Indices Interactive Chapter Test: ICSE and CBSE

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25 Question MCQ Chapter on Indices & Exponents for ICSE, CBSE, WBBSE and other State Boards

👨‍🏫 Author: Vinod Singh

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Indices & Exponents Quiz

Test your understanding of mathematical indices

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• This quiz contains 25 multiple choice questions.
• Select only one correct answer per question.
• Use the navigator to jump between questions.
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Question 1

\( \big( 125^{-4}\times 256^{-3/2}\big)^{-1/6} \times \big( (x^{2}y^{-4})^{1/3} \times \sqrt{y^{3}x^{-5}}\big)^{12}\times (x^{2})^{11}\)

A\( 10y^{2}\) B\( 100y^{2}\) C\( 10x^{2}\) D\( 100x^{2}\)

Question 2

The value of \( (5^{0} + 3^{0} + 2^{0}) ÷\bigg( \frac{2^{n}(2^{n-1})^n}{2^{n+1}.2^{n-1}} \times \bigg( \frac{\sqrt [3] {8^{n}}}{4}\bigg)^{-n} \bigg) \) is:

A0 B1 C2 D3

Question 3

Simplify: \( \big(\frac{1728}{729}\big)^{\frac{2}{3}}\times \frac{3^{2}}{\sqrt{144}}\times \sqrt{5} \)

A\( \frac{4\sqrt{5}}{3} \) B\( \frac{4\sqrt{5}}{7} \) C\( \frac{\sqrt{5}}{3} \) D\( \frac{7\sqrt{5}}{3} \)

Question 4

If \(5^{10x}=4900 \) and \( 2^{ \sqrt{y}}=25 \), the value of \(4^ { \sqrt{y}}\times 5^{5x-5} \) is:

A12 B16 C14 D13

Question 5

If \(\big( \frac{2a}{b}\big)^{2x-4} \) = \(\big( \frac{b}{2a}\big)^{2x-4} \), then the value of \( x \) is:

A2 B4 C3 D-2

Question 6

\( \big[1-\big(1-\big(1-n\big)^{-1}\big)^{-1} \big]^{-1} = \) where \(n \neq 0,1 \)

A\( n \) B\( 2n \) C\( -n \) D\( \frac{1}{n} \)

Question 7

If \( 2016 = 2^{a}\times 3^{b} \times 5^{c}, \) then the value of \(3^{a}\times 2^{-b} \times 5^{-c} \) is

A\( \frac{243}{4} \) B\( \frac{247}{4} \) C\( \frac{241}{4} \) D\( \frac{234}{4} \)

Question 8

If \( 2^{x}=3^{y}=6^{-z} \) then the value of \(\frac{1}{x}+\frac{1}{y}+\frac{1}{z} =\)

A0 B1 C-1 D\( \frac{1}{2} \)

Question 9

If \( a^{x}=b^{y}=c^{z} \) and \(b^{2} = ac \) then the value of \( \frac{2xz}{z+x}\) is

Ay B2x Cx D-x

Question 10

The simplest value of \( \frac{(x^{a+b})^{2} . (x^{b+c})^{2} . (x^{c+a})^{2}}{(x^{a}.x^{b}.x^{c})^{4}} \) is

A0 B1 C2 D-1

Question 11

Simplest value of \( \big( \frac{2^{-1}\times 3^{2}}{2^{2}\times 3^{-4}}\big)^{7/2} \times \big( \frac{2^{-2}\times 3^{3}}{2^{3}\times 3^{-5}}\big)^{-5/2} \) is

A12 B22 C2 D11

Question 12

The value of \(x\) satisfying \( 9^{x}-9^{x-1}=648 \) is

A3 B\( \frac{1}{3} \) C2 D-3

Question 13

The simplest value of \( \big[ 5\big(8^{1/3}+27^{1/3}\big)^{3}\big]^{\frac{1}{4}} \) is

A5 B6 C8 D12

Question 14

If \( y= x^{1/3}-x^{-1/3}, \) then \( y^{3}+3y = \)

A\( x-x^{-1} \) B\( x^{2} - x^{-2} \) C\( x^{2}+x^{-2} \) D\( x+x^{-1} \)

Question 15

If \( (10^{11}+25)^{2}-(10^{11}-25)^{2} = 10^{n}\) then the value of \( n \) is

A11 B13 C17 D7

Question 16

The least value of the expression \( 4^{x}+4^{1-x} \) is

A2 B4 C8 D16

Question 17

Value of \(x\) and \(y\) satisfying the equations \( 5^{x}-3^{y}=16; \quad 5^{x-1}+3^{y+1}=32\) are

A\( x=2 \quad y = 2 \) B\( x=2 \quad y = -2 \) C\( x=-2 \quad y = 2 \) D\( x=-2 \quad y = -2 \)

Question 18

If \(\big( x^{n^{2}}\big)^{n}= \big( x^{2^{n}}\big)^{2}\), then the value of \( \sqrt[n+1]{n^{3}} \) is

A2 B4 C1 D\( 2^{4} \)

Question 19

If \( x = 3+3^{2/3}+3^{1/3}\) then the value of \( x^3-9x^2+18x-12 \) is

A0 B1 C3 D-3

Question 20

If \( a^{x}=bc, \quad b^{y}= ca, \quad c^{z}=ab\), then the value of \(\frac{x}{x+1}+\frac{y}{y+1}+\frac{z}{z+1} \quad \) is

A1 B2 C0 D-1

Question 21

The value of \(x\) satisfying \( 4^{x}-3^{x-1/2}=3^{x+1/2}-2^{2x-1}\) is

A\( \frac{3}{2} \) B2 C\( \frac{1}{2} \) D\( \frac{2}{3} \)

Question 22

The value of \( \frac{\big(2^{2n}-3.2^{2n-2}\big)\big(3^{n}-2.3^{n-2}\big)}{3^{n-4}\big( 4^{n+3}-2^{2n}\big)} \quad \) is

A\( \frac{1}{4} \) B\( \frac{3}{4} \) C\( \frac{-3}{4}\) D\( \frac{1}{3} \)

Question 23

If \( a^{x}=b^{y}\) and \( b^{x}=a^{y} \quad ( ab \neq 1)\) then which of the following relation is true

A\( a=b^{2} \) B\( a=b \) C\( b=a^{2} \) D\( ab=2 \)

Question 24

Solve for \(x \) and \( y: \quad 2^{x}+2^{y}=12; \quad x+y= 5\)

A\( x=3, \quad y = 2 \) B\( x=2, \quad y = 3 \) C\( x=4, \quad y = 1\) D\( x=1, \quad y = 4 \)

Question 25

The value of \( \bigg( \frac{9^{n+1/4}.\sqrt{3.3^{n}}}{3.\sqrt{3^{-n}}}\bigg)^{1/n}\) is

A3 B9 C27 D81

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