MBOSE Class 10 Question Paper 2026 for Mathematics

FOR MBOSE CLASS 10 EXAM PREPARATION

MBOSE Class 10 2026
Question Paper ·
Mathematics
EXAM YEAR TYPE SUBJECT

MBOSE Class 10 2026 Question Paper Mathematics

Notes · Sample Papers · Previous Year Papers · Mock Tests

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m .co s e m
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a

Total No. of Printed Pages—16
X/26/M

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2026

m s e
s e l a
g l a MATHEMATICS
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a Full Marks : 80
Pass Marks : 24

Time : 3 hours

The figures in the margin indicate full marks for the questions

General Instructions :
m
(i) Please check that this Question c. o Paper contains
55 questions.
e m
(ii) For candidates without a
l s
g
Internal Assessment their
a
marks will be multiplied by 1·25 to adjust their total to a
maximum of 100 marks.
(iii) 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
Script.
o m
m . c
. co C and D.
(iv) The Question Paper contains 4 Sections, Sections A,
s e
B,
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s em (v) Section—A contains Multiple Choice Questions (MCQ). g l a
g la a given
a Choose the most appropriate answer from the
options. The answers to this Section must be provided
in the boxes provided in the Answer Script. Answers
given anywhere else will not be counted for
marking.

/2 [ P.T.O.

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( 2 )

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

SECTION—A

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

1. The quadratic polynomial with 0 and − as its two
zeroes is

(A) +

(B) −

(C) +
(D) − 1

2. If = and = is the solution of the equations
− = and + = , then the values of a and b are
respectively
(A) 3 and 5
(B) 3 and 1
(C) 5 and 3
(D) – 1 and – 3 1

X/26/M/2 [ Contd.

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m
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( 3 )

m
.co
3. If = is a solution of the quadratic equation
m
.co
+ − + = , then k is equal to
e m
(A) 11
em l as
l
(B) –11as ag
g
a 13
(C)
(D) –13 1

4. The ratio of LCM and HCF of the least composite and the
least prime numbers is
(A) 1 : 2

m
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(B) 2 : 1

em
(C) 1 : 1
(D) 1 : 3
las 1
g
a lies above or below the
5. If the graph of a polynomial
x-axis without touching or intersecting it, then the
number of its zeroes is
(A) 0
(B) 1
(C) 2
m
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(D) 3 1

c. o6. What is the 100th term of the sequence 1, 1, 1, 1, 1, ...s?em 1
s em g l a
la (A) 1
a
ag (B) 100
(C) 50
(D) 200

X/26/M/2 [ P.T.O.

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( 4 )

7. The coordinates of reflection of the point − − in
the x-axis are
(A) (– 1, 3)
(B) (1, 3)
(C) (1, – 3)
(D) (– 1, – 3) 1

°
8. The value of is equal to
− °
(A) cos 60°
(B) sin 60°
(C) tan 60°
(D) sin 45° 1

9. If − + = has real and equal roots, then the
value of k is
(A) 1
(B) 2
(C) ±
(D) 4 1

10. The perimeter of an equilateral triangle with side 9 cm is
(A) 9 cm
(B) 18 cm
(C) 36 cm
(D) 27 cm 1

X/26/M/2 [ Contd.

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( 5 )

11. From a point Q, the length of the tangent to a circle is
m
m
4 cm and the distance of Q from the centre is 5 cm. Then
.co
.co
the radius of the circle is
s e m
(A) 4 cm
s em l a
(B) l3acm ag
ag 5 cm
(C)
(D) 1 cm 1

12. The area of a sector of angle P (in degrees) of a circle with
radius R is

(A) × π
m
m .co
(B) ×π
s e
g la
(C) × π a
(D) × π 1

13. If r and h represent the radius of the base and height of
m
.co
a right circular cone respectively, then its curved surface
m
.co
area is
e m
e m (A) π
l as
las ag
ag (B) π

(C) π

(D) π + 1

X/26/M/2 [ P.T.O.

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( 6 )

14. If ∆ and ∆ are two triangles in which

= , then the two triangles are similar if

(A) ∠ =∠
(B) ∠ =∠
(C) ∠ =∠
(D) ∠ =∠ 1

15. The sum of the values of all the observations divided by
the total number of observations is called
(A) mode
(B) median
(C) mean
(D) frequency 1

16. If the probability of a player winning a game is 0·79, then
the probability of his losing the same game is
(A) 0·21
(B) 1·79
(C) 0·31
(D) 0·11 1

17. The product and sum of the zeroes of the quadratic
polynomial + + respectively are
−
(A)

(B)

(C)

−
(D) 1

X/26/M/2 [ Contd.

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( 7 )

18. If tangents PA and PB from a point P to a circle with
m
m
centre O are inclined to each other at an angle of 80°,
.co
then ∠
m .co
is equal to
s e m
(A) 50°
se l a
a
(B) l60° ag
ag 70°
(C)
(D) 80° 1

19. If a pair of linear equations is consistent, then the lines
will be
(A) parallel
m
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(B) always coincident
(C) intersecting or coincident
e m
(D) always intersecting
las 1
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20. If TP and TQ are the two tangents to a circle with centre
O so that ∠ = ° , then ∠ is equal to
(A) 60°
(B) 70°
(C) 80°
m
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(D) 90° 1
m
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m 21. The angle described by a minute hand in 1 hour lisase
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l a a
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(A) 360°
(B) 180°
(C) 120°
(D) 60° 1

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( 8 )

22. Let R and r be the outer and inner radii of a spherical
shell, then its volume is equal to

(A) π −

(B) π −

(C) π −

(D) π − 1

23. If − − = , then the values of x are
(A) 2, 5
(B) 2, – 5
(C) – 2, – 5
(D) – 2, 5 1

24. The distance of the point from the x-axis is
(A) 5 units
(B) 3 units
(C) 2 units
(D) 1 unit 1

25. If the diameter of a sphere is d, then its volume is

(A) π

(B) π

(C) π

(D) π 1

X/26/M/2 [ Contd.

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( 9 )

26. If the mean of 6, 8, 5, 7, 4 and x is 7, then x is equal
m
to
m .co
(A) 12
m .co s e m
s e l a
a ag
(B) 24
(C)gl28
a
(D) 30 1

27. The value of − is equal to
(A) 1
(B) 9
m
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(C) 8
(D) 0
s em 1

g la event is
a
28. The probability of an impossible
(A) – 0·5
(B) 1

(C)

(D) 0 1

o m
m The perimeters of two similar triangles are 24 cm and .c
co 18 cm respectively. If one side of the first triangle is 8 cm, m
29.
. s e
s em then the corresponding side of the second triangle is a
g l
l a a
ag
(A) 6 cm
(B) 8 cm
(C) 10 cm
(D) 12 cm 1

X/26/M/2 [ P.T.O.

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( 10 )

30. Which of the following can be the probability of an event? 1
(A) –1·5
(B) 1·005

(C)

(D)

SECTION—B

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

31. Find the HCF and LCM of 12, 15 and 21 by applying the
prime factorisation method. 2

32. On comparing the ratios , and , find out

whether the lines, representing the following pair of
linear equations, intersect at a point, are parallel or
coincident : 2
+ + =
+ + =

33. Represent the given situations in the form of a quadratic
equation : 2
The area of a rectangular plot is 528 m2. The length of
the plot (in metres) is one more than twice its breadth.

34. Find the value of

°+ °− ° 2

X/26/M/2 [ Contd.

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( 11 )

35. Prove that
m
− m
c. oθθ = m .co
θ− θ 2
s e
em a
+
s l
la
36. 12gdefective
ag
a It is not
ones.
pens are accidentally mixed with 132 good
possible to just look at a pen and tell
whether or not it is defective. One pen is taken out at
random from this lot. Determine the probability that the
pen taken out is a good one. 2

37. If ∆ ∼∆ such that = and = ,
find the length of EF.
m
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s e
g la
a
2

[ For Visually Impaired Candidates only,
instead of Question No. 37 given above ]

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37. When are two triangles said to be similar?
e m
e m l as
las 38. Show that + is an irrational number.
ag 2
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39. Explain why × × + and × × × × + are
composite numbers. 2

X/26/M/2 [ P.T.O.

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( 12 )

SECTION—C

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

40. Find a quadratic polynomial whose zeroes are
−
and . 3

41. Is it possible to design a rectangular park of perimeter
80 m and area 400 m2 ? If so, find its length and
breadth. 3

42. Find the values of a for which the distance between the
points − and is 5 units. 3

43. Find the ratio in which the line segment joining the
points (– 3, 10) and (6, – 8) is divided by (– 1, 6). 3

44. A circle touches the side BC of ∆ at P and touches
AB and AC produces at Q and R respectively. Prove that

= (Perimeter of ∆ ).

3

X/26/M/2 [ Contd.

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( 13 )

[ For Visually Impaired Candidates only,
m
c o m
instead of Question No. 44 given on Page No. 12 ]
m .co
m .a circle. s e
44. (a) Define
s e perimeter of a triangle. 2
l a
l a
(b) Define
g
1
ag
a
45. In the figure below, if = , prove that = .

m
.co 3

s em
g la Candidates only,
a
[ For Visually Impaired
instead of Question No. 45 given above ]

45. (a) Define scalene triangle. 2

(b) State whether True or False : 1
The length of a tangent from an external point on a
circle is always less than the radius of the circle.

o m
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. co
46. Find the area of a quadrant of a circle whose
s e m
s em circumference is 22 cm. (Use π = )
g l a 3
l a a
ag 47. Find the median, if—
l = lower limit of the median class = 125
n = number of observations = 68

X/26/M/2 [ P.T.O.

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( 14 )

cf = cumulative frequency of the class preceding
the median class = 22
f = frequency of the median class = 20
h = class size = 20 3

48. The following table shows the ages of the patients
admitted in a hospital during a year :

Find the mode. 3

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

49. If the sum of the first 7 terms of an AP is 49 and that
of 17 terms is 289, find the sum of the first n terms. 5

50. Prove that the lengths of tangents drawn from an
external point to a circle are equal. 5

[ For Visually Impaired Candidates only,
instead of Question No. 50 given above ]

50. (a) Define a tangent. 2
(b) How many tangents can be drawn through a point
lying on the circle? 1
(c) Fill in the blank : 2
The distance between two parallel tangents to a
circle of radius 3 cm is _____.

X/26/M/2 [ Contd.

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( 15 )

51. In the figure below, ABC and AMP are two right triangles,
m
m
right angled at B and M respectively. Prove that
.co
(i) ∆
m .co
∼∆ !
s e m
s e l a
(ii) a =
g l ! ag
a

5

o m
. c
m
[ For Visually Impaired Candidates only,
instead of Question No. e51 given above ]
51. (a) Define a right-angled g las
a
(b) Define similar figures.
triangle. 2
2
(c) State whether True or False : 1
The greatest side of a right-angled triangle is called
hypotenuse.

52. The angle of elevation of the top of a building from the
foot of the tower is 30° and the angle of elevation of the
m
.c5o
top of the tower from the foot of the building is 60°. If the
m
.co
tower is 50 m high, find the height of the building.
e m
e m [ For Visually Impaired Candidates only,
l as
las instead of Question No. 52 given above ]
ag
ag 52. (a) Define the line of sight. 2
(b) State whether True or False : 1
cot A is the product of cot and A.
(c) Express θ in terms of θ and θ. 2

X/26/M/2 [ P.T.O.

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( 16 )

53. Two cubes each of volume 64 cm3 are joined end to end.
Find the surface area of the resulting cuboid. 5

54. Five years hence, the age of a man will be three times
that of his son. Five years ago, the man’s age was seven
times that of his son. What are their present ages? 5

55. The following table gives the literacy rate (in percentage)
of 35 cities. Find the mean literacy rate : 5

"

HHH

X/26/M/2 26K—53970

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