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.
• Submit when you are finished to see results.

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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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Factorisation Worksheet | CBSE | ICSE | Class IX

ICSE & CBSE Class IX Factorisation - Prime Maths

Master the Art of Factorisation with 39 Progressive Problems

Factorisation Overview

What is Factorisation?

Factorisation is the process of breaking down algebraic expressions into simpler components called "factors" that, when multiplied together, give the original expression.

Worksheet Structure

• Problems 1-10: Basic factorisation
• Problems 11-20: Difference of squares
• Problems 21-30: Grouping techniques
• Problems 31-39: Challenge mastery

How to Use This Worksheet:

1. Work through problems one by one using the slides.

2. Try to solve before clicking "Next".

3. Use the list below to jump to specific questions.

Practice Area

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Problem 1 of 39

$$10xy - 15xz$$

Hint: Look for common factors

Full Problem List

ICSE Class IX Mathematics - Factorisation Worksheet

Worksheet Prepared By:

Vinod Singh

M.Sc. Pure Mathematics, Calcutta University (First Class)

B.Sc. Mathematics, St. Xavier's College Kolkata (First Class)

maths.programming@gmail.com

Chapter Test Class IX: Real Numbers and Compound Interest

COMPLETE MCQ MATHEMATICS ASSESSMENT - Prime Maths

Full Marks: 32

Time: 55 minutes

Format: All Multiple Choice Questions

Group A [4 × 1 = 4]

Select the correct option in each case.

1. At present the population of a village is P and if the rate of increase of population per year be 2r%, the population after n years will be

(a)

\( P \left( 1 + \frac{r}{100} \right)^n \)

(b)

\( P \left( 1 + \frac{r}{50} \right)^n \)

(c)

\( P \left( 1 + \frac{r}{100} \right)^{2n} \)

(d)

\( P \left( 1 - \frac{r}{100} \right)^n \)

2. A person deposited Rs. 100 in a bank and received Rs. 121 after two years, the rate of compound interest is

(a)

10%

(b)

20%

(c)

5%

(d)

10.5%

3. \(\sqrt{5} - 3 = 2\) is

(a)

A rational number

(b)

A natural number

(c)

Equal to zero

(d)

An irrational number

4. Which of the following rational numbers have a terminating decimal expression?

(a)

\( \frac{125}{441} \)

(b)

\( \frac{77}{210} \)

(c)

\( \frac{15}{1600} \)

(d)

\( \frac{129}{2^2 \times 5^2 \times 7^2} \)

Group B [4 × 2 = 8]

All questions converted to multiple choice format.

1. To prove that \( 3\sqrt{7} \) is not a rational number, which approach is correct?

(a)

Assume \(3\sqrt{7}\) is rational, then \(\sqrt{7} = \frac{a}{3b}\) where a, b are integers, which implies \(\sqrt{7}\) is rational - a contradiction

(b)

Assume \(3\sqrt{7}\) is rational, then \(\sqrt{7} = \frac{a}{b}\) where a, b are integers with no common factors - leads to contradiction as 7 divides a²

(c)

Since \(\sqrt{7}\) is irrational and 3 is rational, their product must be rational

(d)

\(3\sqrt{7}\) can be written as \(\sqrt{63}\), and since 63 is not a perfect square, it's rational

2. If a sum of money doubles itself at certain rate compounded annually in n years, in how many years will the sum become four times of itself?

(a)

n years

(b)

2n years

(c)

3n years

(d)

n² years

3. Using the formula of simple interest, the amount at the end of 2nd year for a sum P at the compound interest rate of r% per annum is:

(a)

\( P \left(1 + \frac{r}{100}\right)^2 \)

(b)

\( P \left(1 + \frac{2r}{100}\right) \)

(c)

\( P \left(1 + \frac{r}{50}\right) \)

(d)

\( P + \frac{2Pr}{100} \)

4. Which of the following is an irrational number between 2 and 3?

(a)

2.5

(b)

\( \sqrt{4} \)

(c)

\( \sqrt{5} \)

(d)

\( \sqrt{9} \)

Group C [5 × 4 = 20]

All questions converted to multiple choice format. For questions with "OR", both parts are included as separate options.

1. The expression \( \left( 3 + 2\sqrt{5} \right)^2 \) is:

(a)

Irrational because it simplifies to \( 29 + 12\sqrt{5} \), which is a sum of rational and irrational

(b)

Rational because it equals \( 49 \)

(c)

Irrational because \( \sqrt{5} \) is irrational

(d)

Rational because it simplifies to \( 29 + 12\sqrt{5} \) and \( 12\sqrt{5} \) is rational

2. If p is a prime number, \( \sqrt{p} \) is:

(a)

Always rational

(b)

Always irrational

(c)

Rational if p is even, irrational if p is odd

(d)

Irrational except when p = 4

3. After rationalizing the denominator, \( \frac{1}{3-2\sqrt{2}+\sqrt{5}} \) simplifies to:

(a)

\( \frac{3+2\sqrt{2}-\sqrt{5}}{2} \)

(b)

\( \frac{3-2\sqrt{2}+\sqrt{5}}{12} \)

(c)

\( \frac{3+2\sqrt{2}-\sqrt{5}}{12} \)

(d)

\( \frac{3-2\sqrt{2}-\sqrt{5}}{4} \)

OR

The simplest value of \( \frac{\sqrt{7}-\sqrt{3}}{\sqrt{7}+\sqrt{3}} + \frac{\sqrt{7}+\sqrt{3}}{\sqrt{7}-\sqrt{3}} \) is:

(e)

2

(f)

5

(g)

10

(h)

\( \frac{10}{\sqrt{21}} \)

4. If simple interest and compound interest on a certain sum for two years are Rs. 8400 and Rs. 8652 respectively, then:

(a)

Rate = 5%, Sum = Rs. 80,000

(b)

Rate = 6%, Sum = Rs. 70,000

(c)

Rate = 8%, Sum = Rs. 60,000

(d)

Rate = 10%, Sum = Rs. 50,000

5. In how many years will Rs. 50000 amount to Rs. 60500 at 10% compound interest per annum?

(a)

1 year

(b)

2 years

(c)

3 years

(d)

4 years

OR

The height of a tree increases at 20% yearly. If present height is 28.8m, its height 2 years before was:

(e)

20 m

(f)

22 m

(g)

24 m

(h)

26 m

Assessment Results

Your Score: 0/32

Group A

0/4

4 × 1 mark questions

Group B

0/8

4 × 2 mark questions

Group C

0/20

5 × 4 mark questions

Question-wise Results:

Note: For questions with "OR" options, only one part needs to be answered. If you answer both, only the first selected option is considered.

Complete MCQ Mathematics Assessment - Irrationals & Compound Interest | For Class IX | © Prime Maths - 9038126497