Are these practice questions for Binomial Theorem based on the CBSE pattern?

Yes. Every practice question is modeled on the CBSE Class 11 - Science Mathematics exam pattern — including MCQs, assertion-reason questions, and short-answer formats that frequently appear in CBSE papers.

Are the practice questions for Binomial Theorem free?

Yes. Every chapter includes free practice questions for Class 11 - Science students to get you started.

What types of questions are included?

The practice set for Binomial Theorem mainly includes MCQs and CBSE-style short-answer questions, with instant feedback on each answer. For full-length textbook practice, use the NCERT Solutions page.

Are the practice questions suitable for board exam preparation?

Yes. The questions test the same concepts and depth that CBSE asks in board exams. After finishing, also solve the NCERT and NCERT Exemplar exercises for Binomial Theorem for full coverage.

How many practice questions are there for Binomial Theorem?

The number scales with chapter length and concept density. Each chapter typically has 15-50 practice questions across MCQ and short-answer formats.

Binomial Theorem Class 11 Mathematics Practice Questions with Answers

easy

Examine the expansion of

(a+b)^{12}

and write the 5th term using combination notation.

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easy

Critique the statement: "The binomial expansion of

(a+b)^n

for any rational index

n

always results in a finite number of terms."

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easy

Justify why the sum of the coefficients in the expansion of

(2x - 3y)^n

is equal to

(-1)^n

.

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easy

Calculate the sum of the coefficients in the expansion of

(3x-2y)^{10}

.

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easy

How many terms are in the expansion of

(x+2y)^{15}

? Explain your reasoning.

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easy

State the Binomial Theorem for any positive integer

n

.

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easy

Calculate the total number of terms in the expansion of

(2x - \frac{y}{3})^9

.

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easy

Define 'Pascal's Triangle' and name the French mathematician it is named after.

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easy

Recall the expression for the binomial coefficients

{}^{n}\mathrm{C}_{r}

in terms of factorials.

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easy

Justify which of the two numbers is larger without using a calculator:

(1.001)^{1000000}

or

1001

.

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medium

Create a trinomial expression of the form

(1+ax+bx^2)^n

such that the coefficient of

x

is

8

and the coefficient of

x^2

is

30

. Justify your steps and find the values of

a

,

b

, and

n

, assuming they are positive integers.

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medium

Solve for the 6th term in the expansion of

(2x^2 + \frac{1}{x})^8

.

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medium

Evaluate whether the middle term in the expansion of

(x - \frac{1}{x})^{2n}

can ever be zero for

x \neq 0

. Justify your answer.

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medium

Propose a method to find the term independent of

x

in the expansion of

(x^p + \frac{1}{x^q})^n

without writing the full expansion.

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medium

Describe how to construct the row for index 5 in Pascal's triangle, given the row for index 4, which is 1 4 6 4 1.

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medium

Apply the binomial theorem to expand the expression

(\frac{x}{2} - \frac{3}{y})^4

.

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medium

Calculate the value of

(\sqrt{5}+1)^5 - (\sqrt{5}-1)^5

using the binomial expansion.

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medium

What is the sum of the indices of

a

and

b

in any term of the expansion of

(a+b)^{20}

?

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medium

Write the complete expansion for

(1+x)^n

as a special case of the Binomial Theorem.

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medium

List the binomial coefficients for the expansion of

(a+b)^4

.

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medium

Analyze the expansion of

(3x - \frac{x^3}{6})^8

and find the middle term.

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medium

Explain the pattern of the powers of the first quantity (

a

) and the second quantity (

b

) in the successive terms of the expansion

(a+b)^n

.

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medium

Explain how the binomial theorem can be used to evaluate numerical values of numbers with high powers, such as

(99)^4

. You do not need to calculate the final value.

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medium

Formulate an expression for the sum of the coefficients of the odd-powered terms of

x

in the expansion of

(1+x)^n

.

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medium

Summarize the three main observations regarding the terms in the expansion of

(a+b)^n

for a positive integral index

n

.

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medium

Compare

(1.2)^{4000}

and

800

to determine which one is larger.

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medium

The sum of the coefficients of the first three terms in the expansion of

(x - \frac{3}{x^2})^m

, where

x \neq 0

and

m

is a natural number, is 559. Formulate an equation and determine the term containing

x^3

.

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medium

Using the binomial theorem, calculate the value of

(10.2)^4

.

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medium

Identify the first and last terms in the expansion of

(3x-5y)^{12}

.

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medium

Prove by using the binomial theorem that for any integer

n \geq 2

, the number

(2^{2n}) - (3n+1)

is divisible by 9, but not necessarily by 27. Provide a counterexample for divisibility by 27.

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medium

Using Pascal's triangle, determine the coefficients for the expansion of

(x+y)^5

.

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medium

Apply the binomial theorem to find the first three terms in the expansion of

(1-3x)^7

.

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medium

Design a proof to show that the coefficient of the middle term in the expansion of

(1+x)^{2n}

is the sum of the coefficients of the two middle terms in the expansion of

(1+x)^{2n-1}

.

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hard

Formulate a proof using the binomial theorem to show that

\sum_{r=0}^{n} {^nC_r} \sin(rx) \cos((n-r)x) = 2^{n-1} \sin(nx)

.

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hard

Apply the binomial theorem to demonstrate that

7^{2n} - 48n - 1

is divisible by

2304

for all positive integers

n

.

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hard

Justify that for any positive integer

n

, the expression

7^{2n} + 2^{3n-3} \cdot 3^{n-1}

is divisible by 25.

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hard

What is the value of the sum

{}^{n} \mathrm{C}_{0}+{ }^{n} \mathrm{C}_{1}+{ }^{n} \mathrm{C}_{2}+\ldots+{ }^{n} \mathrm{C}_{n}

?

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hard

State the formula for the expansion of

(x-y)^n

and explain how the signs of the terms behave.

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hard

In the expansion of

(1+ax)^n

, the first three terms are

1, 12x,

and

60x^2

respectively. Analyze these terms to find the values of

a

and

n

.

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hard

Evaluate the expression

\sum_{r=0}^{n} (-1)^r {^nC_r} \frac{1+r \log_e 10}{ (1+\log_e 10^n)^r }

.

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hard

If

C_r

stands for

{^nC_r}

, design a method to prove the identity:

C_1 - 2C_2 + 3C_3 - \dots + (-1)^{n-1} nC_n = 0

for

n>1

. Then, evaluate the sum

S = C_0 + 2C_1 + 3C_2 + \dots + (n+1)C_n

.

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hard

Solve for the term independent of

x

in the expansion of

(\frac{3}{2}x^2 - \frac{1}{3x})^9

.

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hard

Analyze the expansion of

(x^2 + \frac{2}{x})^8

to find the coefficient of

x^7

.

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hard

What is the value of the alternating sum

{}^{n} \mathrm{C}_{0}-{ }^{n} \mathrm{C}_{1}+{ }^{n} \mathrm{C}_{2}-\ldots+(-1)^{n}{ }^{n} \mathrm{C}_{n}

?

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hard

Create a problem where the ratio of the coefficient of the third term to the fourth term in the expansion of

(1+ax)^n

is

1:2

and the ratio of the coefficient of the fourth term to the fifth term is

3:4

. Then, solve for the constants

a

and

n

.

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Binomial TheoremClass 11 Mathematics Practice Questions