Algebra Set 1 2021-2022 SSC (English Medium) 10th Standard Question Paper Solution

Which one is the quadratic equation?

`5/x - 3 = x^2`

x(x + 5) = 2

n – 1 = 2n

`1/x^2(x + 2)` = x

First four terms of an A.P., are ______ whose first term is –2 and the common difference is –2.

– 2, 0, 2, 4

– 2, 4, – 8, 16

– 2, – 4, – 6, – 8

– 2, – 4, – 8, – 16

For simultaneous equations in variables x and y, D_x = 49, D_y = – 63, D = 7, then what is the value of y?

9

7

– 7

– 9

Which number cannot represent a probability?

`2/3` 

1.5 

15%

0.7

`15/10`

To draw a graph of 4x + 5y = 19, find y when x = 1.

Determine whether 2 is a root of quadratic equation 2m² – 5m = 0.

Write second and third term of an A.P. whose first term is 6 and common difference is – 3.

Two coins are tossed simultaneously. Write the sample space ‘S’.

Complete the activity to find the value of the determinant.

Activity: `|(2sqrt3, 9),(2, 3sqrt(3))| = 2sqrt(3) xx square - 9 xx square`

= `square` – 18

= `square`

Complete the following activity to find the 19^th term of an A.P. 7, 13, 19, 25, ........ :

Activity: 

Given A.P. : 7, 13, 19, 25, ..........

Here first term a = 7; t₁₉ = ?

t_n + a + `(square)`d .........(formula)

∴ t₁₉ = 7 + (19 – 1) `square`

∴ t₁₉ = 7 + `square`

∴ t₁₉ = `square`

If one die is rolled, then find the probability of the following event by completing the activity.

Event A: The number on the upper face is prime.

Activity: Let ‘S’ be the sample space.

S = {1, 2, 3, 4, 5, 6}  

∴ n(S) = 6

Event A: Prime number on the upper face.

A = {`square`}            

∴ n(A) = 3

P(A) = `square/(n(S))`    .....[Formula]

= `square/6`

∴ P(A) = `1/square`

To solve the following simultaneous equations by Cramer's rule, find the values of D_x and D_y.

3x + 5y = 26

x + 5y = 22

A box contains 5 red, 8 blue and 3 green pens. Rutuja wants to pick a pen at random. What is the probability that the pen is blue?

Find the sum of first 'n' even natural numbers.

Solve the following quadratic equation by factorisation method:

x² + x – 20 = 0

Find the values of (x + y) and (x – y) of the following simultaneous equations:

49x – 57y = 172

57x – 49y = 252

One of the roots of equation kx² – 10x + 3 = 0 is 3. Complete the following activity to find the value of k.

Activity:

One of the roots of equation kx² – 10x + 3 = 0 is 3.

Putting x = `square` in the above equation

∴ `"k"(square)^2 - 10 xx square + 3` = 0

∴ `square` – 30 + 3 = 0

∴ 9k = `square`

∴ k = `square`

A card is drawn at random from a pack of well shuffled 52 playing cards. Complete the following activity to find the probability that the card drawn is:

Event A: The card drawn is an ace.

Event B: The card drawn is a spade.

Activity: 'S' is the sample space.

∴ n(S) = 52

Event A: The card drawn is an ace.

∴ n(A) = `square`

P(A) = `square`  ......(formula)

∴ P(A) = `square/52`

∴ P(A) = `square/13`

Event B: The card drawn is a spade.

∴ n(B) = `square`

P(B) = `(n(B))/(n(S))`

∴ P(B) = `square/4`

Solve the simultaneous equations by using graphical method

x + 3y = 7
2x + y = –1

There is an auditorium with 27 rows of seats. There are 20 seats in the first row, 22 seats in the second row, 24 seats in the third row and so on. Find how many total seats are there in the auditorium?

Solve the Following Word Problem.
Sum of the present ages of Manish and Savita is 31. Manish’s age 3 years ago was 4 times the age of Savita. Find their present ages.

Solve the following quadratic equation using formula:

x² + 10x + 2 = 0

If 460 is divided by a natural number, then quotient is 2 more than nine times the divisor and remainder is 5. Find the quotient and divisor.

If the 9^th term of an A.P. is zero, then prove that 29^th term is double of 19^th term.

The perimeter of an isosceles triangle is 24 cm. The length of its congruent sides is 13 cm less than twice the length of its base. Find the lengths of all sides of the triangle.

A bag contains 8 red and some blue balls. One ball is drawn at random from the bag. If ratio of probability of getting red ball and blue ball is 2:5, then find the number of blue balls.

Measures of angles of a triangle are in A.P. The measure of smallest angle is five times of common difference. Find the measures of all angles of a triangle. (Assume the measures of angles as a, a + d, a + 2d)