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WEST CLUSTER SAHODAYA CLUSTER SCHOOLS
CHENNAI
TERM 1
SUBJECT: MATHEMATICS
CODE: 041
CLASS: X, 2021 - 22

MAX. MARKS: 40 TIME: 90 MINUTES

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 MARKSS

1 The least number that is divisible by all the numbers from 1 to 8

(both inclyusive) is

2520 (b) 100 (c) 840 (d) 304

2 he pair of equations x = 0 and x = -5 have

(a) 1 solution (b)2 solutions 1
(c) inflnitely many solutions n o solution

3 The areas of two similar triangles are 144 cm2 and 81 cm2. If the
length of the median of the first triangle is 16 cm, then the length of
the corresponding median of the second triangle iss 1

(a) 9 cm (b) 27 cma U12 cm (d) 16 cm

InAABC,DE I BC, the value of x will be
x X+3

D 1
X+1/ X+5

(a) 1 (6) 2 (d) 4

 In the given triangle POR, ZQPR = 90°,PQ=24 cm and QR = 26 cm and in

5
APKR, 2PKR= 90° and KR=8 cm,the length of PK will be

Q R

(a) 3 cm (b) 4 cmn (c) 5 cma 6 cm

6
Ina single throw of a pair ofdifferent dice, what is the probability of
getting a prime number on each dice?

(a) (b) 36
(c)
A man steadily goes 20 m due east and then 21 m due north. What is
the distance from the
starting point? 1
(a) 25 m r29 m (c) 30 m (d) 41 ma
The decimal expansion of 41/1250 will terminate after
(a) 1decimal place (b) 2 decimal places (c) 3 decimal places 1
4 decimal places

9 If 23X 3 xbX7is the prime factorisation of 2520, then 5a +2b is

1
(a) 10 20 (c) 40 (d) 60
10
Ifaretheparallel,
lines given
then by
thethe equations
value of k is 3x +5ky 4 and 2x +6y 9 =O

(a)
11
Theperimeter of atríangle with vertices (0, 6),0, 0) and (8, o)is
24 (b) 14 (c) 11 (d) 14+S
12
Ifsine +cosê =v2 cose ,(6 90°) then the value of tane is
(a) 2 - 1 (b) 1 (c) 1
(d)-V2
13
The LCM of smallest 2-digit composite number and the smallest
composite number is

(a) 10 20 (c) 44 (d) 12

14 Ifk+ 1 sec20 (1+ sin®)}|1 -
sin6), then the value of k will be
(b) 1 (c) 2 (d) 15 1

15 The minute hand of a clock is 12 cm long. What is the area of the face
of the clock described by the minute hand in 35 minutes?

(a) 148 cm2 2 6 4 ema (c) 132 cma (d) 198 cma
16 In AABC, if ZADE-AB and AADEAABc, also AD-7.6 em, AE =7.2
cm, BE = 4.2 cm and BC = 8.4 cm, then the length of DE will be pt
(a) 5.6 cm (b) 2.8 cm (c) 4.8 cm (d) 3.8 cm
17 If x = p sec0 and y = q tan0, then

18 I f31x +43y 117 and 43x + 31y 105, then the value of x + y is
1
(a)-3 (b) 1/3 (c) 1/3 3
I r C o s 6
+ COs6 4, 0s 90, then the value ofe will be
19 " 1-sine0
1
1+ sin6
 a) 30
(b) 45 c) 60 (d)90
20 A
letter is chosen at random from the letters of the word
PROBABILITY, then the probability that the letter chosen is a vowel
is in the 12
form of thenx is 1
2x-3 equal to
(a) 10 (b) 15 18 (d) 20

SECTION B

Section B consists of 20 questions of 1 mark each.

Any 16 questions are to be attempted.
Q.NO. MARKS

21 If sum of two natural numbers is 85 and their LCM is 102, then the
two numbers are

34
(a) 30 and 55 (b) 17 and 68 (c) 35 and 50 5 1 and
22 The values of x and y from the following rectangle are
x+ 3y

3 + 7 1

C 13 D

Ux =
1, y =4 6) x =
4, y
=
1 ¬)x =
2, y = 5 ) x =
5, y =2
23

two concentric circles with centre

O have radii
In the given flgure, of the shaded
21 cm and 42 cm. If LAOB =60°, what is the area

region? Use n = 22/7.

J3465 cm2 (b) 1236 cm (c) 4168 cm2 (d) 1968 cm2

axis at the points P and Q

24 A line intersects the y axds and x
-
-

of PQ, then the coordinates

respectively. If (4, -10) is the mid-point
ofP andQ are, respectively
(b)0 , 20) and (-8, 0)
(a) (0,-10) and (4, 0)
(c) (0, 8) and (-10, 0) 0,-20) and (8, 0)

25 T h evalue of
245+320 1
25 (d) 3 V
6 (b) 12 (c) VS

Ifa card isred fromis a

selectedcard deck of 52 cards, then the probability of
26 its being face

(b) (
27 What is the area of a circle that can be inscribed in a
square of side
10 cm? 1
(d) 100 n cm2
25 cm2 b)50 r em c) 75r cma
28 The solution of pair of linear equations 3**7 = 81 and 81*-7 =3
will be

1
(a) x = 17, y 15 (b)x y=
x y- (d) no solution
29 The lengths of the diagonals of a rhombus are 40 cm and 30 cm.
Then the length of the side of the ghombus is 1
(a) 15 cm (b) 20 cm 2 5 cm (d) 30 cm
30 n tossing two coins together, the probability of getting at least 1
tail is

1
(a) 1 (b)
31 In
(d
AABC, LA =
90, AB =
AC to 12 cm and =
16 cm. If AD is
perpendicular to BC, then AD is equal
(a 9.5 cm (b) 9.6 cm (c) 9.8 cm (d) 9 cma
32 If HCF{336, 54) 6, then LCM(336, 54) will be
(a) 2024 1
3024 (c) 1012 (d) 1512
33 If sec A + tan A =x, then the value of tan A is

a2 2x (b) 2x
( dx1 1
34 What is the ratio in which the point P(m, 6) divides the line
segment joining the points A(-4, 3) and B(2, 8) ?
(a) 2 3 3:2 1
(c)3:1 (d) 1 3

35 The diameter of the front and rear wheels of a

and 200 cm respectively. What is the number of tractor are 80 made
revolutions cm
bythe rear wheel to cover the distance which the front wheel
covers in 800 revolutions?
(a) 320 (b) 420 ( c ) 820 (d) 640

36 I f 3 sin + 4 cose and y 3 cose -4 sin6, then the value of

25 (b) 45 (c) 7 (d) 49

1

IfP 4 ) i s the mid - point of the line segment joining the points
6 , 5) and R{-2, 3), then the value of a I

()-4 12 (o) 12 (d)-6

38 The perimeter of two similar trlangles ABC and PQR are 60 cm and
36 cm respectively. If PQ = 9 cm, then the length of AB is

(a) 16 em (b) 12 cm T 1 5 em (d) 14 cm

39 I fa andß are the zeroes of the polynomial fx) x3- p(x + 1x-
such that (a 1 )B+ 1) 0 then thevalue of c i

(b) (d) 2
40 4y ix 2y 9:4, then 3x 5y: 3x-y is
(a)4:1 (b) 1:4 (d) 1:7

SECTIONc

Case study based questions

questions
Section C consists of 10be
to
of 1 mark each.
attempted
Any 8 questions are
 241-045 are based on Case Study -1
Case Study -1
Priya and her husband Aman who is an architect by profession, visited France. They
went to see Mont Blanc Tunnel which is a
highway tunnel between France and itay
under the Mont Blane Mountain
mathematical
in the Alps, and has a parabolie cross-section. The
representation
of the tunnel is shown in the graph.

6
-x)
6 +1 6

Based on the above information, answer the following questions: (

The zeroes of the polynomial whose graph is given,
41
are
2, 8
(a)
(b 2,-8
-2, 8
(d 2,0
What will be the expression of the polynomial given in diagram?
42
(a)x-6x + 16

-x+6x+16
(c)*+6x+16
(d)-x-6x-16
What is the value of the polynomial represented by the graph, when
x= 4?
(a) 26
(b) 22
(c) 20
O 24
44
1f the tunnel is represented by -x+3x-2. then its zeroes are
(a)-1,-2
 (b) 1, -2
1,2
(d) 1, 2
45 If one of the zero is 4 and sum of zeroes is -3, then
tunnel as a polynomial is representation of
(a) x2- x + 24
(b)-2 3x + 28
(c) x2+x+ 28
(d)x2- x +28
Q46 Q50 are based on Case Study -2
Case Study -2
Resident Welfare Association (RWA) of a Gulmohar
Delhi have installed three electric Society in
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 system given above. On

the basis of the above information, answer the following questions:
46
What is the position of the pole C
(a14 ,5)
(5, 4)
(c) (6, 5)
(d) (5, 6)

47 What is the distance of the pole B from the corner O (origin) of the
park?
6 2 units
(b) 3 v2 units
(c) 6 V3 units
(4) 3 V3 units

48 Pind the position of thefourth pole D so that four points A, B, C and

D form a parallelogram.
5 , 2)
( 1 , 5)
(c) (1, 4)
(d)_(2, 5
49 What is the distance between poles A and C?
( a ) 2 units
3 2 units
(c) 6 3 units
(d) 3 V3 units
50 What is the distance between poles B and D?
(a) 23 units
(b) v28 units
( c s 3 units
K V26 units