 d) 17
15. The wickets taken by a bowler in 10 cricket matches are 2, 6, 4, 5, 0, 2, 1, 3, 2, 3. The median of the data [1]
is

a) 2.5 b) 1

c) 2 d) 3

16. Two dice are rolled simultaneously. The probability that they get different faces on both dices is , [1]

a) 5 b) 1
6 6

c) 1 d) 2
3 3

17. Two dice are thrown simultaneously. The probability that the product of the numbers appearing on the [1]
dice is 7 is

a) 7 b) 2

c) 0 d) 1

18. A tower subtends an angle of 30° at a point on the same level as its foot. At a second point h metre [1]
above the first, the depression of the foot of the tower is 60°. The height of the tower is

a) h
m b) h
m
2 3

c) √–3h m d) h
m
√3

Section B
2
19. Assertion (A): If the sum of the zeroes of the quadratic polynomial x - 2kx + 8 are is 2 then value of k is [1]
1.
Reason (R): Sum of zeroes of a quadratic polynomial ax2 + bx + c is - ab

a) Both A and R are true and R is the b) Both A and R are true but R is not the
correct explanation of A. correct explanation of A.

c) A is true but R is false. d) A is false but R is true.

20. Assertion (A): If kx - y - 2 = 0 and 6x - 2y - 3 = 0 are inconsistent, then k = 3 [1]

a1 b1 c1
Reason (R): a1x + b1y + c1 = 0 and a2x + b2y + c2 = 0 are inconsistent if a2 = b2
≠ c2

a) Both A and R are true and R is the b) Both A and R are true but R is not the
correct explanation of A. correct explanation of A.

c) A is true but R is false. d) A is false but R is true.

Section C
21. Find the largest number which on dividing 1251, 9377 and 15628 leaves remainders 1, 2 and 3 [2]
respectively.
22. If in an A.P., the sum of first m terms is n and the sum of its first n terms is m, then prove that the sum of [2]
its first (m + n) terms is –(m + n).

23. Find the value(s) of y for which the distance between the points A(3, -1) and B(11, y) is 10 units. [2]

24. Prove the trigonometric identity: (cosecθ − cot θ)2 = 1−cos θ [2]
1+cos θ

25. A bag contains 5 red balls and some blue balls. If the probability of drawing a blue ball is double that of [2]
a red ball, determine the number of blue balls in the bag.

2 – [3]
26. Find the zeroes of the polynomial 4x + 5√2x - 3 by factorisation method and verify the relationship
between the zeroes and coefficient of the polynomial.

27. Reena has pens and pencils which together are 40 in number. If she has 5 more pencils and 5 less [3]
pens, then number of pencils would become 4 times the number of pens. Find the original number of
pens and pencils.

st th th
28. Find the 31 term of an AP whose 11 term is 38 and the 16 term is 73. [3]

29. Calculate the mean of the following data: [3]

Class 4–7 8 – 11 12 – 15 16 – 19

Frequency 5 4 9 10

30. i. Two dice, one blue and one grey, are thrown at the same time. Complete the following table: [3]
Event: Sum on 2 dice 2 3 4 5 6 7 8 9 10 11 12
1 5 1
Probability 36 36 36

ii. A student argues that there are 11 possible outcomes 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 and 12. Therefore,
1
each of them has a probability 11
. Do you agree with this argument? Justify your answer.

31. A peacock is sitting on the top of a tree.It observes a serpent on the ground making an angle of [3]
depression of 30 . The peacock catches the serpent in 12 s with the speed of 300 m/min. What is the
o

height of the tree?

– [5]
32. Show that (4 + 3√2) is irrational number.

33. Draw the graphs of the following equations: [5]

2x - y - 2 = 0
4x + 3y - 24 = 0
y+4=0
Obtain the vertices of the triangle so obtained. Also, determine its area.

34. Prove the trigonometric identity: [5]

2sec2 θ− sec4 θ − 2 cos ec2 θ + cos ec4 θ = cot4 θ
− tan4 θ

35. A survey regarding the heights (in cm) of 50 girls of X of a school was conducted and the following data [5]
was obtained:

Height (in cm) 120 - 130 130 - 140 140 - 150 150 - 160 160 - 170 Total
 Number of girls 2 8 12 20 8 50

Find the mean and mode of the above data.

Section D
36. Read the following text carefully and answer the questions that follow: [4]
The students of a school decided to beautify the school on an annual day by fixing colourful flags on the
straight passage of the school. They have 27 flags to be fixed at intervals of every 2 metre. The flags are
stored at the position of the middlemost flag. Ruchi was given the responsibility of placing the flags.
Ruchi kept her books where the flags were stored. She could carry only one flag at a time.

i. How much distance did she cover in pacing 6 flags on either side of center point? (1)
ii. Represent above information in Arithmetic progression. (1)
iii. How much distance did she cover in completing this job and returning to collect her books? (2)
OR
What is the maximum distance she travelled carrying a flag? (2)

37. Read the following text carefully and answer the questions that follow: [4]
In order to facilitate smooth passage of the parade, movement of traffic on certain roads leading to the
route of the Parade and Tableaux ah rays restricted. To avoid traffic on the road Delhi Police decided to
construct a rectangular route plan, as shown in the figure.

i. If Q is the mid point of BC, then what are the coordinates of Q? (1)
ii. What is the length of the sides of quadrilateral PQRS? (2)
iii. What is the length of route PQRS? (2)
OR
What is the length of route ABCD? (2)

38. Tower Bridge is a Grade I listed combined bascule and suspension bridge in London, built between 1886 [4]
and 1894, designed by Horace Jones and engineered by John Wolfe Barry. The bridge is 800 feet (240
m) in length and consists of two bridge towers connected at the upper level by two horizontal
walkways, and a central pair of bascules that can open to allow shipping.
In this bridge, two towers of equal heights are standing opposite each other on either side of the road,
which is 80 m wide. During summer holidays, Neeta visited the tower bridge. She stood at some point
on the road between these towers. From that point between the towers on the road, the angles of
o o
elevation of the top of the towers was 60 and 30 respectively.
i. Neeta used some applications of trigronomatry she learned in her class to find the height of the
towers without actually measuring them. What would be the height of the towers she would have
calculated?
ii. Also find the distances of the point from the base of the towers where Neeta was standing while
measuring the height.