Quantitative Aptitude - Surds and Indices
Exam Duration: 45 Mins Total Questions : 30
The value of \({ (\sqrt { 8 } ) }^{ \frac { 1 }{ 3 } }\)is:
- (a)
2
- (b)
4
- (c)
\(\sqrt { 2 } \)
- (d)
8
The value of \((\frac { 32 }{ 243 } )^{ -\frac { 4 }{ 5 } }\)is:
- (a)
\(\frac { 4 }{ 9 } \)
- (b)
\(\frac { 9 }{ 4 } \)
- (c)
\(\frac { 16 }{ 81 } \)
- (d)
\(\frac { 81 }{ 16 } \)
The value of \(({ -\frac { 1 }{ 216 } ) }^{ -\frac { 2 }{ 3 } }\)is :
- (a)
36
- (b)
-36
- (c)
\(\frac { 1 } { 36 }\)
- (d)
\(-\frac { 1 } { 36 } \)
The value of \({ 5 }^{ \frac { 1 }{ 4 } }\times ({ 125 })^{ 0.25 }\) is :
- (a)
\(\sqrt { 5 } \)
- (b)
5
- (c)
\(5\sqrt { 5 } \)
- (d)
25
The value of \([{ (10) }^{ 150 }\div { (10) }^{ 146 }]\) is:
- (a)
1000
- (b)
10000
- (c)
100000
- (d)
\({ 10 }^{ 6 }\)
\({ (256) }^{ 0.16 }\times { (256) }^{ 0.09 }=?\)
- (a)
4
- (b)
16
- (c)
64
- (d)
256.25
\(({ 0.04) }^{ -1.5 }=?\)
- (a)
25
- (b)
125
- (c)
250
- (d)
625
The value of \(({ 8 }^{ -25 }-{ 8 }^{ -26 })\)is :
- (a)
\(7\times { 8 }^{ -25 }\)
- (b)
\(7\times { 8 }^{ -26 }\)
- (c)
\(8\times { 8 }^{ -26 }\)
- (d)
None of these
\({ (18) }^{ 3.5 }\div { (27) }^{ 3.5 }\times { 6 }^{ 3.5 }={ 2 }^{ ? }\)
- (a)
3.5
- (b)
4.5
- (c)
6
- (d)
7
- (e)
None of these
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)
\(2 \frac { 2 } {7 }\)
If \({ (\frac { a }{ b } ) }^{ x-1 }={ (\frac { b }{ a } ) }^{ x-3 }\), then the value of x is:
- (a)
\(\frac { 1 } { 2 }\)
- (b)
1
- (c)
2
- (d)
\(\frac { 7 } { 2 }\)
If \({ 2 }^{ 2n-1 }=\frac { 1 }{ { 8 }^{ n-3 } } \), then the value of n is:
- (a)
3
- (b)
2
- (c)
0
- (d)
-2
If \({ 5 }^{ a }\)=3125,then the value of \({ 5 }^{ (a-3) }\)is:
- (a)
25
- (b)
125
- (c)
625
- (d)
1625
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
If \(\sqrt { { 2 }^{ n } } =64\), then the value of n is:
- (a)
2
- (b)
4
- (c)
6
- (d)
12
If \(\frac { { 9 }^{ n }\times { 3 }^{ 5 }\times { (27) }^{ 3 } }{ 3\times { (81) }^{ 4 } } =27,\)then the value of n is:
- (a)
0
- (b)
2
- (c)
3
- (d)
4
If \({ 2 }^{ n+4 }-{ 2 }^{ n+2 }=3,\)then n is equal to :
- (a)
0
- (b)
2
- (c)
-1
- (d)
-2
If \({ 3 }^{ x }-{ 3 }^{ x-1 }=18\),then the value of \({ x }^{ x }\)is :
- (a)
3
- (b)
8
- (c)
27
- (d)
216
\(\frac { { 2 }^{ n+4 }-2\times { 2 }^{ n } }{ 2\times { 2 }^{ (n+3) } } +{ 2 }^{ -3 }\) is :
- (a)
\({ 2 }^{ n+1 }\)
- (b)
(\(\frac { 9 }{ 8 } -{ 2 }^{ n }\))
- (c)
(\({ -2 }^{ n+1 }+\frac { 1 }{ 8 } \))
- (d)
1
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)
\(3\sqrt {3}\)
\(\frac { 1 }{ 1+{ a }^{ n-m } } +\frac { 1 }{ 1+{ a }^{ m-n } } =?\)
- (a)
0
- (b)
\(\frac { 1 } { 2 }\)
- (c)
1
- (d)
\({a}^{m+n}\)
\(\frac { 1 }{ 1+{ x }^{ (b-a) }+{ x }^{ (c-a) } } +\frac { 1 }{ 1+{ x }^{ (a-b) }+{ x }^{ (c-b) } } +\frac { 1 }{ 1+{ x }^{ (b-c) }+{ x }^{ (a-c) } } =?\)
- (a)
0
- (b)
1
- (c)
\((x)^{a-b-c}\)
- (d)
none of these
\((\frac { { x }^{ b } }{ { x }^{ c } } )^{( b+c-a )}.(\frac { { x }^{ c } }{ { x }^{ a } } )^{ (c+a-b) }.(\frac { { x }^{ a } }{ { x }^{ b } } )^{( a+b-c) }=?\)
- (a)
\({x}^{abc}\)
- (b)
1
- (c)
\({x}^{ab+bc+ca}\)
- (d)
\({x}^{a+b+c}\)
\({ (\frac { { x }^{ a } }{ { x }^{ b } } ) }^{ \frac { 1 }{ ab } }.{ (\frac { { x }^{ b } }{ { x }^{ c } } ) }^{ \frac { 1 }{ bc } }.{ (\frac { { x }^{ c } }{ { x }^{ a } } ) }^{ \frac { 1 }{ ca } }=?\quad \)
- (a)
1
- (b)
\({ x }^{ \frac { 1 }{ abc } }\)
- (c)
\({ x }^{ \frac { 1 }{ (ab +bc+ca) } }\)
- (d)
None of these
If a,b,c are real numbers, then the value of \(\sqrt { { a }^{ -1 }b } .\sqrt { b^{ -1 }c } .\sqrt { c^{ -1 }a } \) is :
- (a)
abc
- (b)
\(\sqrt { abc } \)
- (c)
\(\frac { 1 } { abc }\)
- (d)
1
If \({ 3 }^{ (x-y) }\)=27 and \({ 3 }^{ (x+y) }\)=243, then x is equal to:
- (a)
0
- (b)
2
- (c)
4
- (d)
6
If \({ a }^{ x }={ b }^{ y }={ c }^{ z }\)and \({ b }^{ 2 }=ac\), then y equals.
- (a)
\(\frac { xz }{ x+z } \)
- (b)
\(\frac { xz }{ 2(x-z) } \)
- (c)
\(\frac { xz }{ 2(z-x) } \)
- (d)
\(\frac { 2xz }{ (x+z) } \)
If \({ a }^{ x }=b, { b }^{ y }=c,\) and \({ c }^{ z }=a\), then the value of xyz is:
- (a)
0
- (b)
1
- (c)
\(\frac { 1 } { abc }\)
- (d)
abc
If \({ 2 }^{ x }={ 4 }^{ y }={ 8 }^{ z }\) and \(\frac { 1 }{ 2x } +\frac { 1 }{ 4y } +\frac { 1 }{ 6z } =\frac { 24 }{ 7 } \), then the value of z is :
- (a)
\(\frac { 7 }{ 16 } \)
- (b)
\(\frac { 7 }{ 32 } \)
- (c)
\(\frac { 7 }{ 48 } \)
- (d)
\(\frac { 7 }{ 64 } \)
If \(x=5+2\sqrt { 6 } ,then\quad \frac { (x-1) }{ \sqrt { x } } \)is equal to:
- (a)
\(\sqrt { 2 } \)
- (b)
\(2\sqrt { 2 } \)
- (c)
\(\sqrt { 3 } \)
- (d)
\(2\sqrt { 3 } \)