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SSC Quantitative Aptitude - Surds and Indices Practice Questions

Quantitative Aptitude - Surds and Indices

Exam Duration: 45 Mins Total Questions : 30

1 )

The value of \({ (\sqrt { 8 } ) }^{ \frac { 1 }{ 3 } }\)is:

(a)
2
(b)
4
(c)
\(\sqrt { 2 } \)
(d)
8

2 )

The value of \((\frac { 32 }{ 243 } )^{ -\frac { 4 }{ 5 } }\)is:

(a)
\(\frac { 4 }{ 9 } \)
(b)
\(\frac { 9 }{ 4 } \)
(c)
\(\frac { 16 }{ 81 } \)
(d)
\(\frac { 81 }{ 16 } \)

3 )

The value of \({ 5 }^{ \frac { 1 }{ 4 } }\times ({ 125 })^{ 0.25 }\) is :

(a)
\(\sqrt { 5 } \)
(b)
5
(c)
\(5\sqrt { 5 } \)
(d)
25

4 )

The value of \([{ (10) }^{ 150 }\div { (10) }^{ 146 }]\) is:

(a)
1000
(b)
10000
(c)
100000
(d)
\({ 10 }^{ 6 }\)

5 )

\({ (\frac { 1 }{ 216 } ) }^{ -\frac { 2 }{ 3 } }\div { (\frac { 1 }{ 27 } ) }^{ -\frac { 4 }{ 3 } }=?\)

(a)
\(\frac { 3 } { 4 }\)
(b)
\(\frac { 2 } { 3 }\)
(c)
\(\frac { 4 } { 9 }\)
(d)
\(\frac { 1 } { 8 }\)

6 )

\({ (256) }^{ 0.16 }\times { (256) }^{ 0.09 }=?\)

(a)
4
(b)
16
(c)
64
(d)
256.25

7 )

\({ (17) }^{ 3.5 }\times ({ 17) }^{ ? }=17 ^{ 8 }\)

(a)
2.29
(b)
2.75
(c)
4.25
(d)
4.5

8 )

\(49\times 49\times 49\times 49={ 7 }^{ ? }\)

(a)
4
(b)
7
(c)
8
(d)
16

9 )

\({ (18) }^{ 3.5 }\div { (27) }^{ 3.5 }\times { 6 }^{ 3.5 }={ 2 }^{ ? }\)

(a)
3.5
(b)
4.5
(c)
6
(d)
7
(e)
None of these

10 )

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

(a)
\(\frac { 3 } {7 }\)
(b)
\(\frac { 7 } {3 }\)
(c)
\(1\frac { 3 } { 7 }\)
(d)
\(2 \frac { 2 } {7 }\)

11 )

If \({ 2 }^{ 2n-1 }=\frac { 1 }{ { 8 }^{ n-3 } } \), then the value of n is:

(a)
3
(b)
2
(c)
0
(d)
-2

12 )

If \(5\sqrt { 5 } \times { 5 }^{ 3 }\div { 5 }^{ -\frac { 3 }{ 2 } }={ 5 }^{ a+2 }\), then the value of a is:

(a)
4
(b)
5
(c)
6
(d)
8

13 )

If \(\sqrt { { 2 }^{ n } } =64\), then the value of n is:

(a)
2
(b)
4
(c)
6
(d)
12

14 )

If \({ (\sqrt { 3 } ) }^{ 5 }\times { 9 }^{ 2 }={ 3 }^{ n }\times 3\sqrt { 3 } \),then the value of n is:

(a)
2
(b)
3
(c)
4
(d)
5

15 )

If \({ 2 }^{ n+4 }-{ 2 }^{ n+2 }=3,\)then n is equal to :

(a)
0
(b)
2
(c)
-1
(d)
-2

16 )

If \({ 2 }^{ n-1 }+{ 2 }^{ n+1 }=320\),then the n is equal to :

(a)
6
(b)
8
(c)
5
(d)
7

17 )

\(\frac { { 2 }^{ n+4 }-2\times { 2 }^{ n } }{ 2\times { 2 }^{ (n+3) } } +{ 2 }^{ -3 }\) is :

(a)
\({ 2 }^{ n+1 }\)
(b)
(\(\frac { 9 }{ 8 } -{ 2 }^{ n }\))
(c)
(\({ -2 }^{ n+1 }+\frac { 1 }{ 8 } \))
(d)
1

18 )

If \(x=3+2\sqrt { 2 } \), then the value of \((\sqrt { x } -\frac { 1 }{ \sqrt { x } } )\)is :

(a)
1
(b)
2
(c)
\(2\sqrt {2 }\)
(d)
\(3\sqrt {3}\)

19 )

If m and n are whole numbers such that \({ m }^{ n }\)=121,then the value of \(({ m-1) }^{ (n+1) }\)is :

(a)
1
(b)
10
(c)
121
(d)
1000

20 )

\(\frac { { (243) }^{ \frac { n }{ 5 } }\times { 3 }^{ 2n+1 } }{ { 9 }^{ n }\times { 3 }^{ n-1 } } =?\)

(a)
1
(b)
3
(c)
9
(d)
\({ 3 }^{ n }\)

21 )

Number of prime factors in \({ (216 })^{ \frac { 3 }{ 5 } }\times { (2500) }^{ \frac { 2 }{ 5 } }\times { (300) }^{ \frac { 1 }{ 5 } }\)is:

(a)
6
(b)
7
(c)
8
(d)
None of these

22 )

\(\frac { 1 }{ 1+{ x }^{ (b-a) }+{ x }^{ (c-a) } } +\frac { 1 }{ 1+{ x }^{ (a-b) }+{ x }^{ (c-b) } } +\frac { 1 }{ 1+{ x }^{ (b-c) }+{ x }^{ (a-c) } } =?\)

(a)
0
(b)
1
(c)
\((x)^{a-b-c}\)
(d)
none of these

23 )

\((\frac { { x }^{ a } }{ { x }^{ b } } )^{ (a+b) }.(\frac { { x }^{ b } }{ { x }^{ c } } )^{ (b+c) }.(\frac { { x }^{ c } }{ { x }^{ a } } )^{ (c+a) }=?\)

(a)
0
(b)
\({x}^{abc}\)
(c)
\({x}^{a+b+c}\)
(d)
1

24 )

\({ (\frac { { x }^{ a } }{ { x }^{ b } } ) }^{ \frac { 1 }{ ab } }.{ (\frac { { x }^{ b } }{ { x }^{ c } } ) }^{ \frac { 1 }{ bc } }.{ (\frac { { x }^{ c } }{ { x }^{ a } } ) }^{ \frac { 1 }{ ca } }=?\quad \)