NBSE Class 10 Question Paper 2021 for Maths

Total number of printed pages : 5 NB-T/M/1

2021
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.
(a) The sum and product respectively of zeros of the polynomial x 2  4 x  3 are 1
1
(i) 3, 3 (ii) 4, 3 (iii) 3, 4 (iv) 4,
3
(b) The pair of equations x  y  40  0 and x  2 y  14  0 have 1
(i) a unique solution (ii) infinitely many solutions
(iii) exactly two solutions (iv) no solution

(c) The values of k for which the quadratic equation 16 x 2  4kx  9  0 has real
and equal roots are 1
1 3 3
(i) 6,  (ii) 36, –36 (iii) 6, –6 (iv) ,
6 4 4
(d) 30th term of the A.P. 10, 7, 4, … , is 1
(i) 97 (ii) 77 (iii) 77 (iv) 87
12
(e) If cot A  , then the value of sin A  cos A  cosec A is 1
5
12 5 17 5
(i) (ii) (iii) (iv)
5 17 5 13
(f) A is a point on y-axis at a distance of 4 units from x-axis lying below x-axis.
The coordinates of A are 1
(i) (4, 0) (ii) (0, 4) (iii) (–4, 0) (iv) (0, –4)

(g) If the tangents PA and PB from a point P to a circle with centre O are inclined
to each other at an angle of 80, then POA is equal to 1
(i) 50 (ii) 60 (iii) 70 (iv) 80

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7
(h) The perimeter of quadrant of a circle whose radius is cm is 1
2
(i) 3.5 cm (ii) 5.5 cm (iii) 7.5 cm (iv) 12.5 cm

(i) The radius of the sphere whose surface area is 154 cm2 is 1
(i) 14 cm (ii) 7 cm (iii) 3.5 cm (iv) 3 cm

(j) Which of the following cannot be the probability of an event? 1
2
(i) (ii) 1.5 (iii) 15% (iv) 0.7
3

Section – B
2. Use Euclid’s division algorithm to find the HCF of 135 and 225. 2

3. Find the roots of the quadratic equation 2 x 2  x  6  0 by factorisation. 2

4. Find the coordinates of the point which divides the join of (1, 7) and (4, 3) in
the ratio 2 : 3 2

5. In ABC, B = 90, BD  AC, BAD = DBC = 75. If B
AD = 6 cm and DC = 12 cm, then find the length of BD.
75

75
A D C
2
6. The radii of two circles are 19 cm and 9 cm respectively. Find the radius of the
circle which has circumference equal to the sum of the circumferences of the two
circles. 2

Section – C
7. If α and β are the zeros of the quadratic polynomial x 2  5 x  6 , find a quadratic
polynomial whose zeros are 2  1 and 2  1 3

8. a. Solve the following pair of linear equations by substitution method:
x  y  14 and x  y  4 .
Or 3
b. Find the roots of the quadratic equation 2 x  7 x  3  0 by the method of
2

completing the square.

9. a. How many three-digit numbers are divisible by 7?
Or 3

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b. An A.P. consists of 50 terms of which 3rd term is 12 and the last term is 106.
Find the 29th term.
1  tan 2 A
10. If 3 cot A = 4, then prove that  cos 2 A  sin 2 A with the help of a right
1  tan A
2

triangle. 3

1  cos 
11. a. Prove that cosec   cot  2  , where the angles involved are acute.
1  cos 
Or 3
1
b. If tan A  B   3 and tan A  B  ; 0  A  B  90 ; A  B , then find
3
A and B.

12. a. Find the ratio in which the line segment joining the points (3, 10) and (6, 8)
is divided by (1, 6).
Or 3
b. Find the area of a rhombus if its vertices are (3, 0), (4, 5), (1, 4) and
(2, 1) taken in order.

13. Draw a circle of radius 6 cm. From a point 10 cm away from its centre, construct
the pair of tangents to the circle and measure their lengths. (Traces of construction
only is required.) 3

14. a. A chord of a circle of radius 15 cm subtends an angle of 60 at the centre.
Find the areas of the corresponding minor and major segments of the circle.
(Use  = 3.14 and 3  1.73 )
Or 3
b. A well of diameter 3 m is dug 14 m deep. The earth taken out of it has been
spread evenly all around it in the shape of a circular ring of width 4 m to
form an embankment. Find the height of the embankment.

15. The following data gives the information on the observed lifetimes (in hours) of 225
electrical components: 3
Lifetimes
0-20 20-40 40-60 60-80 80-100 100-120
(in hours)
Frequency 10 35 52 61 38 29
Determine the modal lifetimes of the components.

16. A box contains 90 discs which are numbered from 1 to 90. If one disc is drawn at
random from the box, find the probability that it bears: (i) a two-digit number
(ii) a perfect square number (iii) a number divisible by 5. 3

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Section – D

17. a. The taxi charges in a city consist of a fixed charge together with the charge
for the distance covered. For a distance of 10 km, the charge paid is 105
and for a journey of 15 km, the charge paid is 155. What are the fixed
charges and the charge per km? How much does a person have to pay for
travelling a distance of 25 km?
Or 5
b. If we add 1 to the numerator and subtract 1 from the denominator, a
1
fraction reduces to 1. It becomes if we only add 1 to the denominator.
2
What is the fraction?

18. a. State and prove Basic Proportionality theorem.
Or 5
b. ABCD is a trapezium in which AB || DC and its diagonals intersect each
AO CO
other at the point O. Show that 
BO DO

19. a. The angles of elevation and depression of the top and bottom of a lighthouse
from the top of a 60 m high building are 30 and 60 respectively. Find:
(i) the difference between the height of the lighthouse and the building.
(ii) the distance between the tops of the lighthouse and the building.
(Use 3  1.732 )
Or 5
b. The angle of elevation of an aeroplane from a point A on the ground is 60.
After a flight of 30 seconds, the angle of elevation changes to 30. If the
plane is flying at a constant height of 3600 3 m, find the speed of the
aeroplane in m/s.

20. a. In the adjoining figure, XY and XY are two X P AY
parallel tangents to a circle with centre O and
another tangent AB with point of contact C O C
intersecting XY at A and XY at B. Prove that
AOB = 90
X Q B Y
Or 5
b. PAQ is a tangent to the circle with centre O at a point P C
A as shown in the adjoining figure. If OBA = 35,
A O
find the value of BAQ and ACB.
Q
B

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21. a. A wooden article was made by scooping out a
hemisphere from each end of a solid cylinder as shown
in the adjoining figure. If the height of the cylinder is 10
cm, and its base is of radius 3.5 cm, find the total surface
area of the article. Also, find the cost of painting the
wooden article at the rate of 15 per cm2
Or 5
b. A gulab jamun, contains sugar syrup up to about 30% of
its volume. Find approximately how much syrup would
be found in 45 gulab jamuns, each shaped like a cylinder
with two hemispherical ends with length 5 cm and
diameter 2.8 cm.

22. a. The following table gives production yield per hectare of wheat of 100
farms of a village. Change the distribution to a more than type distribution
and draw its ogive.
Production yield(in kg/ha) 50-55 55-60 60-65 65-70 70-75 75-80
Number of farms 2 8 12 24 38 16
Or 5
b. The median of the following data is 525. Find the values of x and y, if the
total frequency is 100.
Class interval Frequency
0-100 2
100-200 5
200-300 x
300-400 12
400-500 17
500-600 20
600-700 y
700-800 9
800-900 7
900-1000 4

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