MH 12th Question Paper June 2026 Maths (Commerce)

FOR MAHARASHTRA BOARD (MSBSHSE) CLASS 12 EXAM PREPARATION

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

Maharashtra Board (MSBSHSE) Class 12 2026
TYPE SUBJECT

June Session Question Paper Maths (Commerce)

Notes · Sample Papers · Previous Year Papers · Mock Tests

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Page No. 1/11 Subject Code J-280 a
Seat No.

Page No. 1/11 Subject Code J-280 Seat No.

DATE : 24/06/2026 E
SUBJECT : MATHEMATICS &
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Time : 11.00 - 2.00

o m STATISTICS (COMMERCE) (88)
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DURATION : 3 Hours. c s e
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General Instructions :
(i) All questions are compulsory.
(ii) There are six questions divided into two sections.
(iii) Write answers of Section-I and Section-II in the same answer book.
(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
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sketch of graph is expected.

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(vi) Start answer to each question on a new page.
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(vii) For each objective type oflquestion (i.e. Q.1 and Q.4) only the first attempt
will be considered foraevaluation.

SECTION - I

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Q. 1. (A) Select and write the correct answer of the following multiple 12

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choice type of questions (1 mark each) :
. c (6)
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(a) Contradiction
a (c) Contingency (d) None of them

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Page No. 2/11 Subject Code J-280
4 x
(ii) If A 6 3 is a singular matrix then x is
(a) 2 (b) –2
(c) 3 (d) –3

dy
(iii) If y e log x then is
dx

(a) e log x (b)
1
x 2
(c) 1 (d) both (a) and (c)

(iv) If 0 1, then the demand is
(a) elastic (b) unitary elastic
(c) relatively elastic (d) relatively inelastic

3
(v) _____

x3
(a) (b) x3
(3)

x3 2 x3
(c) (log 3)(3) (d) x (3) c
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(vi) dx _____.

(a) 1 (b) 0

3x 2
(c) –1 (d)

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

(i) The slope of the tangent at any point (a, b) is called as gradient of
the curve.

(ii)

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Page No. 3/11 Subject Code J-280 a
Seat No.

(iii) Order and degree of a differential equation are always positive
integers.

(C) Fill in the following blanks (1 mark each) : (3)
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(i) The dual of is _____.
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(ii)
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dy
(iii) The integrating factor of the differential equation
dx
is _____.

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

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(i) Write the converse, inverse and contrapositive of the following

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statement.
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'If a man is rich, then he
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(ii) Find the inverse of matrix by adjoint method.

(iii) Find the rate of change of demand (x) of a commodity with respect

to its price (y) if y

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(B) Attempt any TWO of the following questions (4 marks each) : .c
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x

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dx
a
(i) Evaluate :

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x
(ii) Evaluate :

2 2
(iii) Find the area of ellipse x

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Page No. 4/11 Subject Code J-280
Q. 3. (A) Attempt any TWO of the following questions (3 marks each) : (6) 14

(i) Determine whether the following statement pattern is tautology,
contradiction or contingency.

dy log x
(ii) If then prove that dx .
x 2

(iii) The manufacturing company produces x items at the total cost of
` (180+4x). The demand function for this product is P = (240 – x).
Find x for which profit is increasing.

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

(i) Solve the following equation by method of reduction :

(ii) In a certain culture of bacteria, the rate of increase is proportional
to the number present. If it is found that the number doubles in
4 hours, find the number of times the bacteria increased in 12 hours
by using the concept of application of differential equations.

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

(i) Demand function x, for a certain commodity is given as
x = 200 – 4p, where p is the unit price. Find

(a) elasticity of demand as a function of p.
(b) elasticity of demand when p = 10. Interpret your result.

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Page No. 5/11 Subject Code J-280 a
Seat No.

Solution :

(a) Here, x = 200 – 4p

Elasticity of demand is
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(b) When p = 10

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= 0.25
Demand is
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for p = 10

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(ii) Solve the following differential equations
dy

a
dx
dy
Solution :
dx
Given equation is a linear differential equation.
Here P Q=5

I.F. = e

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I.F. =
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Page No. 6/11 Subject Code J-280
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 date on which period of the bill expires is called ____.
(a) Legal due date (b) Date of discounting
(c) Nominal due date (d) Date of drawing

(ii) Loss = ____.

(a) Claim (b) Claim

(c) Claim × Property value (d) Claim × Policy value

(iii) In regression analysis _____.

(a) V(x) (b)

(c) (d) r2

(iv) Moving averages are useful in identifying ____.
(a) Trend component (b) Irregular component
(c) Seasonal component (d) Cyclical component

(v) Price Index Number by Simple Aggregate Method is given by

(a) (b)
0

(c) (d)

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Page No. 7/11 Subject Code J-280 a
Seat No.

(vi) Objective function of LPP is
(a) a constraint
(b) a function to be maximized or minimized
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(c) a relation between the decision variables
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(d)
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a feasible region
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(B) Statea whether the following statements are true or false
a(3)
a(1g mark each) :
(i) The difference between the banker's discount and true discount is
called the Banker's gain.

(ii) One of the assumptions made while sequencing n jobs on 2

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machines is : two jobs must be loaded at a time on any machine.

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(iii) Quantity Index Number by simple
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(C) Fill in the following blanks (1 mark each) : (3)

(i) If then P01 ( F ) _____.

(ii) Graphical solution set of the inequations lies in _____

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quadrant.
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matrix.

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Page No. 8/11 Subject Code J-280
Q. 5. (A) Attempt any TWO of the following questions (3 marks each) : (6) 14

(i) Obtain the 4-yearly centered moving averages for the following

data :
Years 1971 1972 1973 1974 1975 1976
Production 1 0 1 2 3 2

Years 1977 1978 1979 1980 1981 1982
Production 3 6 5 1 4 10

(ii) Find the sequence that minimizes the total elapsed time to

complete the following jobs. Each job is processed in order AB. Also

find the idle time for machine B.
Jobs (Processing times in minutes)
I II III IV V VI VI I
M a c h i n e A 12 6 5 11 5 7 6
Machine B 7 8 9 4 7 8 3

(iii) A car firm has 2 cars, which are hired out day-by-day. The number

of cars hired on a day follows Poisson distribution with mean 1.5.

Find the probability that some demand is refused on a given day.
[ Given e–1.5 = 0.2231 ]

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

(i) Minimize :
Subject to :

Solve the above L.P.P. by graphical method.

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Page No. 9/11 Subject Code J-280 a
Seat No.

(ii) Four different machines can do any of the three required jobs, with
different profits resulting from each assignment as shown below :
Jobs Machines Profit (in `)
`
A B C D
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1 35 40 43 41

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2 40 48 44 43
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3 50 45 46 48

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a Find the optimal assignment schedule.
(iii) A random variable X has the following probability distribution :

x 1 2 3 4 5 6 7
P[X = x] k 2k 2k 3k k2 2k2 7k2+k

Determine (a) k (b) P(X < 3) (c) P(X > 6) (d) P(0 < X < 1)
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Q. 6.
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(A) Attempt any TWO of the following questions (3 marks each) : (6) 14

g la should set aside at the end of every
(i)
a
Find the amount a company
year if it wants to buy a machine expected to cost ` 4,31,000 at the
end of 4 years and interest rate is 5% p.a. compounded annually.
[ Given (1.05)4 = 1.2155 ]

(ii) For the following bivariate data obtain equation of regression line
Y on X:
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(iii) Following table shows the number of traffic fatalities (in a state)
a resulting from drunken driving from years 1975 to 1983 :
Years 1975 1976 1977 1978 1979 1980 1981 1982 1983
No. of deaths 0 6 3 8 2 9 4 5 10

Fit a trend line by least square method.

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Page No. 10/11 Subject Code J-280
(B) Attempt any ONE of the following questions (4 marks each) : (4)

(i) Given that and
Find Laspeyre's, Paasche's, Dorbish-Bowley's and Marshall-
Edgeworth's Price Index Numbers.

(ii) A die is thrown 4 times. If 'getting an odd number' is a success,
find the probability of (a) 2 successes (b) at least 3 successes (c) at
the most 2 successes.

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

(i) Rajesh gets a commission at 10% on cash sales and 8% on credit
sales. If he receives ` 4,400 as commission on the total sales of
` 50,000, find the sales made by him on cash and on credit sales.

Solution :
Let cash sales be ` x

Credit sales = `
Total commission = 10% on x + 8% on (50,000 – x)

x=

Commission on cash sales is ` 20,000 and on credit sales is

`

(ii) The equations of two regression lines are 16y + x = 64 and
x + 4y = 5. Find regression coefficients and correlation coefficient.

Solution :
Suppose that equation of regression line of Y on X be
16y + x = 64 and equation of regression line of X on Y be x + 4y = 5

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Page No. 11/11 Subject Code J-280 a
Seat No.

Now 16y + x = 64 and x + 4y = 5

and x = –4y + 5

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Page No. 12/11 Subject Code J-280

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