NBSE Class 9 Question Paper 2020 Maths

Total number of printed pages : 5 NB-N/M/I
2020
CLASS-IX
MATHEMATICS
Total marks : 80 Time : 3 hours

General Instructions:
i) The question paper consists of 22 questions.
ii) Internal choice has been provided in some questions.
iii) 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.
4
(a) 2 3 is same as 1
(i) 4
23 (ii) 3 4 (iii) 3 2 4 (iv) 6 32

(b) If p x   x 2  2 3 x  1 , then p 2 3  is equal to 1
(i) 0 (ii) 1 (iii) 4 2 (iv) 8 2  1

(c) If  x  1 is a factor of mx 2  2 x  1 , then the value of m is 1
(i) 2 (ii) 2  1 (iii) 1 (iv) 2  1

(d) The equation of the line whose graph does not pass through the origin, is 1
(i) x  y  0 (ii) x  y  0 (iii) x  2 y  0 (iv) x  2 y  1

(e) If x-coordinate of a point is zero, then it always lies on 1
(i) quadrant I (ii) quadrant II (iii) x-axis (iv) y-axis

(f) Lines AB and CD intersect at O. If AOC : BOC = 5 : 7, then BOD = 1
(i) 105 (ii) 100 (iii) 75 (iv) 60
(g) In ABC, if AB = AC & A = 80, then values of B &C respectively are 1
(i) 50, 60 (ii) 50, 50 (iii) 40, 40 (iv) 80, 50
(h) In a parallelogram ABCD, bisectors of two adjacent angles A and B meet at O.
The measure of AOB is equal to 1
(i) 90 (ii) 120 (iii) 180 (iv) 200

-2- NB-N/M/I

(i) If the area of an equilateral triangle is 9 3 cm2, then its perimeter is 1
(i) 10 cm (ii) 18 cm (iii) 21 cm (iv) 24 cm

(j) An experiment was conducted. Probabilities of an event was calculated by
some students. Which of the following could be the correct answer? 1
2 3 2
(i) 1.6 (ii)  (iii) (iv)
5 2 3
Section - B

2. Simplify: 3  3 2  2  2

3. If the point (3, 4) lies on the graph of the equation 3 y  ax  7 , find the value of a. 2

4. Write the coordinates of the point which: (i) lies on the x-axis with abscissa 3,
(ii) lies on the y-axis with ordinate 5. 2

5. If ABC  PQR, A + B = 100, AB = 3 cm, BC = 5 cm, then find:
(i) the measure of R, (ii) sum of the lengths of PQ and QR. 2

6. The following observations have been arranged in ascending order. If the median
of the data is 63, find the value of x. 2
29, 32, 48, 50, x, (x + 2), 72, 78, 84, 95

Section - C
21
7. a. Express with rational denominator.
3 5 3
Or 3
b. Visualise 3.765 on the number line, using successive magnification

8. a. Find p(0), p(1) and p(2) for the polynomial, pt   2  t  2t 2  t 3 .
Or 3
b. Find the value of k, if x  1 is a factor of p x   kx 2  2 x  1

9. Draw a quadrilateral PQRS on a graph paper whose vertices are P(3, 3), Q(3, 3),
R(3, 3) and S(3, 3). What is the special name of the quadrilateral PQRS? 3

10. a. It is given that XYZ = 64 and XY is produced to point P. Draw a figure from
the given information. If ray YQ bisects ZYP, find XYQ and reflex QYP.
Or 3

-3- NB-N/M/I

b. In the given figure, if AB || CD, EF  CD and AG F B
GED = 126, find AGE, GEF and FGE.

C E D
11. In the adjoining figure, X = 62, XYZ = 54. If X
YO and ZO are the bisectors of XYZ and XZY
respectively of XYZ, then find OZY and YOZ 62
O

54
Y Z 3
12. a. In the adjoining figure, AC = AE, AB = AD and E
BAD = EAC. Show that BC = DE.
A

B D C
Or 3
b. In the adjoining figure, if TR = TS, 1 = 22 T
and 4 = 23, then prove that RBT  SAT
A B
P
1 4

2 3
R S
13. Construct a triangle ABC in which BC = 8 cm, B = 45 and AB  AC = 3.5 cm.
(Traces of construction only is required.) 3

14. a. The length, breadth and height of a room are 5m, 4m and 3m respectively.
Find the cost of white washing the walls of the room and the ceiling at the
rate of `7.50 per m2.
Or 3
b. The inner diameter of a circular well is 3.5 m. It is 10 m deep. Find:
(i) its inner curved surface area,
(ii) the cost of plastering this curved surface at the rate of `40 per m2.

15. The weight of 50 apples (in grams) from a consignment are as below:
113 131 75 82 204 81 84 118 110 104
107 80 141 111 123 136 78 90 115 90
110 98 106 99 84 107 186 76 82 109
100 115 125 107 115 93 119 187 139 129

-4- NB-N/M/I

130 68 123 195 111 125 86 92 126 70
Construct a grouped frequency distribution table for the above data taking
class width of 20 grams if the mid-value of the first class interval is 70
grams. 3

16. 1500 families with 2 children were selected randomly and the following data were
recorded:
Number of girls in a family 2 1 0
Number of families 475 814 211
Compute the probability of a family, chosen at random, having
(i) 2 girls, (ii) 1 girl, (iii) No girl.
Also check whether the sum of these probabilities is 1. 3

Section – D
17. a. Let R1 and R2 be the remainder when the polynomials x 3  2 x 2  5ax  7
and x 3  ax 2  12x  6 are divided by  x  1 and  x  2 respectively. If
2R1 + R2 = 6, find the value of a.
Or 5
b. Without actual division, prove that 2x 4  6 x 3  3x 2  3x  2 is exactly
divisible by x 2  3x  2

18. a. The taxi fare in a city is as follows:
For the first kilometre, the fare is `8 and for the subsequent distance, it is
`5 per km. Taking the distance covered as x km and total fare as `y, write a
linear equation for this information and draw its graph.
Or 5
b. The force exerted to pull a cart is directly proportional to the acceleration
produced in the body. Express this statement as a linear equation in two
variables and draw the graph of the same by taking the constant mass equal
to 6 kg. Read from the graph the force required when the acceleration
produced is: (i) 5m/sec2 (ii) 6 m/sec2.

19. a. In ABC and DEF, AB = DE, AB || DE, BC = EF
and BC || EF. Vertices A, B and C are joined to A
vertices D, E and F respectively. Show that:
(i) quadrilateral ABED is a parallelogram, D
C
(ii) quadrilateral BEFC is a parallelogram, B
(iii) AD || CF and AD = CF,
(iv) quadrilateral ACFD is a parallelogram, E F
(v) AC = DF.
Or 5
b. ABCD is a rhombus and P, Q, R and S are the mid-points of the sides AB, BC,
CD and DA respectively. Show that the quadrilateral PQRS is a rectangle.

-5- NB-N/M/I

20. a. A triangle and a parallelogram have the same base and the same area. If the
sides of the triangle are 26 cm, 28 cm and 30 cm, and the parallelogram
stands on the base 28 cm, find the height of the parallelogram.
Or 5
b. A field is in the shape of a trapezium whose parallel sides are 25 m and
10 m. The non-parallel sides are 14 m and 13 m. Find the area of the field.

21. a. A metal pipe is 77 cm long. The inner diameter of a cross
section is 4 cm, the outer diameter being 4.4 cm. Find its:
(i) inner curved surface area, (ii) outer curved surface area,
(iii) total surface area.
Or 5
b. A bus stop is barricaded from the remaining part of the road, by using 50
hollow cones made of recycled cardboard. Each cone has a base diameter of
40 cm and height 1 m. If the outer side of each of the cones is to be painted
and the cost of painting is `12 per m2, what will be the cost of painting all
these cones? (Use  = 3.14 and take 1.04  1. 02 )

22. a. The following data on the number of girls (to the nearest ten) per thousand
boys in different sections of Indian society is given below:
Section Number of girls per thousand boys
Scheduled Caste (SC) 940
Scheduled Tribe (ST) 970
Non SC/ST 920
Backward districts 950
Non-backward districts 920
Rural 930
Urban 910
Represent the information above by a bar graph.
Or 5
b. The length of 40 leaves of a plant are measured correct to one millimetre and the
obtained data is represented in the following table:

Length (in mm) 118-126 127-135 136-144 145-153 154-162 163-171 172-180
Number of leaves 3 5 9 12 5 4 2

Draw a histogram to represent the given data.

. ************************************