Principle of Mathematical Induction Practice Questions

Class 11 · Mathematics · 2812 free MCQs with instant results and detailed explanations.

2812

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1386

Medium

429

Hard

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Topics in Principle of Mathematical Induction

Applications 884

Principle 968

Proving Statements 960

Sample Questions from Principle of Mathematical Induction

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Easy

Which of the following is a basic principle of mathematical induction?

A. If a statement holds for n = 1, it holds for all n.

B. If a statement holds for n = k, it holds for n = k + 1.

C. If a statement holds for n = 0, it holds for n > 0.

D. If a statement holds for all integers, it must be true.

Show Answer & Explanation

Correct Answer: B

Mathematical induction requires proving a base case and then showing that if it holds for n = k, it holds for n = k + 1.

Easy

Which of the following can be proven using mathematical induction?

A. The sum of the first n odd numbers is n^2.

B. The product of any two numbers is commutative.

C. The square root of 2 is irrational.

D. The sum of angles in a triangle is 180 degrees.

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Correct Answer: A

The sum of the first n odd numbers can be expressed as n^2, which is easily provable by induction.

Easy

If P(k) is true, what must you show to prove P(k + 1) in induction?

A. P(k) is true.

B. P(k + 2) is true.

C. P(k - 1) is true.

D. P(k) is false.

Show Answer & Explanation

Correct Answer: A

To prove P(k + 1), we need to rely on the assumption that P(k) is true.

Medium

Which of the following statements about the Principle of Mathematical Induction is true?

A. It can only be used for natural numbers.

B. It requires validation for all integers.

C. It is applicable only for even numbers.

D. It can be used for real numbers.

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Correct Answer: A

The Principle of Mathematical Induction is primarily used to prove statements about natural numbers.

Medium

Using mathematical induction, which of the following is true for n ≥ 1: 1 + 2 + 3 + ... + n = n(n + 1)/2?

A. True for all n.

B. False for n = 1.

C. True only for odd n.

D. False for n ≥ 2.

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Correct Answer: A

The formula holds true for all natural numbers n by induction.

Medium

If P(n) is true for n = k, which of the following proves it for n = k + 1?

A. P(k) implies P(k+1).

B. P(k) is irrelevant.

C. P(k+1) is independent of P(k).

D. P(k) contradicts P(k+1).

Show Answer & Explanation

Correct Answer: A

The principle states if P(k) is true, we must show it leads to P(k+1) being true.

Medium

Which of the following sequences can be proven using the Principle of Mathematical Induction?

A. The sum of cubes.

B. The square of primes.

C. The factorial of numbers.

D. The Fibonacci sequence.

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Correct Answer: A

The sum of cubes can be demonstrated via induction, while others require different methods.

Hard

Prove by induction that for all integers n ≥ 1, 1 + 2 + 3 + ... + n = n(n + 1)/2.

A. True for all n ≥ 1

B. False for all n ≥ 1

C. True only for n = 1

D. True only for even n

Show Answer & Explanation

Correct Answer: A

The formula is derived from the sum of the first n natural numbers and holds true for all integers n ≥ 1.

Hard

Using mathematical induction, prove that for any integer n ≥ 1, 3^n - 1 is divisible by 2.

A. True for all n ≥ 1

B. True for odd n only

C. True for even n only

D. True for n = 1 only

Show Answer & Explanation

Correct Answer: A

The expression can be shown to be divisible by 2 for all integers n by induction since both the base and inductive cases confirm it.

Q10

Hard

Prove by induction that for all n ≥ 1, n! > 2^n.

A. True for n ≥ 4

B. False for all n

C. True for n = 1

D. True for n ≥ 5

Show Answer & Explanation

Correct Answer: A

The inequality n! > 2^n holds true starting from n = 4 based on the base and induction hypothesis.

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Principle of Mathematical Induction — Class 11 Mathematics Practice Questions Online

This page contains 2812 practice MCQs for the chapter Principle of Mathematical Induction in Class 11 Mathematics. The questions are organized by difficulty — 997 easy, 1386 medium, 429 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.