Binomial Theorem Practice Questions

Class 11 · Mathematics · 524 free MCQs with instant results and detailed explanations.

524

Total

236

Easy

209

Medium

Hard

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Topics in Binomial Theorem

General Term 186

Binomial Theorem 171

Middle Term 167

Sample Questions from Binomial Theorem

Here are 10 sample questions. Start a quiz to get randomized questions with scoring.

Easy

What is the value of (x + y)^3 when x = 1 and y = 2?

A. 27

B. 9

C. 8

D. 6

Show Answer & Explanation

Correct Answer: A

Using the binomial expansion (1 + 2)^3 = 3^3 = 27.

Easy

What is the value of (3 + 4)^2 using the Binomial Theorem?

A. 49

B. 14

C. 20

D. 25

Show Answer & Explanation

Correct Answer: A

Using the expansion (3 + 4)^2 = 3^2 + 2 * 3 * 4 + 4^2 = 49.

Easy

In the expansion of (a + b)^n, which term is the general term?

A. C(n, k) * a^(n-k) * b^k

B. C(n, k) * a^k * b^(n-k)

C. C(n, k) * a^(n+k) * b^k

D. C(n, k) * a^(n-k) * b^(n-k)

Show Answer & Explanation

Correct Answer: A

The general term in the binomial expansion is represented by C(n, k) * a^(n-k) * b^k.

Medium

Which of the following is true for the coefficients in the expansion of (x - y)^6?

A. They are all positive.

B. They alternate in sign.

C. All coefficients are equal.

D. They are all negative.

Show Answer & Explanation

Correct Answer: B

In the expansion of (x - y)^n, the coefficients alternate in sign due to the subtraction, leading to positive and negative values.

Medium

What is the expansion of (x + y)^4?

A. x^4 + 4x^3y + 6x^2y^2 + 4xy^3 + y^4

B. x^4 + 2x^3y + 3x^2y^2 + 2xy^3 + y^4

C. x^4 + 3x^3y + 3x^2y^2 + y^4

D. x^4 + 5x^3y + 5x^2y^2 + 2y^4

Show Answer & Explanation

Correct Answer: A

The expansion uses the binomial theorem formula: (a + b)^n = Σ(nCk * a^(n-k) * b^k). For n=4, we get the terms listed in option A.

Medium

What is the sum of the coefficients in the expansion of (x + y)^{10}?

A. 1024

B. 512

C. 1000

D. 2048

Show Answer & Explanation

Correct Answer: A

The sum of coefficients in the expansion of (a + b)^n is given by substituting 1 for a and b.

Medium

What is the general term in the expansion of (a + b)^n?

A. nCk * a^(n-k) * b^k

B. nCk * a^k * b^(n-k)

C. na^(n-k) * b^k

D. a^(n-k) * b^(n-k)

Show Answer & Explanation

Correct Answer: A

The general term in the binomial expansion follows the given formula in option A.

Hard

In the expansion of (x - 2)^4, which term contains x^2?

A. C(4,2)(-2)^2 x^2

B. C(4,2)(-2)^0 x^4

C. None of these

D. C(4,2)(-2)^3 x^1

Show Answer & Explanation

Correct Answer: A

The term containing x^2 occurs when k = 2, giving us the required term C(4,2)(-2)^2 x^2.

Hard

In the expansion of (x + y + z)^3, what is the coefficient of x^2y?

A. 6

B. 3

C. 9

D. 12

Show Answer & Explanation

Correct Answer: A

Using multinomial expansion, the coefficient of x^2y^1z^0 is given by C(3,2,1) = 6.

Q10

Hard

Evaluate the binomial coefficient C(10,5) using Pascal's Triangle properties.

A. 20

B. 252

C. 300

D. 240

Show Answer & Explanation

Correct Answer: B

Using Pascal's Triangle, C(10,5) can be derived from the sum of C(9,4) and C(9,5).

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Binomial Theorem — Class 11 Mathematics Practice Questions Online

This page contains 524 practice MCQs for the chapter Binomial Theorem in Class 11 Mathematics. The questions are organized by difficulty — 236 easy, 209 medium, 79 hard — so you can choose the right level for your preparation.

Every question includes a detailed explanation to help you understand the concept, not just memorize answers. Take a timed quiz to simulate exam conditions, or practice at your own pace with no time limit. This chapter covers 3 topics, giving you comprehensive coverage of the entire chapter.