Pre Mid Term Exam Sept 21

Class – X Session -2021-22

Subject- Mathematics
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 ratio of LCM and HCF of the least composite and the least prime numbers is 1
(a) 1:2 (b) 2:1 (c) 1:1 (d) 1:3

2 The value of k for which the lines 5x+7y=3 and 15x + 21y = k coincide is 1
(a) 9 (b) 5 (c) 7 (d) 18

3 A girl walks 200m towards East and then 150m towards North. The distance of the girl 1
from the starting point is
(a)350m (b) 250m (c) 300m (d) 225

4 The lengths of the diagonals of a rhombus are 24cm and 32cm, then the length of the side 1
of the rhombus is
(a) 32cm (b) 24 cm (c) 40 cm` (d) 20cm

5 Two fair coins are tossed. What is the probability of getting at the most one head?
(a) ¾ (b) ¼ (c) ½ (d) 3/8 1

6 ∆ABC~∆PQR. If AM and PN are altitudes of ∆ABC and ∆PQR respectively and AB2 : 1
PQ2 = 4 : 9, then AM:PN =
(a) 16:81 (b) 4:9 (c) 3:2 (d) 2:3

7 Which of the following statements are true for the graph of a line represented by the equation 1
y = x?
(i) line passes through origin (ii) line lies in second and fourth quadrants.
(iii) line lies in first and third quadrants. (iv) line lies only in first quadrant.
(v) line does not pass through (a, a).

(a) I,iii,v (b) I, iii iv (c) i, iii, iv (d) I, iii.

8 Prime factors of the denominator of a rational number with the decimal expansion 1
44.123 are
(a) 2,3 (b) 2,3,5 (c) 2,5 (d) 3,5
9 The lines x = a and y = b, are 1
(a) intersecting (b) parallel (c) overlapping (d) (None of these)

10 The distance of point A(-5, 6) from the origin is 1

(a) 11 units (b) 61 units (c) √11 units (d) √61 units

11 If a² = 23/25, then a is
(a) rational (b) irrational (c) whole number (d) integer 1

12 If LCM(x, 18) =36 and HCF(x, 18) =2, then x is 1

(a) 2 (b) 3 (c) 4 (d) 5

13 The points (a, b + c), (b, c + a) and (c, a + b) 1

(a) form an isosceles triangle (b) do not form a triangle

(c) form a scalene triangle (d) form an equilateral triangle

14 Cards numbered from 1 to 20 are placed in a box. One card is drawm at random from the box. 1
What is the probability that the card drawn has an odd prime number ?

(a) 3/5 (b) 2/5 (c) 9/20 (d) 7/20

15 Assertion : In ∆ ABC , AB = 24 cm, BC = 10 cm and AC = 26 cm, then ∆ABC is a right angle triangle. 1
Reason : If in two triangles, their corresponding angles are equal, then the triangles are similar.

(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 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.

16 ∆ABC is such that AB=3 cm, BC= 2cm, CA= 2.5 cm. If ∆ABC ~ ∆DEF and EF = 1
4cm, then perimeter of ∆DEF is
(a) 7.5 cm (b) 15 cm (c) 22.5 cm (d) 30 cm

17 In the figure, if DE∥ BC, AD = 3cm, BD = 4cm and BC= 14 cm, then DE equals 1

(a) 7cm (b) 6cm (c) 4cm (d) 3cm

18 . If the centroid of a triangle is at origin whose vertices are (a, b), (b, c) and (c, a), then the value 1
of 3(a + b + c) is
 (a) 0 (b) 1 (c) 2 (d) 3

19 One equation of a pair of dependent linear equations is –5x + 7y = 2. The second equation 1
can be
a) 10x+14y +4 = 0 b) –10x –14y+ 4 = 0 c) –10x+14y + 4 = 0 (d) 10x – 14y = –4

20 A letter of English alphabets is chosen at random. What is the probability that it is a letter 1
of the word ‘MATHEMATICS’?
(a) 4/13 (b) 9/26 (c) 5/13 (d) 11/26

SECTION B

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

QN MARKS

21 If sum of two numbers is 1215 and their HCF is 81, then the possible number of pairs of 1
such numbers are
(a) 2 (b) 3 (c) 4 (d) 5

22 Given below is the graph representing two linear equations by lines AB and CD 1
respectively. What is the area of the triangle formed by these two lines and the line x=0?

(a) 3sq. units (b) 4sq. units (c) 6sq. units (d) 8sq. units

23 The least number which is a perfect square and is divisible by each of 1

16, 20 and 24 is
(a) 240 (b) 1600 (c) 2400 (d) 3600

(a) 240 (b) 1600 (c) 2400 (d) 3600

24 If 217x + 131y = 913, 131x + 217y = 827, then x + y is 1

(a) 5 (b) 6 (c) 7 (d) 8

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 cards. What is the probability that the 1
card drawn is neither a king nor a queen?
(a) 11/13 (b) 12/13 (c) 11/26 (d) 11/52

27 Two fair dice are rolled simultaneously. The probability that 5 will come up at least 1
once is
(a) 5/36 (b) 11/36 (c) 12/36 (d) 23/36

28 Assertion : 13/3125 is a terminating decimal fraction. 1

Reason : If q = 2m X 5n where m n, are non-negative integers, p/q is a terminating decimal
fraction.
(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 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.

29 The vertices of a parallelogram in order are A(1,2), B(4, y), C(x, 6) and D(3,5). Then 1
(x, y) is
(a) (6, 3) (b) (3, 6) (c) (5, 6) (d) (1, 4)
30 In the given figure, ∠ACB=∠CDA, AC = 8cm, AD = 3cm, then BD is 1

(a) 22/3 cm (b) 26/3 cm (c) 55/3 cm (d) 64/3 cm

31 The present age of the father is twice the sum of the ages of his 2 children. After 20 years, his 1
age will be equal to the sum of the ages of his children. What will be the age of the father after
20 years?
(a) 20 years (b) 40 years (c) 30 years (d) 60 years

32 X and Y are points on sides AB and BC of triangle ABC such that XY ∥ AC and XY divides 1
triangle into two parts such that area of trapezium ACYX is double of area of triangle BXY,
𝐴𝑋
then 𝐴𝐵 =
1 1 √2− 1 √3− 1
(a) (b) (c) (d)
√3 √2 √2 √3
33 The smallest number by which 1/13 should be multiplied so that its decimal expansion 1
terminates after two decimal places is
(a) 13/100 (b) 13/10 (c) 10/13 (d) 100/13

34 The point P on x -axis equidistant from the points A(- 1, 0) and B(5, 0) is 1

(a) (2,0) (b) (0,2) (c) (3, 0) (d) (-3,5)

35 Point P divides the line segment joining R(-1, 3) and S(9,8) in ratio k:1. If P lies on the 1
line x – y +2=0, then value of k is
(a) 2/3 (b) 1/2 (c) 1/3 (d) 1/4

36 Which of the following points lie on the line 2x – 3y + 11 = 0? 1

(a) (-4,1) (b) (4, 1) (c) (4, -1) (d) (-4, -1)

37 The areas of two similar triangles are 121 sq cm and 64 sq cm. If the median of first 1
triangle is 13.2 cm , then the corresponding median of other triangle is

(a) 11 cm (b) 9.6 cm (c) 11.1 cm (d) 8.1 cm

38 If 2 and ½ are the zeros of px2+5x+r, then 1

(a) p = r = 2 (b) p = r = - 2 (c) p = 2, r= -2 (d) p = -2, r= 2

39 If one zero of the polynomial P(x) 5x2 + 13x – k , is the reciprocal of the other, 1
then k =

(a) 13 (b) 5 (c) -5 (d) -13

40 The number of solutions of 3x+y = 243 and 243x-y = 3 is 1

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

SECTION C

Case study based questions:

Section C consists of 10 questions of 1 mark each. Any 8 questions are to be
attempted.
 Q41-Q45 are based on Case Study -1

Case Study -1
The residents of a housing society, on the occasion of world ozone day (16
september), decided to build two straight paths in the central park of the society
and also plant trees along boundary lines of each path.
Taking one corner of the park as origin and the two mutually perpendicular lines
as the X axis and Y axis, the paths were represented by the two linear equations
2x - 3y = 5 and 6x + 9y = 7
Based on the above answer the following questions.

41 The two paths represented by the two equations are 1

(a) Intersecting (b) overlapping (c) parallel (d) mutually perpendicular.

42 Which of the following points lie on the line 2x - 3y = 5? 1

(a) (-4,1) (b) (4, -1) (c) (4,1) (d) (-4, --1)

43 The point of intersection of the line -6x + 9y = 7 with Y axis is 1

(a) (0, 7/9) (b) (7/9, 0) / (c) (-7/6, 0) (d) (0, -7/6)

44 1
 1
45

Q46-Q50 are based on Case Study -2 Case Study -2

A hockey field is the playing surface for the game of hockey. Historically, the game was played on natural
turf (grass) but nowadays it is predominantly played on an artificial turf.
It is rectangular in shape - 100 yards by 60 yards. Goals consist of two upright posts placed equidistant
from the centre of the backline, joined at the top by a horizontal crossbar. The inner edges of the posts
must be 3.66 metres (4 yards) apart, and the lower edge of the crossbar must be 2.14 metres (7 feet) above
the ground.
Each team plays with 11 players on the field during the game including the goalie. Positions you
might play include-

• Forward: As shown by players A, B, C and D.

• Midfielders: As shown by players E, F and G.
• Fullbacks: As shown by players H, I and J.
• Goalie: As shown by player K
Using the picture of a hockey field below, answer the questions that follow:

46 The coordinates of the centroid of ΔEHJ are 1

(a) (-2/3, 1)
(b) (1,-2/3)
(c) (2/3,1)
(d) ( -2/3,-1)
47 If a player P needs to be at equal distances from A and G, such that A, P and G are in straight 1
line, then position of P will be given by
(a) (-3/2, 2)
(b) (2,-3/2)
(c) (2, 3/2)
(d) ( -2,-3)
48 The point on x axis equidistant from I and E is 1
(a) (1/2, 0)
(b) (0,-1/2)
(c) (-1/2,0)
(d) ( 0,1/2)
49 What are the coordinates of the position of a player Q such that his distance from K is twice 1
his distance from E and K, Q and E are collinear?
(a) (1, 0)
(b) (0,1)
(c) (-2,1)
(d) ( -1,0)

50 The point on y axis equidistant from B and C is 1

(a) (-1, 0)
(b) (0,-1)
(c) (1,0)
(d) ( 0,1)