Maharashtra 10th Std Model Question Paper Mathematics Part I Algebra

Maharashtra State Board Sample Paper 2026

N 684 Seat No.

2025 VII 01 1100 -N 684- 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) Four alternative answers are given for every subquestion.

Choose the correct alternative and write its alphabet with

subquestion number : 4

5 3
(i) The value of determinant is ..........................
–7 –4

(A) –1

(B) –41

(C) 41

(D) 1

P.T.O.

2/N 684
(ii) Out of the following equations which one is not a quadratic

equation ?

(A) x2 + 4x = 11 + x2

(B) x2 = 4x

(C) 5x2 = 90

(D) 2x – x2 = x2 + 5

(iii) For given A.P. a = 3.5, d = 0, then t2 = .........................

(A) 0

(B) 3.5

(C) 7

(D) 10.5

(iv) From the following numbers which number cannot represent a

probability ?

(A) 0.6

(B) 2.0

(C) 0.15

(D) 0.75

3/N 684
(B) Solve the following subquestions : 4

(i) For simultaneous equations in variables x and y Dx = 49,

Dy = –63, D = 7, then find the value of x.

(ii) Write the following quadratic equation in standard form :

2y = 10 – y2

(iii) Face value of one share is ` 100 and premium is ` 10. Find the

market value of the share.

(iv) Find the class mark of the class 6–10.

2. (A) Complete the following activities and rewrite it (any two) : 4

(i) Complete the following activity to solve the quadratic equation

x2 + 8x – 48 = 0 by completing square method.

Activity :

 x2 + 8x – 48 = 0

 x2 + 8x + 16 – – 48 = 0

 (x + 4)2 – =0

 (x + 4)2 = 64

 x + 4 = or x + 4 = –8

 x = 4 or x =

P.T.O.

4/N 684
(ii) Courier service agent charged total ` 590 to courier a parcel from

Nashik to Nagpur. In the tax invoice taxable value is ` 500 on

which CGST is ` 45 and SGST is ` 45. Complete the following

activity to find the rate of GST charged for this service :

Activity :

Total GST = CGST + SGST

= + 45

=`

90
Rate of GST = 
500

 Rate of GST charged by agent is %

(iii) The monthly expenditure of a family on different items is shown

in the following table. Complete the following activity to calculate

the related central angles.

5/N 684
Activity :
Different Percentage of Measure of
items expenditure central angle
40 º
Food 40  360º 
100
20 º
Clothing 20  360º 
100
30 º
Education 30  360º 
100

Other
10 º
expenditure 10  360º 
100

Total 100 360º

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

(i) Find the values of (x + y) and (x – y) of the following given

simultaneous equations :

101x + 99y = 501

99x + 101y = 499

(ii) Solve the following quadratic equation by factorisation

method :

x2 – 15x + 54 = 0

(iii) Which term of the following A.P. is 560 ?

2, 11, 20, 29, .......

P.T.O.

6/N 684
(iv) Market value of a share is ` 200. If the brokerage rate is 0.3%,

then find the purchase value of the share.

(v) If  fidi = 10,000,  fi = 100 and A = 2000, then find mean ( x ) .

3. (A) Complete the following activities and rewrite it (any one) : 3

(i) In an A.P. sum of three consecutive terms is 27 and their product

is 504. Complete the following activity to find the terms.

Activity :

Let three consecutive terms be a – d, a, a + d.

 a – d + a + a + d =

 a =

Similarly :

(a – d) × a × (a + d) =

 [(9)2 – d2] × 9 = 504

 (81 – d2) × 9 = 504

 d2 = 81 –

 d =± 5

Thus by putting a = 9 and d = 5 we get three consecutive

terms =

Or by putting a = 9 and d = –5 we get three consecutive

terms =

7/N 684
(ii) A card is drawn from a well shuffled pack of 52 playing cards.

Complete the following activity to find the probability of the

following events :

(a) A red card

(b) A face card.

Activity :

Let ‘S’ is the sample space

 n(S) =

Event A : Card drawn is a red card.

Total red cards =

 n(A) =

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

26
 P(A) =
52

 P(A) =

P.T.O.

8/N 684
Event B : Card drawn is a face card.

Total face cards = 12

 n(B) =

n(B)
 P(B) = ................. Formula
n(S)
12
 P(B) =
52

 P(B) =

(B) Solve the following subquestions (any two) : 6

(i) In the following table the yearly investment made by 210 families

is given. From this information draw the histogram.

Investment Number of

(Thousand Rupees) families

10–20 30

20–30 50

30–40 60

40–50 55

50–60 15

9/N 684
(ii) Shri Shivajirao has purchased 150 shares of F.V. ` 100, for M.V.

of ` 120. Company has paid 7% dividend. Find the rate of return

on his investment.

(iii) Product of Shraddha’s age 2 years ago and 3 years hence is 84.

Find her present age.

(iv) Solve the following simultaneous equations graphically :

x + y = 6, x – y = 4

4. Solve the following subquestions (any two) : 8

(i) In an agriculture field the ratio of salary of skilled and unskilled workers

is 5 : 4. Total salary of one day of both of them is ` 900. Find daily

wages of skilled and unskilled workers.

(ii) Two dice are thrown. Find the probability of the following events :

(a) Event A : The sum of the numbers on their upper faces is at

least 9.
P.T.O.

10/N 684
(b) Event B : The sum of the numbers on their upper faces is divisible

by 5.

(c) Event C : The number on the upper face of the first die is greater

than the number on the upper face of the second die.

(iii) In the following frequency distribution table ages of 300 patients and

number of patients in a hospital is given. Find the median age of the

patients :

Age Number of

(In years) patients

10–20 60

20–30 42

30–40 55

40–50 70

50–60 53

60–70 20

11/N 684
5. Solve the following subquestions (any one) : 3

(i) Three conditions are given below. Write the quadratic equation for each

of them satisfy that condition :

(a) If discriminant  = 0

(b) If discriminant  > 0

(c) If discriminant  < 0

(ii) If first term of an A.P. is ‘p’, second term is ‘q’ and last term is ‘r’,
( p  r)(q  r – 2 p)
then show that the sum of all terms is .
2( q – p)

P.T.O.

Maharashtra State Board Sample Paper 2026

N 685
Seat No.
2025 VII 01 - 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

5 3
(i)
–7 –4

(A) –1

(B) –41

(C) 41

(D) 1

P.T.O.

2/N 685
(ii)

(A) x2 + 4x = 11 + x2

(B) x2 = 4x

(C) 5x2 = 90

(D) 2x – x2 = x2 + 5

(iii) a = 3.5, d = 0, t2 = ......................

(A) 0

(B) 3.5

(C) 7

(D) 10.5

(iv)

(A) 0.6

(B) 2.0

(C) 0.15

(D) 0.75

3/N 685
(B) 4

(i) x y Dx = 49,

Dy = –63, D = 7 x

(ii)

2y = 10 – y2

(iii) ` 100 ` 10

(iv) 6–10

2. (A) 4

(i) x2 + 8x – 48 = 0

 x2 + 8x – 48 = 0

 x2 + 8x + 16 – – 48 = 0

 (x + 4)2 – =0

 (x + 4)2 = 64

 x + 4 = x + 4 = –8

 x = 4 x =

P.T.O.

4/N 685
(ii)

` 590 ` 500

` 45 ` 45

=

= + 45

=`

90
= 
500

 %

(iii)

5/N 685

40 º
40  360º 
100

20 º
20  360º 
100

30 º
30  360º 
100

10 º
10  360º 
100

100 360º

(B) 8

(i) (x + y) (x – y)

101x + 99y = 501

99x + 101y = 499

(ii)

x2 – 15x + 54 = 0

(iii) 560

2, 11, 20, 29, ....

P.T.O.

6/N 685
(iv) ` 200 0.3%

(v)  fidi = 10,000,  fi = 100 A = 2000 (x)

3. (A) 3

(i) 27 504

a – d, a, a + d.

 a – d + a + a + d =

 a =

:

(a – d) × a × (a + d) =

 [(9)2 – d2] × 9 = 504

 (81 – d2) × 9 = 504

 d2 = 81 –

 d =± 5

a = 9 d = 5 =

a = 9 d = –5 =

7/N 685
(ii) 52

(a)

(b)

‘S’

 n(S) =

A :

=

 n(A) =

n(A)
 P(A) = ..................
n(S)

26
 P(A) =
52

 P(A) =

P.T.O.

8/N 685
B :

 n(B) =

n(B)
 P(B) = .................
n(S)
12
 P(B) =
52

 P(B) =

(B) 6

(i) 210

( )

10–20 30

20–30 50

30–40 60

40–50 55

50–60 15

9/N 685
(ii) 100 150 120

7%

(iii) 2 3 84

(iv)

x + y = 6, x – y = 4

4. 8

(i) 5 : 4

900

(ii)

(a) A : 9

P.T.O.

10/N 685
(b) B : 5

(c) C :

(iii) 300

10–20 60

20–30 42

30–40 55

40–50 70

50–60 53

60–70 20

11/N 685
5. 3

(i)

(a)  = 0

(b)  > 0

(c)  < 0.

(ii) ‘p’ ‘q’ ‘r’

( p  r)(q  r – 2 p)
2( q – p)

P.T.O.