MH 12th Question Paper June 2026 Maths (Arts & Science)

FOR MAHARASHTRA BOARD (MSBSHSE) CLASS 12 EXAM PREPARATION

Maharashtra Board
(MSBSHSE) Class 12
2026
June Session Question
Paper · Maths (Arts &
Science)
EXAM YEAR

Maharashtra Board (MSBSHSE) Class 12 2026
TYPE SUBJECT

June Session Question Paper Maths (Arts & Science)

Notes · Sample Papers · Previous Year Papers · Mock Tests

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Page No. 1/8 Subject Code J-276 a
Seat No.

Page No. 1/8 Subject Code J-276 Seat No.

DATE : 24/06/2026 E
SUBJECT : MATHEMATICS & STATISTICS
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Time : 11.00 - 2.00
(ARTS & SCIENCE) (40)
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DURATION : 3 Hours. c s e
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General instructions :

The question paper is divided into FOUR sections.

(i) Section A : Q. 1 contains Eight multiple choice type questions, each carrying
Two marks.

Q. 2 contains Four very short answer type questions, each carrying
One mark.
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(ii) Section B : Q. 3 to Q. 14 contain Twelve short answer type questions, each
carrying Two marks.
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(Attempt any Eight)
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(iii) a Twelve short answer type questions, each
Section C : Q. 15 to Q. 26 contain
carrying Three marks.
(Attempt any Eight)

(iv) Section D : Q. 27 to Q. 34 contain Eight long answer type questions, each
carrying Four marks.

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(Attempt any Five)

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(v)
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m Use of log table is allowed. Use of calculator is not allowed.
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em(vii) Use of graph paper is not necessary. Only rough sketch
(vi) Figures to the right indicate full marks.

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a (viii) For each multiple choice type of question, only the first attempt will be
considered for evaluation.

(ix) Start answer to each section on a new page.

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Page No. 2/8 Subject Code J-276
SECTION – A
Q. 1. Select and write the correct answer of the following 16
multiple choice type of questions :

(i) If A = {1, 2, 3, 4, 5} then which of the following is not true?

(a) x A such that x + 3 = 8

(b) x A such that x + 2 < 9

(c) x A, x 6 9

(d) x A , x 5 10 (2)

1 1 1 3
(ii) The value of sin sin 3sin
2 2

1 1
(a) (b)
2 2

3 3
(c) (d) (2)
2 2

(iii) If pˆ , qˆ , rˆ are mutually perpendicular unit vectors and form a right
handed triplet then the value of

(a) –2 (b) 0

(c) 1 (d) 3 (2)

(iv) The Cartesian equation of the line passing through the points
A (3, 4, –1) and B (2, –1, 3) is _____.

x 3 y 4 z 1 x 3 y 4 z 1
(a) (b)
1 5 4 1 5 4

x 3 y 4 z 1 x 3 y 4 z 1
(c) (d) (2)
1 5 4 1 5 4

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Page No. 3/8 Subject Code J-276 a
Seat No.

(v) If y log a then dy _____.
x dx

log a
(a) (b) x log a
x (log x )2
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(c) (d) (2)

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a If f (x ) sin 1 x2 and g(x ) esin 1 x then
(vi)
1 x

f ( x ) g ( x )dx _____.

sin 1 x 1 sin 1 x 1
(a) e (1 sin x) c (b) e (sin x 1) c

sin 1 x
o mecos 1 x (cos 1 x 1) c
.c
1
(c) e (sin x 1) c (d) (2)

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(vii)
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The area bounded by the line y = 2x, X – axis and the lines x = –1,

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x = 4 is _____ sq. units.

(a) 15 (b) 17

(c) 16 (d) 14 (2)

(viii) In a Binomial Distribution, E (X ) = 6, Var (X ) = 4.2 then the value
of n is _____
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(a) 22 (b) 24
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a Answer the following questions : 4

(i) Write the dual of p t (1)

(ii) What is the distance of point (3, –5, 6) from XZ plane? (1)

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Page No. 4/8 Subject Code J-276
(iii) The displacement of a particle at time t is given by

S 3t 2 4t 1. Find its velocity at time t. (1)

(iv) Write the order of differential equation

5
2 2
d y 3 dy
2
(1)
dx dx

SECTION – B
Attempt any EIGHT of the following questions : 16

Q. 3. Construct the switching circuit for the statement . (2)

5 2
Q. 4. Find the matrix of cofactors of matrix 16 . (2)

1
Q. 5. Find the general solution of equation cos5 . (2)
2

Q. 6. Find the value of k, if 2x y 0 is one of the lines represented

2
by 3x kxy 2 y2 0. (2)

Q. 7. If a , b , c are the position vectors of points A, B, C respectively
and 10a 7b 3c then find the ratio in which the point C divides the
line segment AB . (2)

Q. 8. Find the angle between the lines

r (iˆ 2 jˆ 3kˆ ) (2iˆ jˆ kˆ )

r (iˆ 2 jˆ 3kˆ ) (iˆ 2 jˆ kˆ ) (2)

1
Q. 9. Test whether the function f ( x ) x , x R, x 0 is increasing
x
or decreasing. (2)

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Page No. 5/8 Subject Code J-276 a
Seat No.

1
Q. 10. Evaluate : |x| dx (2)
1

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Q. 11. Evaluate : x log x dx (2)
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2
Find the area bounded by curve x y 0, X
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Q. 12. axis and lines

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x = 1 and x = 4. (2)

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Q. 13. a probability distribution of r.v. X is as follows:
The

X=x 0 1 2 3 4
P (X = x) 0.1 k 2k 2k k

Find : (i) k (ii) F (2) (2)

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Q. 14. Evaluate : dx (2)
cos2 ( xe )
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SECTION –C
Attempt any EIGHT of the following questions : 24

Q. 15. Using truth table, determine whether statement pattern

[( p q ) p] q is a tautology or a contradiction or a contingency. (3)

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Q. 16.
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a
1 1 1
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sin cos sin
a (3)
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5 13 65

Q. 17. In ABC , if a =10, b = 8, c = 6 then find the value of
C B
(i) sin 2 cos
2

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Page No. 6/8 Subject Code J-276
Q. 18. Are the four points A (1, 2, 1), B (2, –3, 4), C (3, 4, –5), D (2, 3, –2)
coplanar? Justify your answer. (3)

Q. 19. Find the distance between parallel lines

x y z
and
2 1 2

x 1 y 1 z 1
(3)
2 1 2

Q. 20. Find the vector equation of the plane passing through the points

A (2,1,1), B(0,2,3) and C (4,5,6). (3)

2 2
x x a
Q. 21. If y log , find dy . (3)
x
2
a
2
x dx

Q. 22. A wire of length 36 cm is bent to form a rectangle. Find its
dimensions, if the area of the rectangle is maximum. (3)

Q. 23. Verify Rolle’s theorem for the function f ( x ) x 2 5x 9, x [1,4] (3)

dy
Q. 24. Solve the differential equation x x2 y2 y (3)
dx

Q. 25. The following is the p.d.f. of continuous r.v.

x
f (x ) ;
8 0 x 4
=0, Otherwise
Find (i) expression for c.d.f of X.
(ii) F (x) at 0.5 and 5 (3)

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Page No. 7/8 Subject Code J-276 a
Seat No.

Q. 26. If the p.m.f of r.v. X be
x 4 x
4 5 4 for
P( X x) C x 0,1,2,3,4
x 9 9
=0 ; otherwise
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then find E (X ) and Var (X ). (3)
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Attempt any FIVE of the following questions : 20

4 3 3
Q. 27. Find the inverse of matrix 1 0 1 (4)
4 4 3

Q. 28. Prove that the homogeneous equation of degree two in x and y,
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ax 2 2hxy by2 .co
0 represents a pair of lines passing through

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the origin if h2 ab 0 (4)

Q. 29.
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a non coplanar vectors then any vector r in
Prove that, if a ,b , c are three
the space can be uniquely expressed as a linear
combination of a ,b , c . (4)

Q. 30. Solve the linear programming problem (L.P.P.) by graphical method.

Minimize : z 8 x 10 y
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Subject to , 2x y 7
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y 2 (4)

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Page No. 8/8 Subject Code J-276
Q. 31. If x f (t ) and y g (t ) are differentiable functions of t, so that y is

dy
dx dy dt .
differentiable function of x and 0 then prove that
dt dx dx
dt

dy
Hence find , if x sin t y cos t. (4)
dx

2
Q. 32. Evaluate : 2 2
dx (4)
3 2sin x 5cos x

Q. 33. Prove that,

a a
f ( x )dx 2 f ( x )dx , if f ( x ) is even
a 0

= 0, if f ( x ) is odd (4)

Q. 34. A body cools according to Newton’s law from 100ºC to 60ºC in 20 minutes.
The temperature of the surrounding being 20ºC.

How long will it take to cool down to 40ºC? (4)

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