On account of the disruption in education due to the corona pandemic, we're opening up our platform for teachers, free of cost. Know More →

SSC > Algebra

Explore popular questions from Algebra for SSC. This collection covers Algebra previous year SSC questions hand picked by experienced teachers.

Q 1.

Correct4

Incorrect-1

If {tex} a * b = 2 a - 3 b + a b , {/tex} then {tex} 3 * 5 {/tex} {tex} + 5 * 3 {/tex} is equal to :

22

B

24

C

26

D

28

Explanation

Q 2.

Correct4

Incorrect-1

If {tex} \mathrm { p } \times \mathrm { q } = \mathrm { p } + \mathrm { q } + \frac { \mathrm { p } } { \mathrm { q } } , {/tex} the value of {tex} 8 \times 2 {/tex} is:

A

6

B

10

14

D

16

Explanation

Q 3.

Correct4

Incorrect-1

Two numbers {tex} x {/tex} and {tex} y ( x > y ) {/tex} are such that their sum is equal to three times their difference. Then value of {tex} \frac { 3 x y } { 2 \left( x ^ { 2 } - y ^ { 2 } \right) } {/tex} will be:

A

{tex} \frac { 2 } { 3 } {/tex}

1

C

{tex} 1 \frac { 1 } { 2 } {/tex}

D

{tex} 1 \frac { 2 } { 3 } {/tex}

Explanation

Q 4.

Correct4

Incorrect-1

The value of
{tex} \left( 1 + \frac { 1 } { x } \right) \left( 1 + \frac { 1 } { x + 1 } \right) \left( 1 + \frac { 1 } { x + 2 } \right) \left( 1 + \frac { 1 } { x + 3 } \right) {/tex}

A

{tex} 1 + \frac { 1 } { x + 4 } {/tex}

B

{tex} x + 4 {/tex}

C

{tex} \frac { 1 } { x } {/tex}

{tex} \frac { x + 4 } { x } {/tex}

Explanation


Q 5.

Correct4

Incorrect-1

If {tex} a * b = 2 ( a + b ) , {/tex} then {tex} 5 * 2 {/tex} is equal to :

A

3

B

10

14

D

20

Explanation

Q 6.

Correct4

Incorrect-1

If {tex} \frac { 2 a + b } { a + 4 b } = 3 {/tex}, then find the value of {tex} \frac { a + b } { a + 2 b } {/tex}

A

{tex} \frac { 5 } { 9 } {/tex}

B

{tex} \frac { 2 } { 7 } {/tex}

{tex} \frac { 10 } { 9 } {/tex}

D

{tex} \frac { 10 } { 7 } {/tex}

Explanation

Q 7.

Correct4

Incorrect-1

If {tex} x = \sqrt { \frac { \sqrt { 5 } + 1 } { \sqrt { 5 } - 1 } } , {/tex} then the value of {tex} 5 x ^ { 2 } - 5 x - 1 {/tex} is

A

0

B

3

4

D

5

Explanation



Q 8.

Correct4

Incorrect-1

If {tex} a * b = a + b + a b {/tex}, then {tex} 3 * 4 - 2 * 3 {/tex} is equal to :

A

6

8

C

10

D

12

Explanation

Q 9.

Correct4

Incorrect-1

If {tex} \quad x = 7 - 4 \sqrt { 3 } {/tex}, then the value of {tex} \left( x + \frac { 1 } { x } \right) {/tex} is :

A

{tex} 3 \sqrt { 3 } {/tex}

B

{tex} 8 \sqrt { 3 } {/tex}

C

{tex} 14 + 8 \sqrt { 3 } {/tex}

{tex} 14{/tex}

Explanation


Q 10.

Correct4

Incorrect-1

If {tex} \frac { a } { 3 } = \frac { b } { 4 } = \frac { c } { 7 } {/tex} then {tex} \frac { a + b + c } { c } {/tex} is equal to

A

0

B

1

2

D

3

Explanation

Q 11.

Correct4

Incorrect-1

If {tex} \frac { 144 } { 0.144 } = \frac { 14.4 } { x } , {/tex} then the value of {tex} x {/tex} is

A

144

B

14.4

C

1.44

0.0144

Explanation

Q 12.

Correct4

Incorrect-1

If {tex} 1 < x < 2 {/tex}, then the value of {tex} \sqrt { ( x - 1 ) ^ { 2 } } + \sqrt { ( x - 3 ) ^ { 2 } } {/tex} is

A

1

2

C

3

D

{tex} 2 x - 4 {/tex}

Explanation

Q 13.

Correct4

Incorrect-1

If a {tex} \otimes \mathrm { b } = ( a \times b ) + b {/tex}, then {tex} 5 \otimes{/tex} 7 equals to

A

12

B

35

42

D

50

Explanation

Q 14.

Correct4

Incorrect-1

Given that {tex} 10 ^ { 0.48 } = \mathrm { x } , 10 ^ { 0.70 } {/tex} {tex} = \mathrm { y } , {/tex} and {tex} \mathrm { x } ^ { z } = \mathrm { y } ^ { 2 } , {/tex} then the value of {tex} \mathrm { z } {/tex} is close to

A

1.45

B

1.88

2.9

D

3.7

Explanation

Q 15.

Correct4

Incorrect-1

If {tex} \quad 47.2506 = 4 \mathrm { A } + \frac { 7 } { \mathrm { B } } + 2 \mathrm { C } + \frac { 5 } { \mathrm { D } } + 6 \mathrm { E } {/tex}, then the value of
{tex} 5 \mathrm { A } {/tex} {tex} + 3 \mathrm { B } + 6 \mathrm { C } + \mathrm { D } + 3 \mathrm { E } {/tex} is

A

53.6003

B

53.603

153.6003

D

213.0003

Explanation


Q 16.

Correct4

Incorrect-1

If {tex} x * y = x ^ { 2 } + y ^ { 2 } - x y , {/tex} then the value of {tex} 9 * 11 {/tex} is

A

93

103

C

113

D

121

Explanation

Q 17.

Correct4

Incorrect-1

If {tex} \frac { 2 p } { p ^ { 2 } - 2 p + 1 } = \frac { 1 } { 4 } , p \neq 0 {/tex}
then the value of {tex} p + \frac { 1 } { p } {/tex} is

A

4

B

5

10

D

12

Explanation

Q 18.

Correct4

Incorrect-1

If {tex} 5 ^ { 5 x + 5 } = 1 , {/tex} then {tex} x {/tex} equals

A

{tex} 0{/tex}

{tex} - 1 {/tex}

C

{tex} 1{/tex}

D

{tex} - \frac { 4 } { 5 } {/tex}

Explanation


Q 19.

Correct4

Incorrect-1

If {tex} 3 ^ { x + 3 } + 7 = 250 , {/tex} then {tex} x {/tex} is equal

A

5

B

3

2

D

1

Explanation

Q 20.

Correct4

Incorrect-1

If {tex} \frac { 1 } { 4 } \times \frac { 2 } { 6 } \times \frac { 3 } { 8 } \times \frac { 4 } { 10 } \times \frac { 5 } { 12 } \times {/tex} {tex} \ldots \times \frac { 31 } { 64 } = \frac { 1 } { 2 ^ { x } } , {/tex} the value of {tex} x {/tex} is

A

31

B

32

36

D

37

Explanation

Q 21.

Correct4

Incorrect-1

The value of
{tex} \frac { ( 243 ) ^ { \frac { n } { 5 } } \cdot 3 ^ { 2 n + 1 } } { 9 ^ { n } \cdot 3 ^ { n - 1 } } {/tex} is

A

1

9

C

3

D

{tex} 3 ^ { n } {/tex}

Explanation

Q 22.

Correct4

Incorrect-1

If {tex} x = 0.5 {/tex} and {tex} y = 0.2 , {/tex} then value of {tex} \sqrt { 0.6 } \times ( 3 y ) ^ { x } {/tex} is equal to

A

1.0

B

0.5

0.6

D

1.1

Explanation

Q 23.

Correct4

Incorrect-1

If {tex} x ^ { x \sqrt { x } } = ( x \sqrt { x } ) ^ { x } , {/tex} then {tex} x {/tex} equals

A

{tex} \frac { 4 } { 9 } {/tex}

B

{tex} \frac { 2 } { 3 } {/tex}

{tex} \frac { 9 } { 4 } {/tex}

D

{tex} \frac { 3 } { 2 } {/tex}

Explanation


Q 24.

Correct4

Incorrect-1

If {tex} a = 7 , b = 5 {/tex} and {tex} c = 3 , {/tex} then the value of {tex} a ^ { 2 } + b ^ { 2 } + c ^ { 2 } - a b - {/tex} {tex} b c - c a {/tex} is

12

B

-12

C

0

D

8

Explanation

Q 25.

Correct4

Incorrect-1

If {tex} 7 ^ { x } = \frac { 1 } { 343 } , {/tex} then the value of {tex} x {/tex}

A

3

-3

C

{tex} \frac { 1 } { 3 } {/tex}

D

{tex} \frac { 1 } { 7 } {/tex}

Explanation