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SSC > Power, Indices and Surds

Explore popular questions from Power, Indices and Surds for SSC. This collection covers Power, Indices and Surds previous year SSC questions hand picked by experienced teachers.

Q 1.

Correct2

Incorrect-0.5

By how much does {tex} \sqrt { 12 } + \sqrt { 18 } {/tex} exceed {tex} \sqrt { 3 } + \sqrt { 2 } ? {/tex}

A

{tex} 2 ( \sqrt { 3 } - \sqrt { 2 } ) {/tex}

B

{tex} 2 ( \sqrt { 3 } + \sqrt { 2 } ) {/tex}

{tex} \sqrt { 3 } + 2 \sqrt { 2 } {/tex}

D

{tex} \sqrt { 2 } - 4 \sqrt { 3 } {/tex}

Explanation

Q 2.

Correct2

Incorrect-0.5

The value of {tex} \sqrt { 5 + 2 \sqrt { 6 } } - \frac { 1 } { \sqrt { 5 + 2 \sqrt { 6 } } } {/tex} is :

{tex} 2 \sqrt { 2 } {/tex}

B

{tex} 2 \sqrt { 3 } {/tex}

C

{tex} 1 + \sqrt { 5 } {/tex}

D

{tex} \sqrt { 5 } - 1 {/tex}

Explanation

Q 3.

Correct2

Incorrect-0.5

The value of {tex} \sqrt { 2 ^ { 4 } } + \sqrt [ 3 ] { 64 } + \sqrt [ 4 ] { 2 ^ { 8 } } {/tex} is :

12

B

16

C

18

D

24

Explanation

Q 4.

Correct2

Incorrect-0.5

{tex} 2 \sqrt [ 3 ] { 32 } - 3 \sqrt [ 3 ] { 4 } + \sqrt [ 3 ] { 500 } {/tex} is equal

A

{tex} 4 \sqrt [ 3 ] { 6 } {/tex}

B

{tex} 3 \sqrt { 24 } {/tex}

{tex} 6 \sqrt [ 3 ] { 4 } {/tex}

D

916

Explanation

Q 5.

Correct2

Incorrect-0.5

{tex} ( \sqrt { 8 } - \sqrt { 4 } - \sqrt { 2 } ) {/tex} equals :

A

{tex} 2 - \sqrt { 2 } {/tex}

{tex} \sqrt { 2 } - 2 {/tex}

C

2

D

-2

Explanation

Q 6.

Correct2

Incorrect-0.5

{tex} 8 ^ { 2 / 3 } {/tex} is equal to :

A

{tex} 5 \frac { 1 } { 2 } {/tex}

B

{tex} 21 \frac { 1 } { 3 } {/tex}

4

D

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

Explanation

Q 7.

Correct2

Incorrect-0.5

The simplified form of {tex} \left( 16 ^ { \frac{3}{2} } + 16 ^ { \frac{- 3}{2} } \right) {/tex} is :

A

0

{tex} \frac { 4097 } { 64 } {/tex}

C

1

D

{tex} \frac { 16 } { 4097 } {/tex}

Explanation



Q 8.

Correct2

Incorrect-0.5

{tex} 16 ^ { 3 / 4 } {/tex} is equal to :

A

{tex} 4 \sqrt { 2 } {/tex}

8

C

{tex} 2 \sqrt { 2 } {/tex}

D

16

Explanation

Q 9.

Correct2

Incorrect-0.5

{tex} ( 0.01024 ) ^ { \frac{1}{5} } {/tex} is equal to :

A

4

B

0.04

0.4

D

0.00004

Explanation

Q 10.

Correct2

Incorrect-0.5

{tex} \left( 16 ^ { 0.16 } \times 2 ^ { 0.36 } \right) {/tex} is equal to

2

B

16

C

32

D

64

Explanation

Q 11.

Correct2

Incorrect-0.5

The value of {tex} ( 256 ) ^ { 0.16 } \times ( 16 ) ^ { 0.18 } {/tex} is

4

B

-4

C

16

D

256

Explanation

Q 12.

Correct2

Incorrect-0.5

The value of {tex} \frac { ( 243 ) ^ { 0.13 } \times ( 243 ) ^ { 0.07 } } { ( 7 ) ^ { 0.25 } \times ( 49 ) ^ { 0.075 } \times ( 343 ) ^ { 0.2 } } {/tex} is

{tex} \frac { 3 } { 7 } {/tex}

B

{tex} \frac { 7 } { 3 } {/tex}

C

{tex} 1 \frac { 3 } { 7 } {/tex}

D

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

Explanation

Q 13.

Correct2

Incorrect-0.5

{tex} \sqrt { - \sqrt { 3 } + \sqrt { 3 + 8 \sqrt { 7 + 4 \sqrt { 3 } } } } {/tex}

A

1

2

C

3

D

8

Explanation





Q 14.

Correct2

Incorrect-0.5

{tex} \sqrt { \sqrt [ 3 ] { 0.004096 } } {/tex} is equal to

A

4

0.4

C

0.04

D

0.004

Explanation

Q 15.

Correct2

Incorrect-0.5

The approximate value of {tex} \frac { 3 \sqrt { 12 } } { 2 \sqrt { 28 } } \div \frac { 2 \sqrt { 21 } } { \sqrt { 98 } } {/tex} is

A

1.0727

1.0606

C

1.6026

D

1.6007

Explanation

Q 16.

Correct2

Incorrect-0.5

The value of {tex} 2 + \sqrt { 0.09 } - \sqrt [ 3 ] { 0.008 } - 75 \% {/tex} of 2.80

0

B

0.01

C

-1

D

0.001

Explanation

Q 17.

Correct2

Incorrect-0.5

The value of
{tex} ( \sqrt [ 3 ] { 3.5 } + \sqrt [ 3 ] { 2.5 } ) ( \sqrt [ 3 ] { 3 \sqrt { 3.5 } } ) ^ { 2 } - \sqrt [ 3 ] { 8.75 } + ( \sqrt [ 3 ] { 2.5 } ) ^ { 2 } {/tex} is :

A

5.375

B

1

6

D

5

Explanation

Q 18.

Correct2

Incorrect-0.5

The value of {tex} ( 3 + 2 \sqrt { 2 } ) ^ { - 3 } + ( 3 - 2 \sqrt { 2 } ) ^ { - 3 } {/tex} is

A

189

B

180

C

108

198

Explanation



Q 19.

Correct2

Incorrect-0.5

{tex} \frac { \sqrt { 5 } } { \sqrt { 3 } + \sqrt { 2 } } - \frac { 3 \sqrt { 3 } } { \sqrt { 5 } + \sqrt { 2 } } + \frac { 2 \sqrt { 2 } } { \sqrt { 5 } + \sqrt { 3 } } {/tex}

0

B

{tex} 2 \sqrt { 15 } {/tex}

C

{tex} 2 \sqrt { 10 } {/tex}

D

{tex} 2 \sqrt { 6 } {/tex}

Explanation



Q 20.

Correct2

Incorrect-0.5

When {tex} ( 4 + \sqrt { 7 } ) {/tex} is presented in the form of perfect square it will be equal to

A

{tex} ( 2 + \sqrt { 7 } ) ^ { 2 } {/tex}

B

{tex} \left( \frac { \sqrt { 7 } } { 2 } + \frac { 1 } { 2 } \right) ^ { 2 } {/tex}

{tex} \left\{ \frac { 1 } { \sqrt { 2 } } ( \sqrt { 7 } + 1 ) \right\} {/tex}

D

{tex} ( \sqrt { 3 } + \sqrt { 4 } ) ^ { 2 } {/tex}

Explanation

Q 21.

Correct2

Incorrect-0.5

The value of
{tex} \frac { 1 } { \sqrt { 3.25 } + \sqrt { 2.25 } } + \frac { 1 } { \sqrt { 4.25 } + \sqrt { 3.25 } } + {/tex} {tex} \frac { 1 } { \sqrt { 5.25 } + \sqrt { 4.25 } } + \frac { 1 } { \sqrt { 6.25 } + \sqrt { 5.25 } } {/tex} is

1

B

1.25

C

1.5

D

2.25

Explanation



Q 22.

Correct2

Incorrect-0.5

The simplified form of {tex} \frac { 2 } { \sqrt { 7 } + \sqrt { 5 } } + \frac { 7 } { \sqrt { 12 } - \sqrt { 5 } } - \frac { 5 } { \sqrt { 12 } - \sqrt { 7 } } {/tex} is :

A

5

B

2

C

1

0

Explanation





Q 23.

Correct2

Incorrect-0.5

{tex} \left( \frac { 1 } { 2 } \right) ^ { - \frac { 1 } { 2 } } {/tex} is equal to

A

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

B

{tex} 2 \sqrt { 2 } {/tex}

C

{tex} - \sqrt { 2 } {/tex}

{tex} \sqrt { 2 } {/tex}

Explanation

Q 24.

Correct2

Incorrect-0.5

{tex} \frac { 1 } { \sqrt { 3 } + \sqrt { 4 } } + \frac { 1 } { \sqrt { 4 } + \sqrt { 5 } } + \frac { 1 } { \sqrt { 5 } + \sqrt { 6 } } + {/tex} {tex} \frac { 1 } { \sqrt { 6 } + \sqrt { 7 } } + \frac { 1 } { \sqrt { 7 } + \sqrt { 8 } } + \frac { 1 } { \sqrt { 8 } + \sqrt { 9 } } {/tex} is equal to

A

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

B

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

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

D

{tex} 5 - \sqrt { 3 } {/tex}

Explanation



Q 25.

Correct2

Incorrect-0.5

{tex} ( 16 ) ^ { 0.16 } \times ( 16 ) ^ { 0.04 } \times ( 2 ) ^ { 0.2 } {/tex} is equal to :

A

1

2

C

4

D

16

Explanation