Below you will find **MCQ Questions of Chapter 4 Principle of Mathematical Induction Class 11 Maths Free PDF Download** that will help you in gaining good marks in the examinations and also cracking competitive exams. These Class 11 MCQ Questions with answers will widen your skills and understand concepts in a better manner.

# MCQ Questions for Class 11 Maths Chapter 4 Principle of Mathematical Induction with answers

1. 2.4^{2n + 1} + 3^{3n + 1} for all n is divisible by λ for all n ∈ N” is true, then the value of λ is ____

(a) 3

(b) 11

(c) 2

(d) 4

► (b) 11

2. A set S in which x S implies x+1 S is known as a _______ .

(a) Inductive Set

(b) Deductive Set

(c) Subset

(d) All of the above

► (a) Inductive Set

3. If P(n) : (2n + 7) < (n + 3)^{2} then P(3) is

(a) (2 x 3 + 7 x 3) < (3 + 3)^{2}

(b) (2^{3} + 7) < (n + 3)^{2}

(c) (2 x 3 + 7) < (3 + 3)^{2}

(d) (3^{2} + 7) < (2 + 7)^{2}

► (c) (2 x 3 + 7) < (3 + 3)^{2}

4. If n is a +ve integer, then 72n−4 is divisible by

(a) 25

(b) 26

(c) 2309

(d) None of these

► (d) None of these

5. Let P(n) b e a statement 2^{n}<n! where n is a natural number, then P(n) is true for

(a) all n

(b) all n > 3

(c) all n < 3

(d) all n > 2

► (b) all n > 3

6. If a statement is to be proved by mathematical induction, then the different steps necessary to prove it are

(a) Prove Basic step and Inductive step

(b) Inductive step to be proved

(c) Prove P(1), P(2), P(3)

(d) Basic step to be proved

► (a) Prove Basic step and Inductive step

7. Let P(n) : n^{2}−n+41 is a prime number . then :

(a) P (3) is not true

(b) P (5) is not true

(c) P (41) is not true

(d) P (1) is not true

► (c) P (41) is not true

8. For each n ∈ N, 2^{3n}−1 is divisible by :

(a) 16

(b) 7

(c) 8

(d) None of these

► (b) 7

9. For all n ∈ N , 49^{n}+16n−1 is divisible by

(a) 29

(b) 64

(c) 3

(d) 19

► (b) 64

10. The greatest positive integer, which divides n (n + 1) (n + 2) (n + 3) for all n ∈ N, is

(a) 24

(b) 120

(c) 6

(d) 2

► (a) 24

11. Consider the statement P (n) : “n^{2} ≥ 100 “. Here P(n) ⇒ P(n+1) for all natural numbers n. Does it mean

(a) P (n) is true for all n ≥ 2

(b) P (n) is true for all n ≥ 3

(c) P (n) is true for all n.

(d) None of these

► (d) None of these

12. A student was asked to prove a statement P (n) by method of induction. He proved that P (3) is true and that P(n) ⇒ P(n+1) for all natural numbers n. On the basis of this he could conclude that P (n) is true

(a) for no n

(b) for all n ≥ 3

(c) for all n ∈ N

(d) None of these

► (b) for all n ≥ 3

13. If 10^{n}+3×4^{n+1}+k is divisible by 9 for all n ∈ N, then the least positive integral value of k is

(a) 3

(b) 1

(c) 5

(d) 7

► (c) 5

14. The statement P (n) : “(n+3)^{2} > 2^{n+3} “ is true for :

(a) all n ≥ 3

(b) all n ≥ 2

(c) all n

(d) no n ∈ N

► (d) no n ∈ N

15. The sum of cubes of three consecutive natural numbers is divisible by:

(a) 2

(b) 9

(c) 7

(d) 5

► (b) 9

16. 2^{n} > n^{2} when n ∈ N such that

(a) n > 2

(b) n < 5

(c) n > 3

(d) n ≥ 5

► (d) n ≥ 5

17. If n is a positive integer , then 2.7^{n}+3.5^{n}−5 is divisible by

(a) 24

(b) 676

(c) 17

(d) 64

► (a) 24

18. If n is a +ve integer, then 23^{n}−7n−1 is divisible by

(a) 64

(b) 36

(c) 49

(d) None of these

► (c) 49

19. The smallest positive integer for which The statement 3^{n+1}<4^{n }is true for

(a) 1

(b) 3

(c) 4

(d) 2

► (c) 4

20. The inequality n!>2^{n−1} is true

(a) for all n > 2

(b) for all n > 1

(c) for all n ∈ N

(d) for no n ∈ N

► (a) for all n > 2

21. 1.2.3 + 2.3.4 + 3.4.5 + ………..up to n terms is equal to :

(a) 1/4 (n + 1) (n -1) (n + 2) (n + 3)

(b) 1/4 (n + 1) (n + 2) (n + 3)

(c) 1/4 n (n + 1) (n + 2) (n + 3)

(d) None of these

► (c) 1/4 n (n + 1) (n + 2) (n + 3)

22. The principle of mathematical induction is for the set of:

(a) Rational numbers

(b) Positive integers

(c) Whole number

(d) Integers

► (b) Positive integers

Hope the given MCQ Questions will help you in cracking exams with good marks. These **Principle of Mathematical Induction MCQ Questions** will help you in practising more and more questions in less time.