UPSC General Ability and Intelligence - Surds and Indices
Exam Duration: 45 Mins Total Questions : 30
The value of \({ (256) }^{ \frac { 5 }{ 4 } }\)
- (a)
512
- (b)
984
- (c)
1024
- (d)
1032
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
\({ (1000) }^{ 7 }\div { 10 }^{ 18 }=\)?
- (a)
10
- (b)
100
- (c)
1000
- (d)
10000
\(({ 0.04) }^{ -1.5 }=?\)
- (a)
25
- (b)
125
- (c)
250
- (d)
625
\({ (17) }^{ 3.5 }\times ({ 17) }^{ ? }=17 ^{ 8 }\)
- (a)
2.29
- (b)
2.75
- (c)
4.25
- (d)
4.5
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
\({ (64) }^{ -\frac { 1 }{ 2 } }-{ (-32) }^{ -\frac { 4 }{ 5 } }=?\)
- (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
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 \({ (\sqrt { 3 } ) }^{ 5 }\times { 9 }^{ 2 }={ 3 }^{ n }\times 3\sqrt { 3 } \),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
If \({ 2 }^{ n-1 }+{ 2 }^{ n+1 }=320\),then the n is equal to :
- (a)
6
- (b)
8
- (c)
5
- (d)
7
If \({ 3 }^{ x }-{ 3 }^{ x-1 }=18\),then the value of \({ x }^{ x }\)is :
- (a)
3
- (b)
8
- (c)
27
- (d)
216
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)
\(3\sqrt {3}\)
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
\(\frac { { (243) }^{ \frac { n }{ 5 } }\times { 3 }^{ 2n+1 } }{ { 9 }^{ n }\times { 3 }^{ n-1 } } =?\)
- (a)
1
- (b)
3
- (c)
9
- (d)
\({ 3 }^{ n }\)
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
\((\frac { { x }^{ a } }{ { x }^{ b } } )^{ (a+b) }.(\frac { { x }^{ b } }{ { x }^{ c } } )^{ (b+c) }.(\frac { { x }^{ c } }{ { x }^{ a } } )^{ (c+a) }=?\)
- (a)
0
- (b)
\({x}^{abc}\)
- (c)
\({x}^{a+b+c}\)
- (d)
1
If abc=1, then \((\frac { 1 }{ 1+a+{ b }^{ -1 } } +\frac { 1 }{ 1+b+{ c }^{ -1 } } +\frac { 1 }{ 1+c+a^{ -1 } } )=?\)
- (a)
0
- (b)
1
- (c)
\(\frac { 1 } { ab }\)
- (d)
ab
If \(({ \frac { 9 }{ 4 } ) }^{ x }.{ (\frac { 8 }{ 27 } ) }^{ x-1 }=\frac { 2 }{ 3 } \), then the value of x is:
- (a)
1
- (b)
2
- (c)
3
- (d)
4
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
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)
\(2\sqrt { 3 } \)
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