# Class 11 Mathematics Chapter 4 Principle of Mathematical Induction MCQ Questions with Answer

Principle of Mathematical Induction Class 11 MCQ is one of the best strategies to prepare for the CBSE Class 11 Board exam. If you want to complete a grasp concept or work on one’s score, there is no method except constant practice. Students can improve their speed and accuracy by doing more Principle of Mathematical Induction class 11 MCQ which will help them all through their board test.

## Principle of Mathematical Induction Class 11 MCQ Questions with Answer

Class 11 Math MCQ with answers are given here to Chapter 4 Principle of Mathematical Induction. These MCQs are based on the latest CBSE board syllabus and relate to the latest Class 11 Mathematics syllabus. By Solving these Class 11 MCQs, you will be able to analyze all of the concepts quickly in the Chapter and get ready for the Class 11 Annual exam.

Learn Principle of Mathematical Induction Class 11 MCQ with answers pdf free download according to the latest CBSE and NCERT syllabus. Students should prepare for the examination by solving CBSE Class 11 Principle of Mathematical Induction MCQ with answers given below.

Question 1. For all n 2,n n2 (n4 > 1) is divisible by
(a) 60
(b) 50
(c) 40
(d) 70

A

Question 2. For every positive integer n, n7/7 + n5/5 + 2n3/3 – n/105 is
(a) an integer
(b) a rational number
(c) a negative real number
(d) an odd integer

A

Question 3. For n ∈ N, (1/5)n5 +(1/3)n3 + (7/15)n is
(a) an integer
(b) a natural number
(c) a positive fraction
(d) None of these

B

Question 4. For positive integer n, 10n-2 > 81 , if
(a) n > 5
(b) n ≥ 5
(c) n < 5
(d) n > 6

B

Question 5. If x2n – 1 + y2n – 1  is divisible by x + y, if n is
(a) a positive integer
(b) an even positive integer
(c) an odd positive integer
(d) None of these

A

Question 6. If 49n + 16n k is divisible by 64 for n ∈ N, then the least negative integral value of k is
(a) –1
(b) –2
(c) –3
(d) –4

A

Question 7. If  n εN, 72n – 48n – 1 is divisible by
(a) 25
(b) 26
(c) 1234
(d) 2304

D

Question 8. The greatest positive integer, which divides
(n + 2) (n + 3) (n + 4) (n + 5) (n + 6) for all n ε N, is
(a) 4
(b) 120
(c) 240
(d) 24

B

Question 9. If m, n are any two odd positive integer with n m, then the largest positive integers which divides all the numbers of the type m2 – n 2 is
(a) 4
(b) 6
(c) 8
(d) 9

C

Question 10. For all nεN ,3.52n+1 +23n+1  is divisible by
(a) 19
(b) 17
(c) 23
(d) 25

B

Question 11. If P(n) is a statement such that P(3) is true.
Assuming P(k) is true P(k + 1) is true for all k ε 3, then P(n) is true
(a) for all n
(b) for n 3
(c) for n  > 4
(d) None of these

B

Question 12. For all n ε N, n (n+ 1)(n + 5) is a multiple of
(a) 4
(b) 3
(c) 5
(d) 7

B

Question 13. If P(n) is a statement (n∈ N) such that, if P(k) is true, P(k +1) is true for k∈ N, then P(n) is true
(a) for all n
(b) for all n > 1
(c) for all n > 2
(d) Nothing can be said

D

Question 14. The smallest positive integer n for which n! < (n+1 / 2) holds, is
(a) 1
(b) 2
(c) 3
(d) 4

B

Question 15. The inequality n ! > 2n-1 is true for
(a) n > 2
(b) n > N
(c) n > 3
(d) None of these

A

Whoever needs to take the CBSE Class 11 Board Exam should look at this MCQ. To the Students who will show up in CBSE Class 11 Mathematics Board Exams, It is suggested to practice more and more questions. Aside from the sample paper you more likely had solved. These Principle of Mathematical Induction Class 11 MCQ are ready by the subject specialists themselves.

Question 16. For all n εN, 41n-14n is a multiple of
(a) 26
(b) 27
(c) 25
(d) None of these

B

Question 17. The product of three consecutive natural numbers is divisible by
(a) 2
(b) 3
(c) 6
(d) 4

(a,b,c)

Question 18. Sn is divisible by the multiple of
(a) 5
(b) 7
(c) 24
(d) None of these

C

Question 19. For each n ε N, the correct statement is
(a) 2n < n
(b) n2 > 2n
(c) n4 < n10
(d) 23n > 7n + 1

C

Question 20. 23n – 7n 1  is divisible by
(a) 64
(b) 36
(c) 49
(d) 25

C

Question 21. For eachn n εN, 32n-1 is divisible by
(a) 8
(b) 16
(c) 32
(d) None of these

A

Question 22. Let P(n) : n2+n+1 is an even integer. If P(k) is assumed true ⇒P(k + 1) is true. Therefore, P(n) is true
(a) for n > 1
(b) for all n > N
(c) for n > 2
(d) None of these

D

Question 23. If xn – 1 is divisible by x – k, then the least positive integral value of k is
(a) 1
(b) 2
(c) 3
(d) 4

A

Question 24. If Sn is divisible for every n, then Sn is
(a) > 0
(b) > 1
(c) > 5
(d) None of these

A

Question 25. Let P(n) denotes the statement that n 2+n is odd. It is seen that P(n) P(n + 1), P(n) is true for all
(a) n > 1
(b) n
(c) n > 2
(d) None of these

D

Question 26. If nεN, then the highest positive integer which dividesn(n – 1)(n – 2) is
(a) 3
(b) 6
(c) 9
(d) 12

B

Question 27. For all n εN, 2,42n+1 + 33n+1 is divisible by
(a) 2
(b) 9
(c) 3
(d) 11

D

Question 28. For eachn n εN, 102n-1 is divisible by
(a) 11
(b) 13
(c) 9
(d) None of these

A

Question 29. x(xn-1 -nαn-1)1 is divisible by (x – α.)2 for
(a) n > 1
(b) n > 2
(c) all n ∈ N
(d) None of the above

C

Question 30. For all positive integral values ofn n,32n – 2n +1 is divisible by
(a) 2
(b) 4
(c) 8
(d) 12

A

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