MH 10th Question Paper 2025 Maths Part 1 Algebra

Maharashtra Board

Question Paper
2025
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QUESTION PAPER
Presented By

N 819 Seat No.

2025 III 05 1100 -N 819- MATHEMATICS (71) ALGEBRA—PART I (E)

(REVISED COURSE)
Time : 2 Hours (Pages 11) Max. Marks : 40

Note :— (i) All questions are compulsory.

(ii) Use of a calculator is not allowed.

(iii) The numbers to the right of the questions indicate full

marks.

(iv) In case of MCQs [Q. No. 1(A)] only the first attempt will

be evaluated and will be given credit.

1. (A) Choose the correct alternative from given : 4

1 2
(i) . Write the degree of the given determinant.
3 4

(A) 1

(B) 2

(C) 3

(D) 4

P.T.O.

2/N 819
(ii) From the following equations which one is the quadratic

equation ?

5
(A) 3 x2
x

(B) x ( x 5) 2

(C) n 1 2n

1
(D) ( x 2) x
x2

(iii) Find the common difference of the following A.P. :

4, 4, 4, ...

(A) 1

(B) 8

(C) 4

(D) 0

(iv) Which number cannot represent a probability ?

2
(A)
3

15
(B)
10

(C) 15%

(D) 0.7

3/N 819
(B) Solve the following subquestions : 4

(i) If 2x + y = 7 and x + 2y = 11, then find the value of x + y.

(ii) Find the first term of the given sequence :

tn = 3n – 4.

(iii) How many alpha numerals are there in the format of

GSTIN ?

(iv) Two coins are tossed simultaneously. Write the sample space S.

2. (A) Complete and write any two activities from the following : 4

(i) Complete the following table to draw the graph of x + 2y = 4.

Activity :

x –2

y 1

(x, y)

P.T.O.

4/N 819
(ii) Complete the following activity to form a quadratic equation.

Activity :

I am a quadratic equation.

My standard form is .

My roots are 5 and 12.

Sum of my roots .

Product of my roots .

My quadratic equation is .

(iii) Pushpmala has invested ` 24,000 and purchased share of FV

` 20 at a premium of ` 4. Complete the following activity to find

the number of shares she purchased.

Activity :

FV = ` 20

Premium = ` 4

5/N 819
MV = FV +

= 20 +

= ` 24

Total investment
Number of shares =
MV

24,000
=

= shares.

(B) Solve any four subquestions from the following : 8

(i) Solve the following simultaneous equations :

x + y = 3; 3x – 2y = 4

(ii) Solve the following quadratic equation by factorisation

method :

m2 + 14m + 13 = 0

(iii) Find the 19th term of the following A.P. :

7, 13, 19, 25, ...

(iv) A share is sold for the market value of ` 2,000. Brokerage is

paid at the rate of 0.5%. What is the amount received after

the sale ?

P.T.O.

6/N 819
(v) The following table shows the number of students and the time

they utilized daily for their studies. Find the mean time spent

by the students for their studies.

Class Class Marks No. of Students fi xi

Time (xi) (fi)

(In hours)

0–2 1 8 08

2–4 3 14 42

4–6 5 18 90

6–8 7 10 70

8–10 9 10 90

3. (A) Complete and write any one activity from the following : 3

(i) Shri Maniklal has purchased 300 shares of F.V. ` 100, for

M.V. ` 120. Company has paid dividend at 7%. Complete

the following activity to find the rate of return on his

investment.

Activity :

F.V. = ` 100

Number of shares = 300

Market value = ` 120

7/N 819
(a) Sum invested = M.V. × No. of shares

= ×

= ` 36,000

(b) Dividend per share = F.V. × rate of dividend

=
100

= ` 7

Total dividend received = 300 × 7

= `

Dividend income
(c) Rate of return = 100
Sum invested

2,100
= 100
36,000

= %.

P.T.O.

8/N 819
(ii) A two digit number is to be formed from the digits 2, 3, 5

without repetition of the digits. Complete the following activity

to find the probability that the number so formed is an odd

number.

Activity :

Let S be the sample space.

S = {23, 25, 32, , 52, 53}

n(S) =

Event A : The number so formed is an odd number.

A = {23, 25, , 53}

n(A) = 4

P(A) = ............ (Formula)
n(S)

P(A) =
6

P(A) = .
3

9/N 819
(B) Solve any two subquestions from the following : 6

(i) Solve the following simultaneous equations by Cramer’s

rule :

4x + 3y = 18; 3x – 2y = 5

(ii) Solve the following quadratic equation by using formula

method :

x2 – 2x – 3 = 0

(iii) A committee of two members is to be formed from three boys

and two girls. Find the probability of the following events :

Event A : At least one girl must be a member of the committee.

Event B : Committee must be of one boy and one girl.

(iv) In a general store the prices of different articles and its demand

is shown in the following frequency distribution table. Find the

Median of the prices.

Price in Rupees No. of Articles

Less than 20 140

20—40 100

40—60 80

60—80 60

80—100 20

P.T.O.

10/N 819
4. Solve any two subquestions from the following : 8

(i) Find the value of ‘m’ if the quadratic equation

(m – 12) x2 + 2(m – 12) x + 2 = 0

has real and equal roots.

(ii) A farmer borrows ` 1,000 and agrees to repay with a total interest

of ` 140, in 12 instalments. Each instalment being less than the preceding

instalment by ` 10. What should be the amount of his first and last

instalment ?

(iii) The following table shows the marks of 180 students in Mathematics.

Marks No. of Students

0—10 25

10—20 x

20—30 30

30—40 2x

40—50 65

Find the value of ‘x’ and draw histogram.

11/N 819
5. Solve any one of the following subquestions : 3

(i) Draw the graphs representing the equation 2x = y + 2 and 4x + 3y = 24

on the same graph paper. Find the area of the triangle formed by these

lines and the X-axis.

(ii) The following pie-diagram shows percentage of persons according to

blood group in a blood group checking camp. Answer the following

questions :

(a) Find the measure of central angle for each blood group.

(b) Find the total number of persons, if there are 600 persons of
blood group B.

P.T.O.

N 820
Seat No.
2025 III 05 - 1100

Time : 2 Hours MATHEMATICS (71) ALGEBRA—PART I (M)

(REVISED COURSE)
Pages - 11 Total Marks : 40

:— (i)

(ii)

(iii)

(iv) 1(A)]

1. (A) 4

1 2
(i)
3 4

(A) 1

(B) 2

(C) 3

(D) 4

P.T.O.

2/N 820
(ii)

5
(A) 3 x2
x

(B) x ( x 5) 2

(C) n 1 2n

1
(D) ( x 2) x
x2

(iii)

4, 4, 4, ...

(A) 1

(B) 8

(C) 4

(D) 0

(iv)

2
(A)
3

15
(B)
10

(C) 15%

(D) 0.7

3/N 820
(B) 4

(i) 2x + y = 7 x + 2y = 11, x + y

(ii) tn = 3n – 4

(iii) GSTIN

(iv) S

2. (A) 4

(i) x + 2y = 4

x –2

y 1

(x, y)

P.T.O.

4/N 820
(ii)

5 12

(iii) 24,000 20 4

= 20

= 4

5/N 820
= +

= 20 +

= 24

=

24,000
=

=

(B) 8

(i)

x + y = 3; 3x – 2y = 4

(ii)

m2 + 14m + 13 = 0

(iii) 19

7, 13, 19, 25, ...

(iv) 2,000 0.5%

P.T.O.

6/N 820
(v)

fi xi

(xi) (fi)

0–2 1 8 08

2–4 3 14 42

4–6 5 18 90

6–8 7 10 70

8–10 9 10 90

3. (A) 3

(i) 100 300 120

7%

= 100

= 300

= 120

7/N 820
(a) = ×

= ×

= 36,000

(b) = ×

=
100

= 7

= 300 × 7

=

(c) = × 100

2,100
= 100
36,000

= %.

P.T.O.

8/N 820
(ii) 2, 3, 5

S

S = {23, 25, 32, , 52, 53}

n(S) =

A :

A = {23, 25, , 53}

n(A) = 4

P(A) = ............ ( )
n(S)

P(A) =
6

P(A) = .
3

9/N 820
(B) 6

(i)

4x + 3y = 18; 3x – 2y = 5

(ii)

x2 – 2x – 3 = 0

(iii)

A :

B :

(iv)

20 140

20—40 100

40—60 80

60—80 60

80—100 20

P.T.O.

10/N 820
4. 8

(i) (m – 12) x2 + 2(m – 12) x + 2 = 0

m

(ii) 1,000 140 12

10

(iii) 180

0—10 25

10—20 x

20—30 30

30—40 2x

40—50 65

‘x’

11/N 820
5. 3

(i) 2x = y + 2 4x + 3y = 24

X-

(ii)

(a)

(b) B 600

P.T.O.

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