Quantitative Aptitude - Surds and Indices
Exam Duration: 60 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 \(\frac { 1 }{ { (216) }^{ -\frac { 2 }{ 3 } } } +\frac { 1 }{ { (256) }^{ -\frac { 3 }{ 4 } } } +\frac { 1 }{ { (32) }^{ -\frac { 1 }{ 5 } } } \)is:
- (a)
102
- (b)
105
- (c)
107
- (d)
109
The value of \([{ (10) }^{ 150 }\div { (10) }^{ 146 }]\) is:
- (a)
1000
- (b)
10000
- (c)
100000
- (d)
\({ 10 }^{ 6 }\)
\((2.4\times { 10 }^{ 3 })\div (8\times { 10 }^{ -2 })=?\)
- (a)
\(3\times { 10 }^{ -5 }\)
- (b)
\(3\times { 10 }^{ 4 }\)
- (c)
\(3\times { 10 }^{ 5 }\)
- (d)
30
\({ (\frac { 1 }{ 216 } ) }^{ -\frac { 2 }{ 3 } }\div { (\frac { 1 }{ 27 } ) }^{ -\frac { 4 }{ 3 } }=?\)
- (a)
\(\frac { 3 } { 4 }\)
- (b)
\(\frac { 2 } { 3 }\)
- (c)
\(\frac { 4 } { 9 }\)
- (d)
\(\frac { 1 } { 8 }\)
\({ (1000) }^{ 7 }\div { 10 }^{ 18 }=\)?
- (a)
10
- (b)
100
- (c)
1000
- (d)
10000
\(49\times 49\times 49\times 49={ 7 }^{ ? }\)
- (a)
4
- (b)
7
- (c)
8
- (d)
16
\({ (64) }^{ -\frac { 1 }{ 2 } }-{ (-32) }^{ -\frac { 4 }{ 5 } }=?\)
- (a)
\(\frac { 1 } { 8 }\)
- (b)
\(\frac { 3 } { 8 }\)
- (c)
\(\frac { 1 } { 16 }\)
- (d)
\(\frac { 3 } { 16 }\)
- (e)
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
\({ (25) }^{ 7.5 }\times { (5) }^{ 2.5 }\div { (125) }^{ 1.5 }={ 5 }^{ ? }\)
- (a)
8.5
- (b)
13
- (c)
16
- (d)
17.5
- (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 \(5\sqrt { 5 } \times { 5 }^{ 3 }\div { 5 }^{ -\frac { 3 }{ 2 } }={ 5 }^{ a+2 }\), then the value of a is:
- (a)
4
- (b)
5
- (c)
6
- (d)
8
If \({ (\sqrt { 3 } ) }^{ 5 }\times { 9 }^{ 2 }={ 3 }^{ n }\times 3\sqrt { 3 } \),then the value of n is:
- (a)
2
- (b)
3
- (c)
4
- (d)
5
If \({ 2 }^{ n+4 }-{ 2 }^{ n+2 }=3,\)then n is equal to :
- (a)
0
- (b)
2
- (c)
-1
- (d)
-2
Given that \({ 10 }^{ 0.48 }\)=x, \({ 10 }^{ 0.70 }\)=y and \({ x }^{ 2 }={ y }^{ 2 }\), then the value of z is close to :
- (a)
1.45
- (b)
1.88
- (c)
2.9
- (d)
3.7
Number of prime factors in:\(\frac { { 6 }^{ 12 }\times { (35) }^{ 28 }\times { (15) }^{ 16 } }{ { (14) }^{ 12 }\times { (21) }^{ 11 } } \)is :
- (a)
56
- (b)
66
- (c)
112
- (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)
\({x}^{a+b+c}\)
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 \({ 2 }^{ x }=\sqrt [ 2 ]{ 32 } \), then x is equal to
- (a)
5
- (b)
3
- (c)
\(\frac { 3 } { 5 }\)
- (d)
\(\frac { 5 } { 3 }\)
\({ 2 }^{ x }\times { 8 }^{ \frac { 1 }{ 5 } }={ 2 }^{ \frac { 1 }{ 5 } }\), then x is equal to:
- (a)
\(\frac { 1 } { 5 }\)
- (b)
\(-\frac { 1 } { 5 }\)
- (c)
\(\frac { 2 } { 5 }\)
- (d)
\(-\frac { 2 } { 5 }\)
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 \({ 2 }^{ x }={ 3 }^{ y }={ 6 }^{ -z }\),then \((\frac { 1 }{ x } +\frac { 1 }{ y } +\frac { 1 }{ z } )\)is equal to:
- (a)
0
- (b)
1
- (c)
\(\frac { 3 } { 2 }\)
- (d)
\(-\frac { 1 } { 2 }\)
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)
\(\frac { 7 }{ 64 } \)
The largest number from among \(\sqrt { 2 } ,\sqrt [ 3 ]{ 3 } and\sqrt [ 4 ]{ 4 } \)is:
- (a)
\(\sqrt {2}\)
- (b)
\(\sqrt [ 3 ]{ 3 } \)
- (c)
\(\sqrt [ 4 ]{ 4 } \)
- (d)
All are equal
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)
\(2\sqrt { 3 } \)