PRUDENCE SCHOOL

PERIODIC ASSESSMENT 2
SUBJECT: MATHEMATICS (041)
SET B
GRADE: X

Date & Day: 27th September, 2021 & Monday

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
Q. No. Marks

1 The sum of exponents of prime factors in the prime factorisation of 1764 is 1

(a) 3 (b) 4 (c) 5 (d) 6

2 If 𝑎𝑚 ≠ 𝑏𝑙, then the equations 𝑎𝑥 + 𝑏𝑦 = 𝑐; 𝑙𝑥 + 𝑚𝑦 = 𝑛 has 1

(a) a unique solution (b) no solution
(c) Infinitely many solutions (d) may or may not have a solution.
3 If ∆ABC ~ ∆EDF and ∆ABC is not similar to ∆DEF, then which of the following is 1
not true?
(a) BC . EF = AC . FD (b) AB . EF = AC . DE
(c) BC . DE = AB . EF (d) BC. DE = AB . FD
4 The side of square whose diagonal is 16 cm is 1
(a) 8 cm (b) 8√2 cm (c) 5√2 cm (d) none of these

5 If three different coins are tossed together, then What is the probability of getting two 1
heads?
3 1 1 5
(a) 8 (b) 4 (c) 2 (d) 8

6 D and E are respectively the points on the sides AB and AC of a triangle ABC such 1
that AD = 2 cm, BD = 3 cm, BC = 7.5 cm and DE || BC. Then, length of DE (in cm) is
(a) 6 (b) 5 (c) 2.5 (d) 3
7 5 1
If sin A = 13, then the value of tan A is
5 5 12 8
(a) 13 (b) 12 (c) 13 (d) 13
 8 A rational number in its decimal expansion is 547.7801. What would be the prime 1
factors of q, when the number is expressed in the p/q form?
(a) 2 and 3 (b) 3 and 5 (c) 2,3 and 5 (d) 2 and 5
9 The value of c for which the pair of equations cx – y = 2 and 6x – 2y = 3 will have 1
infinitely many solutions is
(a) 3 (b) -3 (c) -12 (d) no value
10 The distance of the point P(3,4) from x-axis is 1
(a) 3 units (b) 4 units (c) 5 units (d) 1 units

11 For some integer m, every odd integer is of the form 1

(a) m (b) m + 1 (c) 2m (d) 2m + 1

12 Which of the following is not an irrational number? 1

(a) 6 + √9 (b) 5 − √3 (c) √2 + √3 (d) 4 + √2

13 If sin A + sin2 A = 1 , then the value of cos2 A + cos4 A is 1

(a) 0 (b) 1 (c) 2 (d) 3

14 1 1
Find the value of sin2 𝜃 + 1+ 𝑡𝑎𝑛2𝜃.
(a) 0 (b) 1 (c) 2 (d) 3

15 If the circumference of a circle increases from 4𝜋 to 8𝜋, then its area is 1

(a) halved (b) doubled (c) tripled (d) quadrapled

16 A man goes 24 m towards West and then 10 m towards North. How far is he from the 1
starting point?
(a) 34 m (b) 21 m (c) 14 m (d) 26 m
17 Corresponding sides of two similar triangles are in the ratio of 2:3. If area of small 1
triangle is 48 sq.cm, then area of large triangle is:
(a) 230 sq.cm (b) 106 sq.cm (c) 107 sq.cm (d) 108 sq.cm
18 5 𝑠𝑖𝑛𝜃−3 𝑐𝑜𝑠𝜃 1
If 5 tan𝜃 = 3, then what is the value of (4 𝑠𝑖𝑛𝜃+3 𝑐𝑜𝑠𝜃)?
(a) 1 (b) 0 (c) 3 (d) 4

19 The area of the triangle formed by the lines y = x, x = 6 and y = 0 is 1

(a) 36 sq. units (b) 18 sq. units (c) 9 sq. units (d) 72 sq. units

20 If a letter is chosen at random from the letter of English alphabet, then the probability 1
that it is a letter of the word DELHI is
1 1 5 21
(a) 5 (b) 26 (c) 26 (d) 26
SECTION B
Section B consists of 20 questions of 1 mark each. Any 16 questions are to be attempted
Q. No. Marks

21 The largest number which divides 70 and 125, leaving remainders 5 and 8, 1
respectively, is
(a) 13 (b) 65 (c)875 (d) 1750
22 If 2x + y = 23 and 4x – y = 19, Find the value of 5y – 2x. 1
(a) 17 (b) 19 (c) 31 (d) 9
23 5 𝑐𝑜𝑠2 60°+ 4 𝑠𝑒𝑐 2 30° − 𝑡𝑎𝑛2 45° 1
=?
𝑠𝑖𝑛2 30°+ 𝑐𝑜𝑠2 30°
7 47 67
(a) 15 (b) 12 (c) 12 (d) 1

24 What are the values of x and y for the following pair of linear equations? 1
99x + 101y = 499 and 101x + 99y = 501
(a) 3 and 6 (b) 3 and 2 (c) 2 and 3 (d) 6 and 3

25 The LCM of two prime numbers p and q (p > q) is 221. Find the value of 3p – q. 1
(a) 4 (b) 28 (c) 38 (d) 48
26 A card is drawn from a well shuffled deck of 52 cards. What is the probability of 1
drawing a red face card?
1 3 5 3
(a) 26 (b) 26 (c) 26 (d) 13

27 What is the probability of getting a sum of 9, when two dice are thrown 1
simultaneously?
1 7 5 2
(a) 9 (b) 9 (c) 9 (d) 9

28 If tan A + sin A = m and tan A – sin A = n, then 4 √𝑚𝑛 is 1

(a) 4cos A tan A (b) 4sin A tan A (c) 2cos A tan A (d) 2sin A tan A

29 What is the ratio in which the line joining points (a + b, b + a) and (a – b, b – a) is 1

divided by the point (a, b)?
(a) 1 : 1 (b) 2 : 1 (c) 2 : 3 (d) 1 : 3
30 Two poles of height 9 m and 15 m stand vertically upright on a plane ground. If the 1
distance between their tops is 10 m, then find the distance between their feet.
(a) 15 m (b) √136 m (c) √19 m (d) 8 m
31 If P(a/3, 4) is the mid- point of the line segment joining the points Q(-6, 5) and R(-2, 1
3), then the value of a is
(a) -4 (b) -12 (c) 12 (d) -6
32 If 7 cosec ∅ - 3 cot ∅ = 7, then 7 cot ∅ - 3 cosec ∅ =? 1
(a) 1 (b) 2 (c) 3 (d) 4
33 On a morning walk, three persons step off together and their steps measure 40 cm, 42 1
cm and 45 cm, respectively. What is the minimum distance each should walk so that
each can cover the same distance in complete steps?
(a) 2520 cm (b) 2525 cm (c) 2555 cm (d) 2528 cm
34 In the given figure the value of x is 1

𝑏𝑐 𝑏𝑐 𝑎𝑐 𝑎𝑐
(a) 𝑎+𝑏 (b) 𝑎+𝑏 (c) 𝑏+𝑐 (d) 𝑎+𝑏
35 If the distance of P(x, y) from A(6, 2) and B (-2, 6) are equal, then 1

(a) x = 2y (b) y = 2x (c) y = 3x (d) x = 3y

36 If the perimeter of a circle is equal to that of a square, then the ratio of their areas is 1
(a) 22:7 (b) 14:11 (c) 7:22 (d) 11:14
37 The minute hand of a clock is 12 cm long. What is the area of the face of the clock 1
described by the minute hand in 35 minutes? (use 𝜋 = 22/7)
(a) 148 cm2 (b) 264 cm2 (c) 132 cm2 (d) 198 cm2

38 1 1
If 𝛼 and 𝛽 are zeroes of 𝑥 2 − (𝑘 − 6)𝑥 + 2(2𝑘 − 1), such that 𝛼 + 𝛽 = 2 𝛼𝛽, value

of k will be
(a) 0 (b) -2 (c) 3 (d) -5

39 A momento is made as shown in the figure. Its base PBCR is silver plated from the 1
front side. What is the area which is silver plated? Use 𝜋 = 22/7

(a) 18 cm2 (b) 23 cm2 (c) 11.5 cm2 (d) 29.5 cm2

40 x and y are 2 different digits. If the sum of the two-digit numbers formed by using 1
both the digits is a perfect square, then value of x + y is
(a) 10 (b) 11 (c) 12 (d) 13
 SECTION C
Case study based questions:
Section C consists of 10 questions of 1 mark each. Any 8 questions are to be
attempted.
Q41 – 45 are based on Case Study – 1

Case Study 1:
Parabola: A parabola is the graph that results from p(x) = ax2 + bx + c. Parabolas are
symmetric about a vertical line known as the Axis of symmetry.
Symmetry: The Axis of Symmetry runs through the maximum or minimum point of
the parabola which is called the vertex.

41 If the highway overpass is represented by x2 – 2x – 8, then its zeroes are: 1

(a) (2, - 4) (b) (4, -2) (c) (-2, -2) (d) (-4, -4)

42 Zeroes of a polynomial can be expressed graphically. Number of zeroes of polynomial 1

is equal to number of points where the graph of polynomial_____________
(a) Intersects x-axis (b) Intersects y-axis
(c) Intersects both (d) none of these
43 Graph of a quadratic polynomial is a 1
(a) Straight line (b) parabola (c) ellipse (d) circle

44 The representation of Highway Underpass whose one zero is 6 and sum of zeroes is 0, 1
is
(a) x2 – 6x + 2 (b) x2 – 36 (c) x2 – 6 (d) x2 – 3

45 The number of zeroes that polynomial f(x) = (x – 2)2 can have is: 1
(a) 1 (b) 2 (c) 0 (d) 3
 Q46 – 50 are based on Case Study – 2

Case Study 2:
Aakash starts walking from his house to office. Instead of going to the office directly,
he goes to a bank first, from there to his daughter’s school and then reaches the office.
(Assume that all distances covered are in straight lines). If the house is situated at
(2,4), bank at (5,8), school at (13,14) and office at (13,26) and coordinates are in km.

46 What is the distance between house and bank? 1

(a) 5 (b) 10 (c) 12 (d) 27

47 What is the distance between daughter’s school and bank? 1

(a) 5 (b) 10 (c) 12 (d) 27

48 What is the distance between house and office? 1

(a) 24.6 (b) 26.4 (c) 24 (d) 26

49 What is the total distance travelled by Aakash to reach his office? 1

(a) 5 (b) 10 (c) 12 (d) 27

50 What is the extra distance travelled by Aakash to reach his office? 1

(a) 5 (b) 2 (c) 2.2 (d) 2.4