MBOSE Class 10 Question Paper 2021 for Maths

Total No. of Printed Pages—12
X/21/M

2021

MATHEMATICS

( FOR CANDIDATES WITH INTERNAL ASSESSMENT )

Full Marks : 80
Pass Marks : 24

( FOR CANDIDATES WITHOUT INTERNAL ASSESSMENT )

Full Marks : 100
Pass Marks : 30

Time : 3 hours

( FOR ALL CATEGORIES OF CANDIDATES )

General Instructions :

(i) This Question Paper comprises of 32 questions divided
into six Sections A, B, C, D, E and F.

(ii) Marks allocated to every question are indicated against
each.

(iii) Question Nos. 1 to 30 (Section—A to Section—E) are to
be answered by all candidates.

(iv) Question Nos. 31 and 32 of Section—F are to
be answered by Candidates without Internal
Assessment.

/63 [ P.T.O.

( 2 )

(v) In question on construction, the drawing should be
neat and exactly as per the given measurements.
(vi) Questions, which are meant for Visually Handicapped
(Blind) Students, should be answered by them only.
(vii) Use of Calculator/Mobile Phone is not permitted.

SECTION—A

( Marks : 8 )

( Question Nos. 1 to 8 carry 1 mark each )

1. Find the prime factorization of 96. 1

2. Find the 5th term of the sequence an  2n  5 . 1

3. Write the discriminant of the quadratic equation
3x 2  2x  8  0 . 1

4. What is the area of an equilateral triangle of side ‘a’ ? 1

5. In how many points does a line intersect the circle at
most? 1

6. Find the area of a circle whose radius is 10·5 m.
(Use   22
7
) 1

7. Evaluate : 1
sin 60º cos 30º  cos 60ºsin 30º

8. Find the class mark of class 10–25. 1

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( 3 )

SECTION—B
( Marks : 14 )
( Question Nos. 9 to 15 carry 2 marks each )

9. Solve the quadratic equation 3x 2  x  2  0 by
factorization. 2

10. If A  30º , verify that
sin 2A  2sin A cos A 2

11. Find the value of x (0º  x  90º ) in
tan 3x  sin 45º cos 45º  sin 30º 2
Or
In  ABC , right angled at B, if AB  5 , BC  12 and
AC  13 , find sin A and tan A . 2

12. Find the distance between the pair of points (–6, 7)
and (–1, –5). 2

13. Find the coordinates of the midpoint of the line
segment joining the points P (12, –8) and Q (8, –4). 2
Or
Find the coordinates of the centroid of the triangle
whose vertices are (8, 0), (0, 6) and (8, 12). 2

14. In the figure below, AB is a common tangent to the given
circles, which touch externally at P. If AP = 3·2 cm, find
the length of AB : 2

X/21/M/63 [ P.T.O.

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[ For Visually Handicapped (Blind) Students only,
instead of Question No. 14 given in Page No. 3 ]

14. (a) Define a secant. 1

(b) A tangent cannot be drawn from a point lying within
the circle.
( State whether True or False ) 1

15.

In the above figure, ABC is a triangle. D and E are the
points on the sides AB and AC respectively, such that
DE ||BC . If AD  x cm, DB  (x  2) cm, AE  (x  2) cm
and EC  (x  1) cm, find the value of x. 2

[ For Visually Handicapped (Blind) Students only,
instead of Question No. 15 given above ]

15. (a) Define a triangle. 1

(b) The greatest side of a _____ triangle is called
hypotenuse.
( Fill in the blank ) 1

X/21/M/63 [ Contd.

( 5 )

SECTION—C
( Marks : 24 )
( Question Nos. 16 to 23 carry 3 marks each )
16. Using ruler and compass only, draw a line segment of
length 7 cm and divide it internally in the ratio 2 : 3.
(Only traces of construction are required.) 3

[ For Visually Handicapped (Blind) Students only,
instead of Question No. 16 given above ]
16. (a) When are two triangles said to be similar? 2
(b) Define an equilateral triangle. 1

17. The two tangents drawn from an external point P to a
circle with centre O are PA and PB. If APB  70º , what
is the value of AOB ? 3

Or
In the figure below, AD is the bisector of A in  ABC ,
intersecting the side BC at D. If AB  5 cm,
AC  42 cm and DC  2 1 cm, find BD : 3

X/21/M/63 [ P.T.O.

( 6 )

[ For Visually Handicapped (Blind) Students only,
instead of Question No. 17 given in Page No. 5 ]

17. (a) State Basic Proportionality Theorem. 2

(b) A tangent to a circle is _____ to the radius through
the point of contact.
( Fill in the blank ) 1

18. Find the angle subtended at the centre of a circle of
5
radius 5 cm by an arc of length cm. 3
3
Or

The difference between the circumference and the radius
of a circle is 37 cm. Find the area of the circle.
(Use   22
7
) 3

19. A bag contains 6 red balls, 8 white balls, 5 green balls
and 3 black balls. One ball is drawn at random from the
bag. Find the probability that the ball drawn is—
(a) white;
(b) red or black. 3

20. Find the HCF and LCM of 84, 90, 120 by applying
prime factorization method. 3
Or
Given that HCF (306, 657) = 9, find the LCM of 306
and 657. 3

X/21/M/63 [ Contd.

( 7 )

21. Which term in the A.P. 68, 64, 60, ..... is –8 ? 3
Or
Find the sum of 100 terms of the A.P. 2, 4, 6, ..... . 3
22. Find a quadratic polynomial whose zeroes are –5 and –7. 3
23. Evaluate : 3
4 1
  2cos2 45º  sin2 0º
2 2
cot 30º sin 30º

Or
1
If tan(A  B )  and tan(A  B )  3 , 0º  (A  B )  90º
3
and A  B , find A and B. 3

SECTION—D
( Marks : 16 )
( Question Nos. 24 to 27 carry 4 marks each )
24. The sum of two numbers is 16. The sum of their
1
reciprocals is . Find the numbers. 4
3
Or
The sum of the numerator and denominator of a fraction
is 12. If the denominator is increased by 3, the
1
fraction becomes . Find the fraction. 4
2
25. A tower stands vertically on the ground. From a point on
the ground 20 m away from the foot of the tower, the
angle of elevation of the top of the tower is 60º. What is
the height of the tower? (Use 3  1732 ) 4
Or
The string of a kite is 100 m long and it makes an angle
of 60º with the horizontal. Find the height of the kite,
assuming that there is no slack in the string.
(Use 3  1732 ) 4

X/21/M/63 [ P.T.O.

( 8 )

[ For Visually Handicapped (Blind) Students only,
instead of Question No. 25 given in Page No. 7 ]

25. (a) The value of cot 90º = _____.
( Fill in the blank ) 1
(b) If cos   1 , then   0º .
( State whether True or False ) 1

(c) Write down the relation between sin  , cos  and
tan  . 2

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

Or

If the points (2, 1) and (1, –2) are equidistant from the
point (x , y ) , prove that x  3y  0 . 4

27. Prove that, in a right triangle, the square of the
hypotenuse is equal to the sum of the squares of the
other two sides. 4

[ For Visually Handicapped (Blind) Students only,
instead of Question No. 27 given above ]

27. (a) Define a right triangle. 2

(b) The length of the diagonal of a square of side ‘a’
is _____.
( Fill in the blank ) 2

X/21/M/63 [ Contd.

( 9 )

SECTION—E
( Marks : 18 )
( Question Nos. 28 to 30 carry 6 marks each )
28. Solve the following system of linear equations graphically :
2x  y  4
3y  x  3
Also, find the points where the lines meet the axis of y.
(Plot at least three points for each graph.) 6

[ For Visually Handicapped (Blind) Students only,
instead of Question No. 28 given above ]

28. Solve the following system of linear equations : 6
2x  y  7
4x  3y  1  0

29. If the total surface area of a solid hemisphere is 462 cm2,
find its volume. (Use   227
) 6
Or
A cone of height 20 cm and radius of base 5 cm is made
up of modelling clay. A child reshapes it in the form of a
sphere. Find the diameter of the sphere. 6

30. Find the mean of the following data : 6
Marks 0–10 10–20 20–30 30–40 40–50 50–60
Number of
12 18 27 20 17 6
Students

Or
Find the mode of the following frequency distribution : 6
Class Interval 10–15 15–20 20–25 25–30 30–35 35–40
Frequency 30 45 75 35 25 15

X/21/M/63 [ P.T.O.

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SECTION—F
( Marks : 20 )
[ For Candidates without Internal Assessment ]
31. Answer the following as directed (any eight) : 1×8=8
(a) The common difference of the A.P. 4, 1, –2, –5, ..... is
(A) 3
(B) –3
(C) 4
(D) 2 ( Choose the correct option )
(b) Every composite number can be expressed as a
product of
(A) primes
(B) coprimes
(C) twin primes
(D) None of the above
( Choose the correct option )
(c) In which quadrant does the point (–2, 6) lie?
(A) 1st quadrant
(B) 2nd quadrant
(C) 3rd quadrant
(D) 4th quadrant ( Choose the correct option )
(d) The area of a circle with radius ‘r’ is

(A) r 2 square units

(B) 2r 2 square units
1 2
(C) r square units
2
(D) 3r 2 square units
( Choose the correct option )

X/21/M/63 [ Contd.

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(e) Define constant polynomial.

(f) If the polynomial ax 2  bx  c is a perfect square, then
b 2  4ac .
( State whether True or False )

(g) What is the degree of a cubic polynomial?

(h) Find the circumference of a circle whose radius is
10·5 m. (Use   22
7
)

(i) How many tangents can be drawn to a circle from a
point outside the circle?

(j) Each quadratic equation has at most two roots.
( State whether True or False )

(k) Write the value of sec 60º .

(l) The total surface area of a right circular cylinder of
radius ‘r’ and height ‘h’ is _____.
( Fill in the blank )

(m) A polynomial having _____ terms is called binomial.
( Fill in the blank )

(n)  is an irrational number.
( State whether True or False )

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( 12 )

32. Answer any six from the following : 2×6=12

(a) Express 0·125 as a rational number.

(b) Find the zeroes of the polynomial x 2  2x  3 .

(c) Find the distance between the pair of points (a , 0)
and (0, b ) .

(d) A chord of a circle of radius 14 cm subtends a right
angle at the centre. What is the area of the minor
sector? (Use   22
7
)

(e) A die is thrown once. What is the probability of
getting a number other than 4?

(f) The difference between two numbers is 26 and one
number is three times the other. Find the numbers.

(g) Find the coordinates of the midpoint of the line
segment joining the points P (7, 0) and Q (–5, 4) .

(h) Find the sum of the first 100 natural numbers.

(i) Find the value of x (0º  x  90º ) in 2cos 3x  1.

(j) If ,  are zeroes of the polynomial P (x )  3x 2  2x  6 ,
1 1
then find  .
 

(k) Determine the value of ‘k’ for which x  1 is a
solution of the equation x 2  kx  3  0 .

  

X/21/M/63 11-21—70050