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

FOR MAHARASHTRA BOARD (MSBSHSE) CLASS 12 EXAM PREPARATION

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

Maharashtra Board (MSBSHSE) Class 12 2026
TYPE SUBJECT

March Session Question Paper Maths (Arts & Science)

Notes · Sample Papers · Previous Year Papers · Mock Tests

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SEAT NUMBER
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DAY — 09 SEAT NUMBER

2026 II 21 1100 (E)
J-165 m
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MATHEMATICS & STATISTICS (40)
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agTime : 3 Hrs. ( 8 Pages ) Max. Marks : 80

General instructions :
The question paper is divided into FOUR sections.
(1) Section A : Q. 1 contains Eight multiple choice type
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questions, each carrying Two marks.

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Q. 2 contains Four very short answer type
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questions,a each carrying One mark.
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(2) Section B : Q. 3 to Q. 14 contain Twelve short answer type
questions, each carrying Two marks.
(Attempt any Eight)
(3) Section C : Q. 15 to Q. 26 contain Twelve short answer type
questions, each carrying Three marks.
(Attempt any Eight)
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(4) Section D : Q. 27 to Q. 34 contain Eight long answer type

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questions, each carrying Four marks.em
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(Attempt any Five)
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a (5) Use of log table is allowed. Use of calculator is not allowed.
(6) Figures to the right indicate full marks.

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(7) Use of graph paper is not necessary. Only rough sketch of
graph is expected.

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

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

SECTION – A

Q. 1. Select and write the correct answer of the following [16]

multiple choice type of questions :

(i) The converse of contrapositive of is _____.

(a) (b)

(c) (d) (2)

(ii) If A , then the adjoint of matrix A is _____.

(a) (b)

(c) (d) (2)

(iii) If then = _____.

1
(a) –1 (b)
6
1 3
(c) (d) (2)
3 2

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(iv) The angle between the line

and the plane is _____.

(a) sin (b) sin
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m . sin s e
a
(d) sin (2)
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l a ag
ag (v) If , then
dy
at x is _____.
dx

1
(a) (b) 1
2

1
(c) (d) 2 (2)
2

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. function
(vi)
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The approximate value of the
is _____. se
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at x

(a) 6.09 ag (b) 6.91

(c) 7.09 (d) 7.91 (2)

2 1
(vii) _____.

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(a) (b)
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(c) e e (d) (2)

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(viii) If the p.d.f. of a continuous r.v. X is

f (x ) , for

= 0 , otherwise

then P X _____
1 2
(a) (b)
9 9
1 2
(c) (d) (2)
27 27

Q. 2. Answer the following questions : [4]

(i) Write the dual of (1)

(ii) Evaluate : (1)

(iii) Evaluate : dx (1)

(iv) Write the degree of the differential equation
(1)

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

Q. 3. Construct the switching circuit of the statement pattern
. (2)

Q. 4. In , prove that . (2)

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Q. 5. Find the general solution of . (2)

Q. 6. Find k, if the sum of the slopes of the lines represented by

is twice their product. (2)
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Q. 7. .co
Find the value of p, for which the vectors
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and
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a (2) ag
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Q. 8. Find the vector equation of the line passing through the points

A(1,2,3) and B(2,3,4) . (2)

dy
Q. 9. Find , if . (2)
dx

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d2 y . co
Find
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Q. 10. , if . (2)
dx 2
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Q. 11.
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Test whether the afunction is

increasing or decreasing for all . (2)

Q. 12. A stone is dropped into a quiet lake and waves in the form of
circles are generated. Radius of the circular wave increases at
the rate of 3 cm/sec. How fast the area enclosed is increasing
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m c. o (2)
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when the radius is 8 cm?
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las Evaluate :
ag (2)

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Q. 14. Given that, X B( n, p ), if then find Var(X). (2)

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SECTION – C

Attempt any EIGHT of the following questions : [24]

Q. 15. Examine whether the statement pattern is

a tautology or contradiction or contingency. (3)

Q. 16. In , if then find the ratio of its sides. (3)

Q. 17. If two vertices of a triangle are A(3,1,4) and B and
the centroid of the triangle is G , then find the
coordinates of the third vertex C of the triangle. (3)

Q. 18. If D , E , F are the mid-points of the sides BC , CA , AB

respectively of , then prove that . (3)

Q. 19. Show that the lines and

intersect each other.. (3)

Q. 20. Find the cartesian equation of the plane

. (3)

Q. 21. If is a differentiable function of u and is a
differentiable function of x then prove that y is a differentiable

function of x and . (3)

Q. 22. Verify LMVT for the function on [1, e]. (3)

Q. 23. Evaluate : dx (3)

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Q. 24. Solve the D.E. . (3)

Q. 25. Find E ( X ) and V ( X ), where X is the number obtained on

uppermost face, when a fair die is thrown. (3)
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Q. 26.
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A pair of dice is thrown 4 times. If getting a doublet is considered
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as success, find the probability of two successes. (3)

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SECTION – D

Attempt any FIVE of the following questions : [20]

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Q. 27. If A , prove that A· (adj A) = (adj A)· A = |A|· I (4)

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Q. 28.
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Show that every homogeneous equation of degree two in

x and y i.e. a represents a pair of lines passing

through the origin, if (4)

Q. 29. If A( a ) and B(b) are any two points in space and R( r ) be a
point on the line segment AB dividing internally in the ratio

m
m m : n then prove that r .
c. o (4)
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m Q. 30. s e m
s e Solve the L.P.P. graphically :
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a Minimize :

Subject to ,

(4)

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Q. 31. Evaluate : (4)

b b
Q. 32. Prove that :
a a

Hence, find (4)

6

Q. 33. Find the area enclosed between the circle and the
line lying in the first quadrant. (4)

Q. 34. Solve the differential equation . (4)

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