SET B

ANNUAL EXAMINATION
SESSION 2023-24
CLASS -IX
SUBJECT-MATHEMATICS
Time allowed - 3hrs
Max Marks: 80
General Instructions:
1. This Question Paper has S Sections A-E.
2 Section A has 20 MCQs carrying l
mark cach
3. Section B has $ questions carrying 02 marks cach.
SectionC has 6 questions carrying 03 marks
5. Scction D has 4 questions carTying 05 marks each,
cach.
Section E has 3 case based integrated units of assessment (04 marks each) with
the values of 1, I and 2 marks each sub-parts of
respectively.
All Questions are compulsory. However, an internal choice in 2 Qs of 5 marks, 2 Qs of 3
marks and 2 Questions of 2 marks has been provided. An internal choice has been provided
in the 2 marks questions of Section E.
8. Draw neat figures wherever required. Take =22/7 wherever required if not stated.
9 The question paper has seven pages.

SECTION A
1 If p(x) = 5, then p(2) is 1

(A)5 (B) 7 (C)0 (D) 2

If A(-5,-2) and B(-2,3) are two points on coordinate axes then the value 1

of (ordinate ofA) + (ordinate of B)' is

(A) -5 (B) 3 (C) 1 (D) -7
3 In the given figure, ZBAO = 30° and BCO = 40°. Then the measure of ZAOC
B

300 40

(A) 70° (B) 140° (C) 90° (D) 30°

4 The zeros of the polynomial 5x(x + 2)(*- 3) are
(A) -2, 0, 3, 5 (B) -2, 3 (C) 5, -2, 3 (D) 0, -2, 3
1
5 Which of the following is irational?
(B)Y2 (C)V7 (D) V81
(A)
 The class size of the class interval 150-170 is(C)170 (D) 20
(A) 150 (B) 160 the value
of
7 If a' + b )40,then
land 2(ab + bc + ca)
(a + b +c is (D) I
(A)40 (B) 4| 1
(C) 81 ?
thepoint(-I,2)
The graph of which equation passes through (D)y=x+3
(A)y =2x- (B) y=3x+ 1(C) y=x is 6 units. 1
distance from origin
Apoint lies on negative side of x-axis. Its
The coordinates of the point are
(DT(0,-6)
(A) (-6. 0) (B) (6, 0) (C)(0,) 1
10 If AB= PQ, BC= QR followingistrue.
and AC = PR, then which ofthe
(A) AABC> ARPQ (B) AACB ARQP
(C) AABCe APQR (D) AABC=APRQ
lf the radius of a sphere is doubled, then what is the ratio oftheir surface area?
(A) 1:2 (B) 2:1 (D) 4:1
(C) 1:4
12 If diagonals of a 1
Parallelogram are equal, then it is a :
(A) Square only
(B) Rectangle only
(C) Rhombus only
(D) both{A) and (B)
13 The radius of a sphere is increased by 50% then the increase in
surface area of a
sphere is
(A) 200% (B) 150% (C) 125% (D) 50%
14 The value of k if x=3 and y=2 is a
solution of the
(A) 1.5 (B) 2 (C) 1.25
equationx+y=4k is 1

15 (D) 1.75
An exterior angle of the triangle is 110°
and its two opposite interior angles
are in the ratio 5:6. The value of those
angles are
(A) S0°,60° (B) 25°,30° (C) 35°,420
(D) 40°,48°
16 If the perimeter of an
equilateral triangle is 60 m then its area is
(A) 10V3 m (B) 15V3 m² (C) 20V3 m
(D) 100V3 m²
17 1f greatest angle of a
parallelogram is 30° more than twice the smallest angle. 1
then greatest angle of the parallelogram is :
(A) 130° (B)S0° (C) 100° (D) 110°
18 The complement of (90 a)° is
(A) -a° (B) (90 a) (C) (90+2a) ° (D) a°
19 Siatement A(Assertion): The graph of the linear equation 2x -y = lpzsses 1

through the point (2, 3).

Statement R( Reason): Every point lying on graph is not a solution of 2x -
y=1.
(A) Both assertion (A) and reason (R) are true and reason (R) is the
correctexplanation of assertion (A)
(B) Both assertion (A) and reason (R) are truc and reason (R) is not the
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.
1
20 Statement A(Assertion): Sum oftwo irational numbers 2 -3 and 4-3
is urrational number.

Statement R( Reason) : Sum of two irational nurmbers is always an irational

number.

(A) Both assertion (A) and reason (R) are true and reason (R) is the
coectexplanation of assertion (A)
(B) Both assertion (A) and reason (R) are true and reason R) is DOt the
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.
SECTION B
21 Find the distance of the point (4, -2) from () y-axis (ii) origin. 2
Or
Name the quadrants/axes in which the following points iie?
P (-5,-3), Q(2,-9), R (0,-1), S (1,1)
22 ABCD is a quadrilateral in which P, R and Qare the mid points of AD, AC and
BC respectively. If AB=8 cm and CD= 10 cm, ind the length of PQ.

D
23 Find the remainder when f(x) =x*-3x+3 is divided by g(*) = 2

(x + 1). Also find whether g (x) is a factor of f(x).

 24 lacory is distubuted us 2
A raen suney vund that the ages of Woráers in a
olows
S0-50 6(0-69
Age (in years) 029 3
Number of workers

years?
How hany eNOOs have their age less than i9
same
another nac lor
(u) Is the given distribution exclusive? Give
kind of distributin
2

Or
In he u PS Ll and RO LL, then tind the value ot'y'.

185

SECTION C
26 The currd surface area of acone is 12320 sq cm. If the radius of its base is
3
$6 cm. îind its height.
Or

The volume of a right circular cone is 9856 cm'. If the diameter of the base is
28 cm, find slant height of the cone.
27 Arandom survey ot the number ot girls of various age groups playing in a park
3
was found as follows :

Age (in years) 4-8 8-12 12-16 16-20 20-24

Number of children 12 20

Draw a frequency polygon representing the above frequeney distribution.

Or
 |00 surnames were
randomly picked up from a local
trequency distributions of the number of letters in telephone directory and
surnanmes was found as follows: the English alphabet in the
Number of letters Number of surnames
|-4
4-6
30
6 8
44
8-12 16
12-20 4

Draw a histogranm to represent the

above data.
28 The sides of a triangle are in the ratio
25: 14: 12 and its perimeter is 510
Find its arca. cm. 3
In the figure, if LABD =
LACE and AB- AC thcn prove that BD-CE. 3

Arabbit covers y metres distance by walking 10 metres in slow motion and 3

the remaining by xjumps, each jump extending 2 metres. Express this

information in linear equation. Find its two solutions.
lfa = 2 and b =3, then 3

(a) Find the value of (a - bay-1

(b) Also find the rationalising factor of byaG

SECTION D

V5+V2 5
32 V5-V2
Ifx= and y = V5+v2' then evaluate x + y.
V5-V2
5
33 (a) Factorize: 8a + (2x- y)
(b) Expand (4x + y -z)
(c) Find (97)²using suitable identity.
Or

I r + = 18, find the valuc of

1 (b)
()
 34
Prove that the angle subtended hy an e at the centre is double thc angie
Suotended by it at any point on the remainine part of the circic.
and
AB, Pis thc mid point of AB. S is the mid point of DQ
35
gue, AD
PO | BR Prove that
a) AS BR

b) QR DR

Or
ABCD Is a rhombus and P. 0, R and S are the mid-points of the sides AB, BCy
Dand DA respectively. Show that the quadrilateral PQRS is a rectangle.

SECTION E
36 Rita draws a circle of radius 10 cm with the help of compass and scale. She
also draws 2 chords AB and CD in such a way that AB and CD are6 cm and
8 cm from the centre O lying opposite to each other. Now she has some doubts
that are given bclow. Help her out by answering these
questions:
Draw a suitable figure of the above situation. 1

(ii) What is the length of AB?

Or
2
What is the length of CD?
(iii) Which statement is not true?
(a) Equal chords of a circle subtend equal angles at the centre. 1
(b) The perpendicular from the centre of a circle to a chord bisects the
chord.

(c) Angles in the same segment ofa circle are equal.

(d) The sum of each pair of opposite angles of a cyclic quadrilateral is
90°.
37 Priti and Nandini started new business under a business blaster. The
investment made by both the partners is represented by a polynomial
p(x) = 12x + 11x - 15. The factors of the polynomial are the
individual shares of both.
Based on this information, answer the following questions:
(i) Ifx-100, then find the money invested.
 (i) What is the degree of invested polynomial.
(ii) Find the shares invested by rit and Nandini seçaraseiy (n
ens
of x).
Or

Find the value of p(10) - p(0).

12 solid spheres of the same size are made by melting asolid merallic come f
base radius 1cm and height of 48 cm.

(i) What is the volume of cone?

(ii) Find the radius of each sphere.
Or

Find the ratio of radius of sphere to the radius of cone

(iiü) Calculate the volume of l sphere.