Explore topic-wise MCQs in Surds & Indices.

This section includes 46 Mcqs, each offering curated multiple-choice questions to sharpen your Surds & Indices knowledge and support exam preparation. Choose a topic below to get started.

1.

(125 times 125 times 125 times 125 times 125 = 5^? )

A. 5
B. 3
C. 15
D. 2
Answer» D. 2
Discussion
2.

If (a^x = b, b^y = c ) and (c^z = a ), then the value of (xyz ) is:

A. 1
B. 1/abc
C. abc
Answer» C. abc
Discussion
3.

If (2^{(x-y)} = 8 ) and (2^{(x+y)} = 32 ), then (x ) is equal to:

A. 2
B. 4
C. 6
Answer» D.
Discussion
4.

If (7^a = 16807 ), then the value of (7^{(a-3)} ) is:

A. 49
B. 343
C. 2401
D. 10807
Answer» B. 343
Discussion
5.

If (3^x - 3^{x-1} = 18 ), then the value of (x^x ) is:

A. 3
B. 8
C. 27
D. 216
Answer» B. 8
Discussion
6.

If (a^x = b^y = c^z ) and (b^2 = ac ), then (y ) equals:

A. xy/x + z
B. xz/2(x + z)
C. xz/2(x - z)
D. 2xz/(x + z)
Answer» E.
Discussion
7.

If (5^{a}=3125 ), then the value of (5^{(a-3)} ) is:

A. 25
B. 125
C. 625
D. 1625
Answer» B. 125
Discussion
8.

Given that (10^{0.48}=x ), (10^{0.70}=y ) and (x^{z}=y^{2} ), then the value of z is close to:

A. 1.45
B. 1.88
C. 2.9
D. 3.7
Answer» D. 3.7
Discussion
9.

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

A. 1000
B. 10000
C. 100000
D. 10^6
Answer» C. 100000
Discussion
10.

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

A. 4
B. 16
C. 64
D. 256.25
Answer» B. 16
Discussion
11.

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

A. 2.29
B. 2.75
C. 4.25
D. 4.5
Answer» E.
Discussion
12.

((0.04)^{-1.5} ) = ?

A. 25
B. 125
C. 250
D. 625
Answer» C. 250
Discussion
13.

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

A. 1
B. 10
C. 121
D. 1000
Answer» E.
Discussion
14.

( frac{1}{1+a^{(n-m)}}+ frac{1}{1+a^{(m-n)}}=n^{?} )

A. 0
B. 1/2
C. 1
D.
Answer» C. 1
Discussion
15.

Solve for (((3^{y})^{ sqrt{}2})^{2} = 729 ).

A. 3
B. 1
C. 2
D. 4
Answer» D. 4
Discussion
16.

Solve for (m ) if (49(7^m) = 343^{3m+6} )

A. -8/6
B. -2
C. -4/6
D. -1
Answer» C. -4/6
Discussion
17.

The simplified form of ( frac{x^{ frac{9}{2}} times sqrt{y^5}}{x^{ frac{7}{2}} times sqrt{y^3}} ) is:

A. x^(2)/y^(2)
B. x^(2).y^(2)
C. xy
D. x^(2)/y
Answer» C. xy
Discussion
18.

If (x ) is an integer, find the minimum value of (x ) such that (0.00001154111 times 10^x ) exceeds 1000.

A. 8
B. 1
C. 7
D. 6
Answer» B. 1
Discussion
19.

If ( sqrt{(3+3 sqrt{x})} = 2 ), then (x ) is equal to:

A. 1
B. 2
C. 4
D. 8
Answer» B. 2
Discussion
20.

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

A. 3/4
B. 2/3
C. 4/9
D. 1/8
Answer» D. 1/8
Discussion
21.

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

A. square root 5
B. 5 square root 5
C. 5
D. 25
Answer» D. 25
Discussion
22.

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

A. 4/9
B. 9/4
C. 16/81
D. 81/16
Answer» E.
Discussion
23.

The value of (( sqrt8)^{ frac{1}{3}} ) is:

A. 2
B. 4
C. square root 2
D. 8
Answer» D. 8
Discussion
24.

If (( frac{a}{b})^{x-1}=( frac{b}{a})^{x-3} ), then the value of (x ) is:

A. 1/2
B. 1
C. 2
D. 7/2
Answer» D. 7/2
Discussion
25.

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

A. 2.29
B. 2.75
C. 4.25
D. 4.5
Answer» E.
Discussion
26.

(( 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+ac)
D. x^(a+b+c)
Answer» C. x^(ab+bc+ac)
Discussion
27.

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

A. 1
B. 10
C. 121
D. 1000
Answer» E.
Discussion
28.

( frac{1}{1+a^{(n-m)}}+ frac{1}{1+a^{(m-n)}}=? )

A. 1/2
B. 1
C. a^(m+n)
Answer» D.
Discussion
29.

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

A. 1000
B. 10000
C. 100000
D. 10^6
Answer» C. 100000
Discussion
30.

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

A. 4
B. 16
C. 64
D. 256.25
Answer» B. 16
Discussion
31.

if (3^{(x-y)}=27 ) and (3^{(x+y)}=243 ), then (x ) is equal to:

A. 2
B. 4
C. 6
Answer» D.
Discussion
32.

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

A. 1
B. 2
C. 9
D. 3^n
Answer» D. 3^n
Discussion
33.

The simplified form of ((x^{ frac{7}{2}} div x^{ frac{5}{2}}) times sqrt{y3} div sqrt{y} ) is:

A. x^(2)/y
B. x^(3)/y^(2)
C. x^(6)/y^(3)
D. xy
Answer» E.
Discussion
34.

If (m ) and (n ) are whole numbers such that (m^n = 169 ), then the value of ((m-1)^{n+1} ) is:

A. 1
B. 13
C. 169
D. 1728
Answer» E.
Discussion
35.

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

A. 2
B. 4
C. 6
D. 12
Answer» E.
Discussion
36.

If (5 sqrt{5} times5^3 div5^{- frac{3}{2}}=5^{a+2} ), the value of (a ) is:

A. 4
B. 5
C. 6
D. 8
Answer» B. 5
Discussion
37.

((2^{n+4}-2.2^{n}) div(2.2^{n+3})=2^{-3} ) is equal to:

A. 2^(n+1)
B. -2^(n+1)+1/8
C. 9/8-2^(n)
D. 1
Answer» E.
Discussion
38.

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

A. 1
B. 2
C. 2rootover2
D. 3rootover3
Answer» C. 2rootover2
Discussion
39.

((25)^{7.5} times(5)^{2.5} div(125)^{1.5}=5^? )

A. 8.5
B. 13
C. 16
D. 17.5
Answer» C. 16
Discussion
40.

( 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. 1
B. x^(a-b-c)
C. None of these
Answer» C. None of these
Discussion
41.

((0.04)^{-1.5}=? )

A. 25
B. 125
C. 250
D. 625
Answer» C. 250
Discussion
42.

((25)^{7.5} times (5)^{2.5} div (125)^{1.5} = 5? )

A. 8.5
B. 13
C. 16
D. 17.5
Answer» C. 16
Discussion
43.

If (2^x times 16^{ frac{2}{5}} = 2^{ frac{1}{5}} ), then (x ) is equal to:

A. 2/5
B. -2/5
C. 7/5
D. -7/5
Answer» E.
Discussion
44.

If (4^{4m+2} = 8^{6m-4} ), solve for (m )

A. 7/4
B. 2
C. 4
D. 1
Answer» E.
Discussion
45.

If (a ) and (b ) are positive numbers, (2^a = b^3 ) and (b^a = 8 ), find the value of (a ) and (b )

A. a = 2, b = 3
B. a = 3, b = 2
C. a = b = 3
D. a = b = 2
Answer» C. a = b = 3
Discussion
46.

( sqrt{[200 sqrt{[200 sqrt{[200....... infty ]}]}]} = ? )

A. 200
B. 10
C. 1
D. 20
Answer» B. 10
Discussion