Sample/Pre-Board Paper 35

Class X Term 1 Exam Nov -Dec 2021

Mathematics (Standard) 041
Time Allowed: 90 minutes Maximum Marks: 40
General Instructions:
1. The question paper contains three parts A, B and C.
2. Section A consists of 20 questions of 1 mark each. Any 16 questions are to be attempted.
3. Section B consists of 20 questions of 1 mark each. Any 16 questions are to be attempted.
4. Section C consists of 10 questions based on two Case Studies. Attempt any 8 questions.
5. There is no negative marking.

SECTION A
Section A consists of 20 questions of 1 mark each. Any 16 questions are to be attempted.

1. The sum of exponents of prime factors in the prime- 6. In figure, MN < BC and AM : MB = 1 : 2 , then
factorisation of 196 is ar (TAMN)
= ................... .
ar (TABC)
(a) 3 (b) 4
(c) 5 (d) 2

2. If one zero of the polynomial 2x2 + 3x + λ is 1

2 , what
is the value of λ and the other zero?
(a) –2 and –2 (b) –3 and –3
(c) –2 and –3 (d) –3 and –2
(a) 1
3 (b) 1
9
3. In the given figure, DE z BC . The value of EC is
(c) 8
9 (d) 5
9

7. Given that sin α = 3 and cos β = 0 , then the value

2
of β − α is
(a) 0c (b) 90c
(c) 60c (d) 30c

8. Which of the following rational number have non-

terminating repeating decimal expansion?
(a) 31 (b) 71
3125 512
(a) 1.5 cm (b) 3 cm
(c) 23 (d) None of these
(c) 2 cm (d) 1 cm 200

9. The value of k for which the system of linear equations

4. It is given that TABC + TPQR with BC = 1 . x + 2y = 3 , 5x + ky + 7 = 0 is inconsistent is
QR 4
ar (TPRQ)
Then is equal to (a) − 14 (b) 2
ar (TBCA) 3 5
(a) 16 (b) 3 (c) 5 (d) 10
(c) 1
4 (d) 1
16
10. The point P on x -axis equidistant from the points
A (− 1, 0) and B (5, 0) is
5. The probability that a number selected at random
from the numbers 1, 2, 3, ......, 15 is a multiple of 4 is (a) (2, 0) (b) (0, 2)
(a) 4
15 (b) 2
15
(c) (3, 0) (d) (− 3, 5)
(c) 1
15 (d) 1
5
11. In the given factor tree what is the composite number x ? arc 44 cm in length ?
(a) 190 sq cm (b) 770 sq cm
(c) 385 sq cm (d) 225 sq cm

16. If triangle ABC is similar to triangle DEF such that

2AB = DE and BC = 8 cm then EF will be
(a) 16 cm (b) 14 cm
(c) 12 cm (d) 10 cm

17. In the given figure, if ABCD is a trapezium in which

ED = ?
AB | | CD | | EF, then AE

(a) 53 (b) 11130

(c) 5565 (d) 19438

12. What are the HCF and LCM of 90 and 144 by the (a) 2FC
(b) 2BF
method of prime factorization. BF FC

(c) FC
(d) BF
(a) 36 and 360 (b) 720 and 18 BF FC

(c) 18 and 720 (d) 360 and 36

18. If k + 1 = sec2 θ ^1 + sin θh^1 − sin θh, then the value of
k. will be
13. In the adjoining figure, the length of BC is (a) 0 (b) 1
(c) 2 (d) 15

19. If a pair of linear equations is consistent, then the

lines will be
(a) parallel
(b) always coincident
(a) 2 3 cm (b) 3 3 cm (c) intersecting or coincident
(c) 4 3 cm (d) 3 cm (d) always intersecting

14. The value of (1 + tan2 θ) (1 − sin θ) (1 + sin θ) = 20. A girl calculates that the probability of her winning
................... . the first prize in a lottery is 0.08. If 6000 tickets are
(a) 0 (b) 1 sold, then how many tickets has she bought?
(c) 2 (d) 1 (a) 40
2
(b) 240
15. The radius of a circle is 17.5 cm. What is the area of (c) 480
the sector of the circle enclosed by two radii and an (d) 750

SECTION B
Section B consists of 20 questions of 1 mark each. Any 16 questions are to be attempted.

21. A tile floor is to be made from 10 inch, 12 inch, and 15 third row uses only 15 inch tiles. Neglecting the grout
inch square tiles. A design is made by alternating rows seams, what is the shortest length of floor space that
with different size tiles. The first row uses only 10 inch can be covered evenly by each row?
tiles, the second row uses only 12 inch tiles, and the
 29. If x − 2y + k = 0 is a median of the triangle whose
vertices are at points A (− 1, 3), B (0, 4) and C (− 5, 2),
then the value of k is
(a) 2 (b) 4
(c) 6 (d) 8

30. In the given figure, if AB | | DC, the value of x will be

(a) 20 inch (b) 39 inch

(c) 60 inch (d) 10 inch

22. The mid-point of the line-segment AB is P (0, 4), if the

coordinates of B are (− 2, 3) then the co-ordinates of
A are
(a) (2, 5) (b) (− 2, − 5) (a) 3 (b) 6
(c) (2, 9) (d) (− 2, 11) (c) 7 (d) 8

23. If cos θ + cos θ = 4; θ # 90º the value of θ will 31. The points ^a, a h , ^− a, − a h and `− 3 a, 3 a j are
1 − sin θ 1 + sin θ
be the vertices of_____
(a) 30° (b) 45° (a) equilateral triangle
(c) 60° (d) 90° (b) scalene triangle
(c) isosceles triangle
24. If the equations kx − 2y = 3 and 3x + y = 5 represent (d) right angled isosceles triangle
two intersecting lines at unique point, then the value
of k is ........... .
32. sin A is equal to
(a) k = − 6 (b) k !− 6
(a) 1 − sec2 A (b) sec2 A − 1
(c) k = 4 (d) k ! 4
sec2 A − 1
(c) sec A
sec2 A − 1
(d) sec A

25. If one zero of a quadratic polynomial (kx2 + 3x + k) is

2, then the value of k is 33. 144 cartons of Coke cans and 90 cartons of Pepsi cans
are to be stacked in a canteen. If each stack is of the
(a) 5
6 (b) − 56 same height and if it equal contain cartons of the same
(c) 6
5 (d) − 65 drink, what would be the greatest number of cartons
each stack would have?
26. If in a lottery, there are 5 prizes and 20 blanks, then (a) 12 (b) 24
the probability of getting a prize is (c) 18 (d) 36
(a) 2
5 (b) 4
5

(c) 1
5 (d) 1 34. In the given figure, BC | | PQ and BC = 8 cm,
PQ = 4 cm, BA = 6.5 cm AP = 2.8 cm.
The length of CA is
27. A number is chosen at random from the numbers − 5 ,
− 4 , − 3 , − 2 , − 1, 0, 1, 2, 3, 4, 5. Then the probability
that square of this number is less than or equal to 1
is .......... .
(a) 9
11 (b) 3
11

(c) 8
11 (d) 7
11

28. Four equal circles are described at the four corners

of a square so that each touches two of the others.
The shaded area enclosed between the circle is 247 cm2.
What is the radius of each circle?
(a) 2.80 cm (b) 5.60 cm
(a) 2 cm (b) 4 cm
(c) 3.25 cm (d) 2.10 cm
(c) 6 cm (d) 1 cm
35. The perpendicular bisector of the line segment joining (a) 217 cm2 (b) 434 cm2
the points A ^1, 5h and B ^4, 6h cuts the y -axis at
(c) 314 cm2 (d) 506 cm2
(a) (0, 13) (b) ^0, − 13h
(c) (0, 12) (d) (13, 0) 38. If the zeroes of the quadratic polynomial
x2 + ^a + 1h x + b are 2 and − 3 , then
36. In the figure, ABC is a right angled triangle right (a) a = − 7, b = − 1 (b) a = 5, b = − 1
angled at +A . if AB = 6 cm, BC = 10 cm and O is
(c) a = 2, b = − 6 (d) a = 0, b = − 6
the centre of the circle of the triangle ABC , what is
the area of the shaded region ?
39. Three semicircles each of diameter 3 cm, a circle of
diameter 4.5 cm and a semicircle of radius 4.5 cm
are drawn in the given figure. The area of the shaded
region will be

(a) 22.6 cm2 (b) 18.9 cm2

(c) 11.5 cm2 (d) 11.43 cm2

37. In the given figure, ABCD is a rectangle of dimensions

21 cm # 14 cm. A semicircle is drawn with BC as (a) 25.6 cm2 (b) 50.6 cm2
diameter. What is the area and the perimeter of the
shaded region in the figure? (c) 12.375 cm2 (d) 28.375 cm2

40. Given the linear equation 3x + 4y = 9 . Select another

linear equation in these two variables such that the
geometrical representation of the pair so formed is
intersecting lines.
(a) 3x − 5y = 10 (b) 6x + 8y = 18
(c) 8x + 12y = 18 (d) above all

SECTION C
Case study based questions:
Section C consists of 10 questions of 1 mark each. Any 8 questions are to be attempted.

Case Based Questions: (41-45)

Resident Welfare Association (RWA) of a Gulmohar
Society in Delhi have installed three electric poles A,
B and C in a society’s common park. Despite these
three poles, some parts of the park are still in dark.
So, RWA decides to have one more electric pole D in
the park.

The park can be modelled as a coordinate systems

On the basis of the above information, answer any
given below.
four of the following questions:
41. What is the position of the pole C ?
(a) (4 ,5) (b) (5, 4)
(c) (6, 5) (d) (5, 6)

42. What is the distance of the pole B from the corner O

of the park ?
(a) 6 2 units (b) 3 2 units
(c) 6 3 units (d) 3 3 units

43. Find the position of the fourth pole D so that four

points A, B C and D form a parallelogram .
(a) (5, 2) (b) (1, 5)
(c) (1, 4) (d) (2, 5) A builder wants to build a tank to store water in an
apartment. The volume of the rectangular tank will
be modelled by V (x) = x3 + x2 − 4x − 4 .
44. What is the distance between poles A and C ?
(a) 6 2 units (b) 3 2 units
46. He planned in such a way that its base dimensions are
(c) 6 3 units (d) 3 3 units (x + 1) and (x + 2) . How much he has to dig ?
(a) (x + 1) (b) (x − 2)
45. What is the distance between poles B and D ? (c) (x − 3) (d) (x + 2)
(a) 2 3 units (b) 28 units
(c) 6 3 units (d) 26 units 47. If x = 4 meter, what is the volume of the water tank?
(a) 30 m3 (b) 20 m3
Case Based Questions: (46-50) (c) 15 m3 (d) 60 m3
Underground water tank is very popular in India. It is
usually used for large water tank storage and can be 48. If x = 4 and the builder wants to paint the entire
built cheaply using cement-like materials. Underground inner portion on the water tank, what is the total area
water tank are typically chosen by people who want to to be painted ?
save space. The water in the underground water tank
is not affected by extreme weather conditions. The (a) 52 m2 (b) 96 m2
underground water tank maintain cool temperatures (c) 208 m2 (d) 104 m2
in both winter and summer.
49. If the cost of paint is ` 25/ per square metre, what is
the cost of painting ?
(a) ` 3900 (b) ` 2600
(c) ` 1300 (d) ` 5200

50. What is the storage capacity of this water tank ?

(a) 3000 litre (b) 6000 litre
(c) 60000 litre (d) 30000 litre
 SAMPLE PAPER - 30 Answer Key
Paper Correct Chapter Question Bank
Q. no. Option no Q. no.
1 (b) Ch-1 1
2 (a) Ch-2 S-12
3 (c) Ch-4 1
Paper Correct Chapter Question Bank
4 (a) Ch-4 12
Q. no. Option no Q. no.
5 (d) Ch-8 1
26 (c) Ch-8 23
6 (b) Ch-4 25
27 (b) Ch-8 33
7 (d) Ch-6 1
28 (a) Ch-6 74
8 (d) Ch-1 21
29 (d) Ch-5 22
9 (d) Ch-3 1
30 (c) Ch-4 56
10 (a) Ch-5 1
31 (a) Ch-5 46
11 (b) Ch-1 36
32 (d) Ch-6 86
12 (c) Ch-1 S-17
33 (c) Ch-1 S-27
13 (d) Ch-6 13
34 (b) Ch-4 D-67
14 (b) Ch-6 29
35 (a) Ch-5 33
15 (c) Ch-7 29
36 (d) Ch-7 82
16 (a) Ch-4 35
37 (a) Ch-7 92
17 (d) Ch-4 45
38 (d) Ch-2 16
18 (a) Ch-6 42
39 (c) Ch-7 102
19 (c) Ch-3 12
40 (a) Ch-3 34
41 (b) Ch-5 112
42 (a) Ch-5 113
43 (b) Ch-5 114
44 (b) Ch-5 115
20 (c) Ch-8 13 45 (d) Ch-5 116
21 (c) Ch-1 53 46 (b) Ch-2 104
22 (a) Ch-5 11 47 (d) Ch-2 105
23 (c) Ch-6 60 48 (d) Ch-2 106
24 (b) Ch-3 24 49 (b) Ch-2 107
25 (d) Ch-2 1 50 (c) Ch-2 108
* S- = Self Test Question, * D- = Direction Based Question