NBSE Class 9 Question Paper 2019 Maths

Total number of printed pages : 6 NB-N/M/1
2019
CLASS-IX
MATHEMATICS
Total marks : 80 Time : 3 hours

General Instructions:
i) Approximately 15 minutes is allotted to read the question paper and revise the answers.
ii) The question paper consists of 22 questions.
iii) All questions are compulsory.
iv) Internal choice has been provided in some questions.
v) Marks allocated to every question are indicated against it.
N.B: Check that all pages of the question paper is complete as indicated on the top left side.

Section - A

1. Choose the correct answer from the given alternatives.
ap
(a) If a > 0 is a real number and p & q are rational numbers, then q is equal to 1
a
p
pq p q p q q
(i) a (ii) a (iii) a (iv) a

(b) When p  y  is divided by  y  a  , then the remainder is 1
(i) p 0  (ii) p a  (iii) p  y  (iv) pa 

(c) Which one of the following lies on y-axis? 1
(i) (0,5) (ii) (5,0) (iii) (5,5) (iv)  5, 0 

(d) The equation of the line whose graph passes through the origin is 1
(i) 2 x  3 y  1 (ii) 2 x  3 y  0
(iii) 2 x  3 y  6 (iv) 2 x  3 y  4
(e) The point a ,  a  lies on 1
(i) quadrant I (ii) quadrant II
(iii) quadrant III (iv) quadrant IV

(f) In the figure if l || m , then the value of x is 60
l
(i) 120° (ii)100°
(iii) 90° (iv) 80° x
m
1

(g) In a ∆ABC, if AB = 3 cm and AC = 4 cm, then BC is 1
(i) 7 cm (ii) less than 7 cm
(iii) more than 7 cm (iv) none of these

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(h) If three angles of a quadrilateral are 100°, 85° and 105°, then the measure of the
fourth angle is 1
(i) 100° (ii) 90° (iii) 80° (iv) 70°

(i) One side of a equilateral triangle is a, then the semi perimeter of a triangle is 1
3
a a 3a
(i) (ii) a (iii) (iv)
2 2 2
(j) The probability of getting a whole number when a die is thrown. 1
1
(i) –1 (ii) 0 (iii) (iv) 1
6

Section – B
5
2. Insert eight rational numbers between x and | x | , where x  2
11
p 1  p  1
If px   x  x  1 , then find the value of
2
3. 2
2
4. In the adjoining figure, ABC is an
equilateral triangle. Find the co-ordinates of
A.

2
5. In the adjoining figure, if AC = BD, then
prove that AB = CD. C D
B
A 2

6. Eleven bags of wheat flour, each marked 5 kg, actually contained the
following weights of flour (in kg):
4.97 5.05 5.08 5.03 5.00 5.06
5.08 4.98 5.04 5.07 5.00
Find the probability that any of these bags chosen at random contains:
(i) more than 5 kg flour.
(ii) less than 5 kg flour. 2

Section - C

7. a. Locate 3 on the number line.
Or 3
4 5 4 5
b. Simplify by rationalising the denominator 
4 5 4 5
3 3 3
8. a. Find the value of  x  a    x  b    x  c   3 x  a  x  b  x  c ,
when a  b  c  3 x
Or 3

b. Give possible expressions for the length and breadth of a rectangle which
2
has area 25a  35a  12

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Y
9. In the adjoining figure, ABCD is a rectangle D R C
in which AB = 8 unit and BC = 6 unit. If P,
Q, R and S are the mid-points of AB, BC, S Q
X' X
O
CD and AD. Then find the co-ordinate of A,
B, C, and D. A B
P
Y' 3

10. a. In the adjoining figure, lines AB and CD
intersect at O. If AOC + BOE = 70° C E
and BOD = 40°. Find BOE and
reflex COE.
A O B

D
Or 3

b. In the adjoining figure, if AB || CD, A P B
APQ = 50° and PRD = 127°, find x 50
y
and y.
x 127
C Q R D

11. a. In the adjoining figure, ABC is an A
isosceles triangle in which altitudes BE
and CF are drawn to equal sides AC and E
F
AB respectively. Show that these
altitudes are equal.

B C
Or 3

b. AD is an altitude of an isosceles triangle ABC in which AB = AC. Show that
(i) AD bisects BC (ii) AD bisects A

12. Prove that parallelograms on the same base and between the same parallels are
equal in area. 3

13. Construct a triangle ABC in which BC = 7 cm, B = 75° and AB + AC = 13 cm
[Traces of construction only is required] 3

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14. a. The radius of a spherical balloon increases from 7 cm to 14 cm as air is being
pumped into it. Find the ratio of surface areas of the balloon in the two cases.

Or 3

b. The inner diameter of a cylindrical wooden pipe is 24 cm and its outer diameter is
28 cm. The length of the pipe is 35 cm. Find the mass of the pipe, if 1 cm3 of wood
has a mass of 0.6 gram.

15. The blood group of 40 students of class IX are recorded as follows:

A, B, O, A, O, AB, A, O, A, O,
B, A, O, B, A, O, A, O, AB, A,
O, A, AB, O, A, A, O, O, AB, B,
A, O, B, A, B, O, A, B, A, O

Represent this data in the form of frequency distribution table. Which is the most
common and which is the rarest, blood group among these students. 3

16. In a mathematics test given to 15 students, the following marks (out of 100)
are recorded:
41, 39, 48, 52, 46, 62, 54, 40,
96, 52, 98, 40, 42, 52, 60
Find the mean, median and mode of this data. 3

Section – D

a. The polynomial px   x  2 x  3x  ax  3a  7 when divided by x  1 ,
4 3 2
17.
leaves the remainder 19. Find the value of a. Also, find the remainder when
p x  is divided by x  2 .
Or 5

3 2
b. Factorise x  13 x  32 x  20 by using the Factor Theorem.

18. a. If the work done by a body on application of a constant force is directly proportional to
the distance travelled by the body, express this in the form of an equation in two variables
and draw the graph of the same by taking the constant force as 5 units. Also, read from the
graph the work done when the distance travelled by the body is
(i) 2 units (ii) 0 unit
Or 5
b. In countries like USA and Canada temperature is measured in Fahrenheit, whereas in
countries like India, it is measured in Celsius. Here is the linear equation that converts
9
Fahrenheit to Celsius F   C  32 . Draw the graph of the linear equation above
5
using Celsius for x-axis and Fahrenheit for y-axis.

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19. a. In the adjoining figure, ABCD is a D
R
quadrilateral in which P, Q, R and S are C
mid points of the sides AB, BC, CD and
DA. AC is a diagonal. Show that: S
1 Q
(i) SR || AC and SR  AC
2
(ii) PQ = SR A B
(iii) PQRS is a parallelogram P

Or 5

b. In the adjoining figure, AE is the diameter of C
the semi-circle with centre O. If AB = BC and B D
AEC = 50°, then prove that BO || CE. Also
find: (i) CBE (ii) CDE
(iii) AOB 50
A E
O

20. a. A park in the shape of a quadrilateral ABCD has C = 90°, AB = 9 m,
BC = 12 m, CD = 5 m and AD = 8 m. How much area does it occupy?

Or 5
A
b. In the adjoining figure, a triangular park 50 m 80 m
ABC has sides 120 m, 80 m and 50 m. A
gardener Dhania has to put a fence all 3m
around it and also plant grass inside. How B C
120 m
much area does she need to plant? Find the
cost of fencing it with barbed wire at the
rate of `20 per metre leaving a space 3 m
wide for a gate on one side.

21. a. A cloth having an area of 165 m2 is shaped into the form of a conical tent of radius 5 m.
5 2
(i) How many students can sit in the tent if a student on an average occupies m
7
on the ground?
(ii) Find the volume of the cone.

Or 5

b. A plastic box 1.5 m long, 1.25 m wide and 65 cm deep is to be made. It is
opened at the top. Ignoring the thickness of the plastic sheet, determine:
(i) The area of the sheet required for making the box.
(ii) The cost of sheet for it, if a sheet measuring 1 m2 costs `20.

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22. a. Construct a frequency polygon for the following data:

Marks Number of students
0-5 5
5-10 11
10-15 4
15-20 9
20-25 10
25-30 3
30-35 2
35-40 5

Or 5

b. The following table gives the life time of 400 neon lamps:

Life time (in hours) Number of lambs
300-400 14
400-500 56
500-600 60
600-700 86
700-800 74
800-900 62
900-1000 48

(i) Represent the given information with the help of a histogram.
(ii) How many lamps have a life time of more than 700 hours?

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