Algebra Mathematics 1 Official 2022-2023 SSC (English Medium) 10th Standard Board Exam Question Paper Solution

The Sum of first five multiples of 3 is ______.

45

55

15

75

Find the value of the determinant `|(3, 2), (4, 5)|`.

2

7

−7

23

Which of the following quadratic equations has roots 3 and 5?

x² − 15x + 8 = 0

x² − 8x + 15 = 0

x² + 3x + 5 = 0

x² + 8x − 15 = 0

Two coins are tossed simultaneously. Write the number of sample points n(S):

2

8

4

6

If 15x + 17y = 21 and 17x + 15y = 11, then find the value of x + y.

Given sequence is an A.P. Find the next two terms of the A.P.:

5, 12, 19, 26, .....

If n(S) = 2 and n(A) = 1, then find P(A).

Complete the following table to draw the graph of the equation x + y = 3:

Complete the following activity to find the value of discriminant of the equation x² + 10x − 7 = 0.

Solution:

Comparing x² + 10x − 7 = 0 with ax² + bx + c = 0

a = 1, b = 10, c = ______

∴ b² − 4ac = ______ − 4 × 1 × (−7)

= 100 + ______

= ______

Complete the following table using given information:

Complete the following table using given information:

Complete the following table using given information:

Complete the following table using given information:

Solve the following simultaneous equations:

x + y = 6; x − y = 4

Solve the following quadratic equation by factorisation method:

x² + 15x + 54 = 0

The first term a = 8 and common difference d = 5 are given. Write an A.P.

Mr. Rohit is a retailer. He paid GST of ₹6,500 at the time of purchase. He collected GST of ₹8,000 at the time of sale.

1.  Find his input tax and output tax.
2. What is his input tax credit?
3. Find his payable GST.
4. Hence find the payable CGST anti payable SGST.

Find the mean from the given values:

∑x_if_i = 1265; N = 50

Smita has invested ₹12,000 and purchased shares of FV ₹10 at a premium of ₹2. Find the number of shares she purchased. Complete the given activity to get the answer.

Solution:

FV = ₹10, Premium = ₹2

∴ MV = FV + ______ = 10 + ______ = ______

∴ Number of shares = `"Total investment"/"MV" = 12000/underline`

= ______ shares

Ans.: Smita has purchased = ______ shares

If one die is rolled once, then find the probability of each of the following events:

1. Number on the upper face is prime
2. Number on the upper face is even.

Solution:

'S' is the sample space.

S = {1, 2, 3, 4, 5, 6} ∴ n(S) = ______

(a) Event A: Prime number on the upper face

A = {2, 3, 5} ∴ n(A) = ______

∴ P(A) = `("n"("A"))/("n"("S"))`

∴ P(A) = `3/underline` = ______

(b) Event B: Even number on the upper face

B = {2, 4, 6} ∴ n(B) = ______

∴ P(B) = `("n"("B"))/("n"("S"))`

∴ P(B) = ______ = `1/2`

Solve the given quadratic equation by using the formula method:

5x² + 13x + 8 = 0

A balloon vendor has 2 red, 3 blue and 4 green balloons. He wants to choose one of them at random to give it to Pranali. What is the probability of the event that Pranali gets, a red balloon

A balloon vendor has 2 red, 3 blue and 4 green balloons. He wants to choose one of them at random to give it to Pranali. What is the probability of the event that Pranali gets, a blue balloon

A balloon vendor has 2 red, 3 blue and 4 green balloons. He wants to choose one of them at random to give it to Pranali. What is the probability of the event that Pranali gets, a green balloon.

The following table shows the number of students of class X and the time they utilized daily for their studies. Find the mean time spent by 50 students for their studies by direct method:

The sum of two roots of a quadratic equation is 5 and sum of their cubes is 35, find the equation.

If p times the p^th term of an A.P. is equal to q times q^th term, then show that (p + q)^th term of that A.P. is zero (p ≠ q).

Draw a pie diagram to represent the world population given in the following table: 

Represent the following data using a histogram:

Observe the following flow chart and solve it: