Maharashtra SSC Algebra (Mathematics Part I) Board Paper March 2026

Q.1 (A)(i) Rate of GST on essential commodities is ....................... .

Q.1 (A)(ii) Out of the following equations which one is not a quadratic equation ?

Q.1 (A)(iii) To draw graph of \(4x + 5y = 19\), find the value of \(y\) when \(x = 1\).

Q.1 (A)(iv) Sum of first five multiples of 3 is ....................... .

Q.1 (B)(i) On certain article if rate of CGST is 9%, then what is the rate of GST ?

Q.1 (B)(ii) For simultaneous equations in variables \(x\) and \(y\), if \(D_x = -42\) and \(D = -3\), then find the value of \(x\).

Q.1 (B)(iii) When two coins are tossed simultaneously, write the sample space ‘S’.

Q.1 (B)(iv) Write the following quadratic equation in the form \(ax^2 + bx + c = 0\) :

\[ 2y = 10 - y^2 \]

Q.2 (A)(i) If one die is rolled, then find the probability of the event, that the number on the upper face is prime.

Solution :

‘S’ is the sample space.
S = {1, 2, 3, 4, 5, 6}
\(\therefore n(S) =\) ____
Event A : Prime number on the upper face.
A = {2, 3, 5}
\(\therefore n(A) =\) ____
\(\therefore P(A) = \dfrac{\text{____}}{\text{____}}\)
\(\therefore P(A) = \dfrac{\text{____}}{6}\)
\(= \dfrac{1}{2}\)

Q.2 (A)(ii) Write the correct number in the given boxes from the given A.P. : 70, 60, 50, 40, ............

Here \(t_1 =\) ____, \(t_2 = 60\), \(t_3 =\) ____
\(\therefore a =\) ____, \(d =\) ____

Q.2 (A)(iii) Complete the following table to draw graph of the equation.

\[ x + y = 3 \]

Q.2 (B)(i) If two coins are tossed simultaneously, find the probability of the event, “getting at least one head.”

Q.2 (B)(ii) Solve the following simultaneous equations :

\[ x + y = 4 \]

\[ 2x - y = 2 \]

Q.2 (B)(iii) Solve the following quadratic equation by factorisation method :

\[ x^2 + x - 20 = 0 \]

Q.2 (B)(iv) Given A.P. is 12, 16, 20, 24, .................... Find the 24th term of this progression.

Q.2 (B)(v) If \(\sum x_i f_i = 1265\) and \(N = 50\), then find the mean of the given data.

Q.3 (A)(i) Shreekar bought a Laptop with 10% discount on printed price. The printed price of that Laptop was ₹ 50,000. 18% GST was charged on discounted price. Find the amount of CGST and SGST. What amount did Shreekar pay ?

Solution :

Discount \(= 10\%\) of \(50{,}000 = \) ₹ ____
\(\therefore\) Taxable value of Laptop \(= 50{,}000 - \) ____ \(= \) ₹ 45,000
\(\therefore\) Rate of GST \(=\) ____
\(\therefore\) Rate of CGST \(= 9\%\)
\(\therefore\) CGST \(= 9\%\) of \(45{,}000\)
\(= \) ____ \(\times 45{,}000\)
\(= \) ₹ ____
\(\therefore\) SGST \(= \) ₹ 4,050
Total amount of Laptop \(= 45{,}000 + 4{,}050 + 4{,}050 = \) ₹ ____

Q.3 (A)(ii) One of the roots of the quadratic equation \(5m^2 + 2m + k = 0\) is \(\dfrac{-7}{5}\). Complete the following activity to find the value of ‘\(k\)’.

Solution :

\(\dfrac{-7}{5}\) is a root of quadratic equation \(5m^2 + 2m + k = 0\).
\(\therefore\) put \(m = \dfrac{-7}{5}\) in the equation.
\(\therefore 5 \times \left(\text{____}\right)^2 + 2 \times \left(\text{____}\right) + k = 0\)
____ \(+\) ____ \(+ k = 0\)
____ \(+ k = 0\)
\(\therefore k =\) ____

Q.3 (B)(i) Two numbers differ by 3. The sum of twice the smaller number and thrice the greater number is 19. Find the numbers.

Q.3 (B)(ii) Sachin invested some amount in a National Saving Certificate Scheme. In the first year he invested ₹ 5,000, in the second year ₹ 7,000, in the third year ₹ 9,000 and so on. Find the total amount that he invested in 12 years.

Q.3 (B)(iii) There are six cards in a box, each bearing a number from 0 to 5. Find the probability of each of the following events, that :

(1) The number on the card drawn is a natural number.
(2) The number on the card drawn is a whole number.

Q.4 (i) The sum of two roots of a quadratic equation is 7 and sum of their cubes is 91, find the equation.

Q.4 (ii) Smt. Tejaswini purchased 100 shares of FV ₹ 80 when the MV is ₹ 900. She paid brokerage at the rate of 0.5% and 18% GST on brokerage. Find the following :

(1) Net amount paid for 100 shares.
(2) Brokerage paid on sum invested.
(3) GST paid on brokerage.
(4) Total amount paid for 100 shares.

Q.4 (iii) The following table shows the funds collected by 105 students for flood affected people. Find the median of the data.

Q.5 (i) A survey was conducted in the school. Student using different modes of transport is given below :

Find the value of \(a\) and draw the Pie diagram.

Q.5 (ii) There are some students in group A and group B. If one student goes from group A to group B, then the number of students in both groups is same. But one student goes from group B to group A, then the number of students in group A becomes twice of group B. Find the number of students in each group.