MBOSE Class 10 Question Paper 2025 for Maths

Meghalaya Board of School Education

QUESTION
PAPERS

Total No. of Printed Pages—16
X/25/M (NC)

2025

MATHEMATICS

( New Course )

( FOR REGULAR CANDIDATES )

Full Marks : 80
Pass Marks : 24

Time : 3 hours

The figures in the margin indicate full marks for the questions

General Instructions :
(i) Please check that this Question Paper contains
55 questions.
(ii) 15 minutes time is given for the candidates to read the
Question Paper. The Question Paper will be distributed
15 minutes before the scheduled time of the
examination. In these 15 minutes, the candidates
should only read the instructions and questions
carefully and should not write answers on the Answer
Sheet.
(iii) The Question Paper contains 4 Sections, Sections A, B,
C and D.
(iv) Section—A contains Multiple Choice Questions (MCQ).
Choose the most appropriate answer from the given
options. The answers to this Section must be provided
in the boxes provided in the Answer Sheet. Answers
given anywhere else will not be counted for
marking.

/3 [ P.T.O.

( 2 )

(v) Section—B contains Very Short Answer-type
Questions. Answer the questions briefly, in minimum
3 steps.
(vi) Section—C contains Short Answer-type Questions.
Answer the questions in minimum 5 steps.
(vii) Section—D contains Long Answer-type Questions.
Answer the questions in minimum 8 steps.
(viii) Use of calculators/mobile phone/any electronic device
is NOT ALLOWED.

SECTION—A

Multiple Choice Questions (Attempt all questions) : 1×30=30

1. For any two positive integers p and q ,
HCF(p, q ) × LCM(p, q ) is equal to

(A) p q (B) p q

p
(C) p q (D) q 1

2. If a pair of linear equations has infinitely many solutions,
then the lines representing them will be

(A) parallel

(B) intersecting or coincident

(C) always intersecting

(D) always coincident 1

X/25/M (NC)/3 [ Contd.

( 3 )

3. The product of prime factors of 156 is

(A) 2  3  13 (B) 22  3  13

2
(C) 2  3  13 (D) 22  32  13 1

4. A quadratic polynomial can have at most

(A) 1 zero (B) 2 zeroes

(C) 3 zeroes (D) 4 zeroes 1

5. A square and a rhombus are always

(A) similar

(B) congruent

(C) similar but not congruent

(D) neither similar nor congruent 1

6. For any polynomial p(x ) , if p(a )  0 , then a is called

(A) constant of the polynomial

(B) zero of the polynomial

(C) degree of the polynomial

(D) coefficient of the polynomial 1

X/25/M (NC)/3 [ P.T.O.

( 4 )

7. The pair of equations x  0 and y  0 has

(A) no solution

(B) one solution

(C) two solutions

(D) infinitely many solutions 1

8. If the roots of the equation ax 2  bx  c  0 are equal,
then c equals to

b b
(A) (B) 
2a 2a

b2 b2
(C) (D)  1
4a 4a

9. The solution of (x  4)(x  2)  0 is

(A) 4, –2 (B) –4, 2

(C) 2, –2 (D) 4, 2 1

10. Which of the following is an AP ? 1

(A) 2, 4, 8, 16, ...

(B) 0, –4, –8, –12, ...

(C) 1, 3, 9, 27, ...

(D) 0·2, 0·22, 0·222, 0·2222, ...

X/25/M (NC)/3 [ Contd.

( 5 )

11. If 5n  3 is the nth term of an AP, then the common
difference is

(A) 15 (B) 12

(C) 5 (D) 1 1

12. If the bisector of an angle of a triangle bisects the
opposite side, then the triangle is

(A) scalene (B) isosceles

(C) equilateral (D) right angled 1

13. The distance of any point P (x , y ) from the origin is

(A) x 3  y3 (B) y2  x 2

(C) x2  y2 (D) x 2  y2 1

14. The area of an equilateral triangle of side a is

2 3
(A) 3a 2 (B)
a

3a 3a 2
(C) (D) 1
4 4

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( 6 )

 (   ) 
15. If cos(  )  0 , then the value of cos   is equal to
 2 

1 1
(A) (B)
2 2

(C) 0 (D) 2 1

16. If   30º , then the value of cos2   sin2  is
1
(A) 1 (B) 
2

1
(C) (D) 1 1
2

a 
17. If the point P  , 4  is the midpoint of the line segment
3 
joining the points A(6, 5) and B (2, 3) , then a equals to

(A) –6 (B) –4
(C) –12 (D) 12 1

18. The distance between two parallel tangents of a circle of
radius 8 cm is
(A) 8 cm (B) 12 cm
(C) 14 cm (D) 16 cm 1

19. A part of the circle whose end points are the end points
of a diameter is called
(A) circumference (B) segment
(C) semicircle (D) perimeter 1

X/25/M (NC)/3 [ Contd.

( 7 )

20. The number of tangents that can be drawn to a circle
from a point inside it is

(A) one (B) two

(C) infinite (D) none 1

21. If the area and circumference of a circle are numerically
equal, then its diameter is

(A) 6 units (B) 4 units

(C) 3 units (D) 2 units 1

22. The total surface area of a hemispherical object of radius
r units is

(A) r 2 sq. units (B) 2r 2 sq. units

(C) 3r 2 sq. units (D) 4r 2 sq. units 1

23. When the degree measure of the angle at the centre
is 360º, then the area of the sector is

 r 2
(A)  r 2 (B)
360º 360º

r 
(C) r 2 (D) 1
180º

X/25/M (NC)/3 [ P.T.O.

( 8 )

24. If the radius of a sphere is doubled, then the ratio of the
volumes of the first sphere to the new sphere is

(A) 1 : 2 (B) 1 : 4

(C) 1 : 6 (D) 1 : 8 1

25. If the curved surface area of a cone is 308 cm2 and its
slant height is 14 cm, then the radius of its base is
22
(take   )
7

(A) 14 cm (B) 7 cm

(C) 21 cm (D) 28 cm 1

26. In a frequency distribution, the class having the
maximum frequency is called

(A) class mark (B) class size

(C) median class (D) modal class 1

1
27. The value of (lower limit + upper limit) of any class
2
interval is called

(A) class size (B) frequency

(C) class mark (D) range 1

X/25/M (NC)/3 [ Contd.

( 9 )

28. If an event cannot occur, then its probability is

3
(A) 1 (B)
4

1
(C) (D) 0 1
2

29. A die is thrown once, then the probability of getting a
number less than 3 is

1 1
(A) (B)
2 3

1 1
(C) (D) 1
4 6

30. A jar contains 25 marbles with 10 green marbles and the
rest are blue marbles. If a marble is drawn at random
from the jar, then the probability that the drawn marble
is blue is

1 2
(A) (B)
5 5

3 4
(C) (D) 1
5 5

X/25/M (NC)/3 [ P.T.O.

( 10 )

SECTION—B

Very Short Answer-type Questions (Answer any six) : 2×6=12

31. Find the least number which is exactly divisible by 15,
24 and 30. 2

32. Given that HCF(306, 657) = 9, find the LCM(306, 657). 2

33. Form a pair of linear equations for the problem given
below : 2
The coach of a cricket team buys 7 bats and 6 balls for
R 3,800. Later, she buys 3 bats and 5 balls for R 1,750.

34. Find the value of k for which the quadratic equation
kx (x  2)  6  0 has two equal real roots. 2

35.

In the figure given above, in ABC , DE BC . Find AD
where BD = 7·2 cm, AE = 1·8 cm and EC = 5·4 cm. 2

[ For Visually Handicapped (Blind) Students only,
instead of Question No. 35 given above ]

35. When are two triangles said to be similar? 2

X/25/M (NC)/3 [ Contd.

( 11 )

36. Find the value of

5 cos2 60º 4 sec2 30º  tan2 45º
2
sin2 30º  cos2 30º

1  tan2 A
37. Express in terms of tan A . 2
1  cot2 A

38. A box contains balls numbered 3 to 50. A ball is drawn
at random from the box. Find the probability that the
drawn ball has a number which is a perfect square. 2

39. Prove that 7 5 is irrational. 2

SECTION—C

Short Answer-type Questions (Answer any six) : 3×6=18

40. Find the zeroes of the quadratic polynomial x 2  2x  8
and verify the relationship between the zeroes and the
coefficients. 3

41. Find a relation between x and y such that the point
(x , y ) is equidistant from the points (7, 1) and (3, 5). 3

42. The age of a man is twice the square of the age of his
son. Eight years hence, the age of the man will be
4 years more than three times the age of his son.
Find their present ages. 3

X/25/M (NC)/3 [ P.T.O.

( 12 )

43. Find the coordinates of a point A, where AB is the
diameter of a circle whose centre is (2, –3) and B is (1, 4). 3

44. From a point Q, the length of a tangent to a circle is
24 cm and the distance of Q from the centre is 25 cm.
Find the diameter of the circle. 3

[ For Visually Handicapped (Blind) Students only,
instead of Question No. 44 given above ]

44. (a) Define tangent to a circle. 1

(b) How many tangents can be drawn from an external
point to a circle? 1

(c) How many tangents are there at a point of the
circle? 1

45. Prove that a parallelogram circumscribing a circle is a
rhombus. 3

[ For Visually Handicapped (Blind) Students only,
instead of Question No. 45 given above ]

45. (a) The tangent at any point of a circle is _____ to the
radius through the point of contact. (Fill in the
blank) 1

(b) Define a secant of a circle. 1

(c) The common point of a tangent to a circle and the
circle is called the point of contact. (State whether
True or False) 1

X/25/M (NC)/3 [ Contd.

( 13 )

46. The length of the minute hand of a clock is 14 cm. Find
the area swept by the minute hand between 9 a.m. to
22
9:05 a.m. (take   ). 3
7

47. The following frequency distribution gives the monthly
consumption of electricity of 68 consumers of a locality :

Monthly consumption (in units) Number of consumers
65–85 4
85–105 5
105–125 13
125–145 20
145–165 14
165–185 8
185–205 4

Based on the above information, answer the following
questions :

(a) Find the median class of the data.

(b) Find the class mark of the median class. 3

48. A student noted the number of cars passing through a
spot on a road for 100 periods each of 3 minutes and
summarized it in the table below :

Number of cars 0–10 10–20 20–30 30–40 40–50 50–60 60–70 70–80
Frequency 7 14 13 12 20 11 15 8

Find the mode of the data. 3

X/25/M (NC)/3 [ P.T.O.

( 14 )

SECTION—D

Long Answer-type Questions (Answer any four) : 5×4=20

49. The first term of an AP is 5, the last term is 45 and the
sum is 400. Find the number of terms and the common
difference. Write the first three terms of the AP. 5

50. Prove that if a line is drawn parallel to one side of a
triangle to intersect the other two sides in distinct points,
the other two sides are divided in the same ratio. 5

[ For Visually Handicapped (Blind) Students only,
instead of Question No. 50 given above ]

50. (a) Define similar figures. 2

(b) Two polygons of same number of sides are
similar, if (i) their corresponding angles are _____
and (ii) their corresponding sides are _____. (Fill in
the blanks) 2

(c) If a line divides any two sides of a triangle in the
same ratio, then the line is parallel to the third side.
(State whether True or False) 1

51. The diagonals of a quadrilateral ABCD intersect each
AO CO
other at point O such that  . Show that
BO DO
ABCD is a trapezium. 5

X/25/M (NC)/3 [ Contd.

( 15 )

[ For Visually Handicapped (Blind) Students only,
instead of Question No. 51 given on Page No. 14 ]

51. (a) Define scalene triangle. 2

(b) Define trapezium. 2

(c) The distance between two parallel lines is same
everywhere. (State whether True or False) 1

52. From a point on the ground, the angles of elevation
of the bottom and the top of a transmission tower
fixed at the top of a 20 m high building are 45º and
60º respectively. Find the height of the tower
(use 3  1  732 ). 5

[ For Visually Handicapped (Blind) Students only,
instead of Question No. 52 given above ]

1
52. (a) If sin   , then find the value of  . 2
2

(b) Define angle of elevation. 2

(c) The greatest side of a right-angled triangle is called
_____. (Fill in the blank) 1

53. From a solid cylinder whose height is 2·4 cm and
diameter 1·4 cm, a conical cavity of the same height
and same diameter is hollowed out. Find the total
surface area of the remaining solid to the nearest cm2
22
(use   ). 5
7

X/25/M (NC)/3 [ P.T.O.

( 16 )

54. Find the value of k such that the quadratic polynomial
x 2  (k  6)x  2(2k  1) has sum of the zeroes as half of
their product. 5

55. Consider the following distribution of daily wages of 50
workers of a factory :

Daily wages (in R) 500–520 520–540 540–560 560–580 580–600

Number of workers 12 14 8 6 10

Find the mean daily wages of the workers of the factory
by using an appropriate method. 5

  

X/25/M (NC)/3 K25—50560

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