MH 12th Question Paper March 2026 Maths (Commerce)

FOR MAHARASHTRA BOARD (MSBSHSE) CLASS 12 EXAM PREPARATION

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

Maharashtra Board (MSBSHSE) Class 12 2026
TYPE SUBJECT

March Session Question Paper Maths (Commerce)

Notes · Sample Papers · Previous Year Papers · Mock Tests

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SEAT NUMBER
a
DAY — 09 SEAT NUMBER

2026 II 21 1100 (E)
J-169 m
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MATHEMATICS & STATISTICS (88)
l a
g la (COMMERCE) ag
a Time : 3 Hrs. ( 15 Pages ) Max. Marks : 80

General Instructions :
(i) All questions are compulsory.
(ii) There are six questions divided into
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two sections. .co
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(iii) Write answers of Section-I and Section-

g laanswer book.
a
II in the same
(iv) Use of logarithmic tables is allowed.
Use of calculator is not allowed.
(v) For L.P.P. and Time Series graph paper
is not necessary. Only rough sketch of
graph is expected.
(vi) Start answer to each question on a
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new page.
e m
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s
s e Q.1 and Q.4) only the first attempt la
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a will be considered for evaluation.

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SECTION - I
Q. 1. (A) Select and write the correct answer of the following multiple [12]
choice type of questions (1 mark each) : (6)

dy
(i) If then = _____.
dx

2 3
(a)
3
2
2 3
(b)
3

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

dy
(ii) If y then = _____.
dx

2 x
(a) (b)
x x

(c) x (d)
e ex

I
Q : the set of all rational numbers
U
I : the set of all integers.
The above Venn diagram represents the truth value
of which of the following statements?
(a) Some integers are rational numbers.
(b) All integers are rational numbers.
(c) No integers are rational numbers.
(d) All rational numbers are integers.

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a
(iv) The equation of normal to the curve at
(1, 3) is _____.
(a) (b)
(c) (d)
m
m
c. oThe solution of dx
dy
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(v)
m (a)
is :
s e
s e l a
a ag
(b)
g l
a (c) 2 2 (d)
a
(vi) If then a = _____.

(a) 2 (b) 0
8
(c) (d) 1
3
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(B) State whether the following statements are true or false
(1 mark each) :
s em (3)

g la dx
(i) If a then 1
.

(ii) If

then A = 1, B = 2.

(iii) Order and degree of a differential equation are always
m
m positive integers.
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s e (C) Fill in the following blanks (1 mark each) :
g l a
g la (i) Statement is true, when p andaq have _____
a truth values.

dy
(ii) If y eax then x = _____.
dx

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(iii) If then its minimum value is _____.

Q. 2. (A) Attempt any TWO of the following questions (3 marks [14]
each) : (6)

(i) Using truth table, examine whether the following
statement pattern is a tautology, a contradiction or a
contingency.

(ii) If then show that dy .
dx

(iii) Evaluate :

(B) Attempt any TWO of the following questions (4 marks
each) : (8)

(i) Find the inverse of by adjoint method.

(ii) The consumption expenditure Ec of a person with

income x is given by .
c

Find average propensity to consume, marginal
propensity to consume when his income is ` 200. Also
find his marginal propensity to save and average
propensity to save.

7
x
(iii) Evaluate :

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SEAT NUMBER
a
Q. 3. (A) Attempt any TWO of the following questions (3 marks [14]
each) : (6)

(i) If the demand function is , find the

m
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elasticity of demand at p . Comment on the result.
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(ii)
c. oIf p : He swims s e m
em q : Water is warm
l a
l as Give the verbal statements for the following symbolic ag
ag statements :
(a)
(b)
(c)

1
(iii) Evaluate : dx

o m
. c
e m
(B) Attempt any ONE of the following questions (4 marks
each):
l as (4)

ag differential equation
(i) Solve the following

(ii) Find the area of the region bounded by the curve
2
and the line y .

(C) Attempt any ONE of the following questions (Activity)
m
m (4 marks each):
c. o (4)
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s e
Express the following equations in matrix form and m
s e g la
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solve them by method of reduction.
g a
a Solution :
The given equations can be written in matrix form
as

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By

By

By

We write equations as
.....(I)
.....(II)
z .....(III)
Solving equations (I), (II) and (III)
We get x , y , z

(ii) Obtain the differential equation from the relation
, where A and B are constants.

Solution :

The given equation is .....(I)
Differentiating equation (I) w.r.t. x ,
we get,

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SEAT NUMBER
a

.....(II)

Differentiating equation (II) w.r.t. x,
we get
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c. oSince equations (I), (II) and (III) are consistent in A
.....(III)
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m and B s e
s e l a
g l a ag
a x
2
y
2
1
dy
x y
dx
1 0

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s e
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ag

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s e g la
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a

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SECTION - II
Q. 4. (A) Select and write the correct answer of the following multiple [12]
choice type of questions (1 mark each) : (6)

(i) The difference between face value and present worth
is called _____.
(a) Banker's discount
(b) True discount
(c) Banker's gain
(d) Cash value

(ii) Insurance companies collect a fixed amount from
their customers at a fixed interval of time. This
amount is called _____.
(a) EMI
(b) Installment
(c) Contribution
(d) Premium

(iii) If b then b is _____.
YX XY
(a)
(b)
(c) =0
(d)

(iv) Which of the following can't be a component of a time
series?
(a) Seasonality
(b) Cyclical
(c) Trend
(d) Mean

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SEAT NUMBER
a
(v) Price Index Number by Simple Aggregate Method is
given by :

(a)
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0

m
c. o(b) s e m
em l a
l as ag
ag (c)

(d)

(vi) If the corner points of the feasible region are (0, 10),
(2, 2) and (4, 0) then the point of minimum
m
is _____.
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(a) (2, 2)
s e
(b) (0, 10)
gl a
(c) (4, 0) a
(d) (2, 4)

(B) State whether the following statements are true or false
(1 mark each) : (3)

(i) The banker's discount is always lower than the true
m
m discount.
.co
m .co (ii) The cost of living Index Number using weighted
s e m
s e g la
g la relative method is given by . a
a
(iii) To convert an assignment problem into a
minimization problem, the smallest element in the
matrix is deducted from all other elements.

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(C) Fill in the following blanks (1 mark each) : (3)

(i) The difference between the banker's discount and the
true discount is called _____.

(ii) If then P01 ( F ) _____.

(iii) A dish washing machine holds up to 40 pieces of large
crockery (x). This constraint is given by _____.

Q. 5. (A) Attempt any TWO of the following questions [14]
(3 marks each) : (6)

(i) A shop is valued at ` 3,60,000 and is insured for 75%
of its value. If the rate of premium is 0.9%, find the
premium paid by the owner of the shop. Also find the
agent's commission if the agent gets commission at
15% of the premium.

(ii) Given the following information about the production
(X) and demand (Y) of a commodity, obtain the
regression line of X on Y.
Production (X) Demand (Y)
Mean 85 90
S.D. 5 6

Coefficient of correlation between X and Y is 0.6.
Also estimate the production when demand is 100.

(iii) The following table shows the production of pig-iron

and ferro-alloys ('000 metric tons)
Years 1974 1975 1976 1977 1978 1979 1980 1981 1982
Production 0 4 9 9 8 5 4 8 10

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SEAT NUMBER
a
Find trend values for the above data by using 5

yearly moving averages.

(B) Attempt any TWO of the following questions (4 marks
m
each) :
c o m (8)
m .co
m . Solve the following L.P.P. by graphical method. s e
s e(i)
l a
g l a Minimize : ag
a Subject to :

(ii) Solve the following assignment problem for

minimization :

o m
Men
c
Tasks (in hours)
III.
I II
e m IV
25as 26
A
B
7
l
12 ag27 3
10
25
C 37 18 17 14
D 18 25 23 9

(iii) The probability distribution of a discrete r.v. X is as

follows :
m
m x 1 2 3 4 5 6
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m .co P(X = x) k 2k 3k 4k 5k 6k
s e m
s e g la
g la (a) Determine the value of k.
a
a (b) Find

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Q. 6. (A) Attempt any TWO of the following questions (3 marks [14]
each) : (6)

3
(i) The true discount on a sum is of the sum due at
8
12% p.a. Find the period of the bill.

(ii) Following data shows the number of bags of cereals
sold in years 1977 to 1984.

Years 1977 1978 1979 1980 1981 1982 1983 1984
No. of bags (in
1 0 3 8 10 4 5 8
ten thousands)

Fit a trend line to the above data by graphical
method.

(iii) The following is the p.d.f. of a r.v. X :

for
f (x )
otherwise
Find (a) P x
(b)
(c) P x

(B) Attempt any ONE of the following questions (4 marks
each) : (4)

(i) For the following bivariate data obtain the equation
of regression line of Y on X.

X 1 2 3 4 5
Y 5 7 9 11 13

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a
(ii) Calculate (a) Laspeyre's and (b) Paasche's Price Index

Numbers for the following data :
Commodity Base Year Current Year
Price Quantity Price Quantity
m
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P 12 20 18 24
e m
em Q 14 12 21 16
l as
l as R 8 10 12 18
ag
ag S 16 15 20 25

(C) Attempt any ONE of the following questions (Activity)

(4 marks each) : (4)

(i) Determine the optimal sequence of jobs that

minimizes the total elapsed time for the data given
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below (processing time on machines is given in hours).
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s e
Also find the total elapsed time and the idle time for
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three machines.

Jobs I II III IV V VI VII
Machine A 3 8 7 4 9 8 7
Machine B 4 3 2 5 1 4 3
Machine C 6 7 5 11 5 6 12

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Solution :
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C = 5, Max B = 5. Since Min
s
s e a
is satisfied, the problem can belconverted
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a into a two machine problem.

Let G and H be two fictitious machines

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The above problem can be written as :

Jobs I II III IV V VI VII
Machine G 7 11 9 9 10 12 10
Machine H 10 10 7 16 6 10 15

Using optimal sequence algorithm, the following

sequence can be obtained.

VI II

Work table :

Jobs Machine A Machine B Machine C
In Out In Out In Out
I 0 3 3 7 7 13
IV 3 7 7 12 13 24
7 14 14 17 24 36
VI 14 22 22 26 36 42
II 22 30 30 33 49

30 37 37 39 49 54
V 37 46 46 47 54 59

Total elapsed time is = 59 hrs.

Idle time for machine A = hrs.

Idle time for machine B = hrs.

Idle time for machine C = 7 hrs.

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a
(ii) In a town 10 accidents take place in the span of 50

days. Assuming that the number of accidents follows

Poisson distribution, find the probability that there

m
.co
will be 3 or more accidents on a day.
m
c. o[ Given that e ]
s e m
em Solution : l a
l as ag
ag Here m and X P (m ) with parameter m.

The p.m.f. of X is :

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s e
l a
ag

m
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s e g la
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a

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