MBOSE Class 12 Question Paper 2026 for Mathematics

FOR MBOSE CLASS 12 EXAM PREPARATION

MBOSE Class 12 2026
Question Paper ·
Mathematics
EXAM YEAR TYPE SUBJECT

MBOSE Class 12 2026 Question Paper Mathematics

Notes · Sample Papers · Previous Year Papers · Mock Tests

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HS/XII/A. Sc. Com/M/26
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MATHEMATICS

Full Marks : 80

Time : 3 hours

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The figures in the margin indicate full marks for the questions.

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General Instructions :

a
Read the following instructions verygcarefully
them.

(i) This Question Paper contains 38 questions. All questions
are compulsory.

(ii) This Question Paper is divided into five Sections—A, B, C,
D and E.
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(iii) Section—A comprises of 20 questions (Q. Nos. 1 to 20) of
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1 mark each. Question Nos. 11 to 20 are multiple choice

l as questions (MCQs).
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2 marks each.

Section—C comprises of 6 questions (Q. Nos. 26 to 31) of
3 marks each.

/66 [ P.T.O.

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( 2 )

Section—D comprises of 3 questions (Q. Nos. 32 to 34) of
4 marks each.

Section—E comprises of 4 questions (Q. Nos. 35 to 38) of
5 marks each.

(iv) There is no overall choice. However an internal choice has
been provided in 3 questions in Section—B, 3 questions
in Section—C, 1 question in Section—D and 3 questions
in Section—E.

(v) Use of calculator is not allowed.

SECTION—A
( Marks : 20 )

é 0 -1 ù é3 5ù
1. Find AB, if A = ê ú and B = ê ú. 1
ë0 2 û ë0 0û

2. Find the value of k, if the function defined by

ì kx 2, if x £1
f (x ) = í
î 5 , if x >1

is continuous at x = 1. 1

dy
3. Find for the following : 1
dx
2x + 3y = sin y

HS/XII/A. Sc. Com/M/26/66 [ Contd.

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( 3 )

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dy

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4. Find , if x = a cos q and y = a sin q. 1
dx
e m
e m l as
5. Evaluatela
s
1 dx
ag
ag ò 0 1 + x 2
. 1

6. Verify that y = e x + 1 is a solution of the differential
equation y ¢¢ - y ¢ = 0. 1

7. Find the anti-derivative of 3x 2 + 4x 3 . 1

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1
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5 4
8. Evaluate ò sin x cos x dx. 1
-1

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g R, given by f (x ) = 2x, is
9. Prove that the function f : R a®
both one-one and onto. 1

10. Find the unit vector in the direction of the vector
r
a = i$ + $j + 2k$ . 1

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Choose the correct answer :
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11. Let R be a relation in the set { 1, 2, 3, 4 } given by
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R = { (1, 2), (2, 2), (1, 1), (4, 4), (1, 3), (3, 3), (3, 2) } . Then
g
l a (a) R is reflexive and symmetric but not transitive a
ag (b) R is reflexive and transitive but not symmetric
(c) R is symmetric and transitive but not reflexive
(d) R is an equivalence relation 1

HS/XII/A. Sc. Com/M/26/66 [ P.T.O.

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( 4 )

12. Let f : R ® R be defined as f (x ) = x 4 . Then

(a) f is one-one and onto

(b) f is many-one and onto

(c) f is one-one but not onto

(d) f is neither one-one nor onto 1

æ 3ö
13. The principal value of cos -1 ç ÷ is
è 2 ø

p
(a)
6
p
(b)
3
p
(c)
4
p
(d) 1
2

3 x 3 2
14. If = , then the value of x is
x 1 4 1

(a) ± 2 2

(b) ± 2

(c) 2

(d) -2 1

HS/XII/A. Sc. Com/M/26/66 [ Contd.

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( 5 )

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15. The order and degree of the differential equation
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4
æ dy ö d 2y
ç ÷ + 3y
è dx ø
e
dx 2 m
= 0 are respectively
l as
as
l 4 ag
ag
(a) 2 and

(b) 4 and 2

(c) 2 and 1

(d) 1 and 2 1

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16. The rate of change of area of a circle with respect to its
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radius r at r = 6 cm is
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(a) 10 p cm
a
(b) 12 p cm

(c) 8 p cm

(d) 11 p cm 1

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i + j+
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17. The magnitude of the vector k is

m (a) 0
3 3 3
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a (b) 3

(c) 1

(d) -1 1

HS/XII/A. Sc. Com/M/26/66 [ P.T.O.

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( 6 )

18. The value of i$ × ( $j ´ k$ ) + $j × ( i$ ´ k$ ) + k$ × ( i$ ´ $j ) is

(a) 0

(b) -1

(c) 1

(d) 3 1

1
19. If P (A ) = and P (B ) = 0, then P (A|B ) is
2

(a) 0

1
(b)
2

(c) 1

(d) Not defined 1

1 1
20. Let E and F be events with P (E ) = , P (F ) = and
3 2
1
P (E Ç F ) = . Then
6

(a) E and F are independent events

(b) E and F are mutually exclusive events

(c) E and F are disjoint events

(d) None of the above 1

HS/XII/A. Sc. Com/M/26/66 [ Contd.

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( 7 )

m
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c. o ( Marks : 10 ) m .co
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21. Simplify l:a ag
ag é cos q sin q ù
2

é sin q - cos q ù
cos q ê ú + sin q ê cos q sin q ú
ë - sin q cos q û ë û

Or

Show that the matrix

é 1 -1 5 ù m
A = ê -1 2 1 ú
ê ú
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êë 5 1 3 úû
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is a symmetric matrix. a
22. Find the value of k if the area of a triangle whose vertices
are (k, 0), (4, 0) and (0, 2) is 4 square units. 2

Or

é 1 1 -2 ù
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If A = ê 2 1 -3 ú, then find |A|.
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ê ú
êë 5 4 -9 úû
e m
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s
la 23. Is the function defined by ag
ag
ì x + 5 , if x £ 1
f (x ) = í
î x - 5 , if x >1

a continuous function at x = 1 ? 2

HS/XII/A. Sc. Com/M/26/66 [ P.T.O.

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( 8 )

Or

Find the point of discontinuity of the function f defined
by

ì 2x + 3 , if x £2
f (x ) = í
î 2x - 3 , if x >2

(log x )2
24. Evaluate ò dx. 2
x

25. If P (A ) = 0 × 8, P (B ) = 0 × 5 and P (B |A ) = 0 × 4, then find—

(a) P (A Ç B )

(b) P (A È B ) 2

SECTION—C
( Marks : 18 )

xe x
26. Evaluate ò dx. 3
(1 + x )2

Or
2x
Evaluate ò dx.
2
x + 3x + 2

27. The radius of a circle is increasing uniformly at the rate of
3 cm/s. Find the rate at which the area of the circle is
increasing when the radius is 10 cm. 3

HS/XII/A. Sc. Com/M/26/66 [ Contd.

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( 9 )

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r
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28. Find the projection of the vector a = 2i$ + 3 $j + 2k$ on the

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vector b = i$ + 2 $j + k$ .
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3
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Find athe angle between the vectors i$ - 2 $j + 3k$ and
3i$ - 2 $j + k$ .

29. Find the equation of the line in vector and Cartesian
form that passes through the point with position
vector 2i$ - $j + 4k$ and in the direction of i$ + 2 $j - k$ .
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3

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30. A particle moves along the curve 6y = x 3 + 2. Find
la the y-coordinate is
changing 8 times as fast as a
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the points on the curve at which
the x-coordinate. 3

p /2 sin x
31. Evaluate ò dx by using the properties of
0 cos x + sin x
definite integrals. 3
Or
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1
Prove that ò x 17 cos4 x dx = 0.
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SECTION—D
g a
a ( Marks : 12 )

32. Find the area of the region bounded by the ellipse
x2 y2
+ = 1. 4
16 9

HS/XII/A. Sc. Com/M/26/66 [ P.T.O.

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( 10 )

Or

Find the area enclosed by the circle x 2 + y 2 = a 2 .

33. Solve graphically : 4
Maximize Z = 5x + 3y
subject to
3x + 5y £ 15
5x + 2y £ 10
x ³ 0, y ³ 0

34. In each of the following cases, state whether the function
is one-one, onto or bijective. Justify your answer : 4

(a) f : R ® R defined by f (x ) = 3 - 4x

(b) f : R ® R defined by f (x ) = 1 + x 2

SECTION—E
( Marks : 20 )

35. Prove that the volume of the largest cone that can be
8
inscribed in a sphere of radius R is of the volume of the
27
sphere. 5
Or

Show that the semi-vertical angle of the right circular
cone of the maximum volume and of given slant height is
tan -1 2.

HS/XII/A. Sc. Com/M/26/66 [ Contd.

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( 11 )

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36. Find the shortest distance between the lines
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r
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r = ( i$ + 2 $j + k$ ) + l ( i$ - $j + k$ )
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s e r
l a
ag
and r = ( 2i$ - $j - k$ ) + m ( 2i$ + $j + 2k$ )
g l a 5

a Or

Find the vector equation of the line passing through the
point (1, 2, - 4 ) and perpendicular to the two lines
x - 8 y + 19 z - 10 x - 15 y - 29 z - 5
= = and = = .
3 -16 7 3 8 -5

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37. Solve the following system of linear equations using

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matrix method : 5
x -y + z = 4 e m
2x + y - 3z = 0 las
x+y+z =2 ag
Or

Verify A (adjA ) = (adj A) A = |A|I for the matrix

é 1 -1 2 ù
A = ê 3 0 -2 ú
ê ú
êë 1 0 3 úû
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38. There are three coins. One is a two-headed coin (having
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g la up heads 75% of the time and third is an unbiased coin.
a
a One of the three coins is chosen at random and tossed, it
shows heads. What is the probability that it is the two-
headed coin? 5

HHH

HS/XII/A. Sc. Com/M/26/66 26K—6160

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