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

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We have completed the NCERT/CBSE chapter-wise Multiple Choice Questions for Class 11 Mathematics book Chapter 4 Principle of Mathematical Induction with Answers by expert subject teacher for latest syllabus and examination. You can Prepare effectively for the exam taking the help of the Class 11 Maths Objective Questions PDF free of cost from here. Students can take a free test of the Multiple Choice Questions of Principle of Mathematical Induction. Each Questions has four options followed by the right answer. Download the Maths Quiz Questions with Answers for Class 11 free Pdf and prepare to exam and help students understand the concept very well.

MCQ Questions for Class 11 Mathematics Chapter wise with Answers

Q1. For all n ∈ N, 32n + 7 is divisible by

(i) 8
(ii) 3
(iii) 11
(iv) non of these

(i) 8

Q2. The sum of the series 1³ + 2³ + 3³ + ………..n³ is

(i) {(n + 1)/2}²
(ii) {n/2}²
(iii) n(n + 1)/2
(iv) {n(n + 1)/2}²

(iv) {n(n + 1)/2}²

Q3. What is the sum of 12 + 22 + 32 + … + n2?

(i) n(n+1)(2n+1) /6
(ii) n(n+1)/6
(iii) n(n+1+2n+1) /6
(iv) n(n+1)(n+2) /3

(i) n(n+1)(2n+1) /6

Q4. By principle of mathematical induction, 24n-1 is divisible by which of the following?

(i) 8
(ii) 3
(iii) 5
(iv) 7

(i) 8

Q5. The sum of the series 1 + 2 + 3 + 4 + 5 + ………..n is

(i) n(n + 1)
(ii) (n + 1)/2
(iii) n/2
(iv) n(n + 1)/2

(iv) n(n + 1)/2

Q6. 1/(1 ∙ 2) + 1/(2 ∙ 3) + 1/(3 ∙ 4) + ….. + 1/{n(n + 1)}

(i) n(n + 1)
(ii) n/(n + 1)
(iii) 2n/(n + 1)
(iv) 3n/(n + 1)

(ii) n/(n + 1)

Q7. If n is a positive integer, then 2 . 42n + 1 + 33n + 1 is divisible by :

(i) 2
(ii) 7
(iii) 11
(iv) 27

(iii) 11

Q8. For all positive integers n, the number n(n² − 1) is divisible by:

(i) 36
(ii) 24
(iii) 6
(iv) 16

(iii) 6

Q9. The sum of the series 1² + 2² + 3² + ………..n² is

(i) n(n + 1)(2n + 1)
(ii) n(n + 1)(2n + 1)/2
(iii) n(n + 1)(2n + 1)/3
(iv) n(n + 1)(2n + 1)/6

(iv) n(n + 1)(2n + 1)/6

Q10. The smallest +ve integer n for which n! (n+1/2) holds is

(i) 1
(ii) 2
(iii) 3
(iv) 4

(ii) 2

Q11. P(n) = n(n² – 1). Which of the following does not divide P(k+1)?

(i) k
(ii) k + 2
(iii) k + 3
(iv) k + 1

(iii) k + 3

Q12. If n is an odd positive integer, then aⁿ + bⁿ is divisible by :

(i) a² + b²
(ii) a + b
(iii) a – b
(iv) none of these

(ii) a + b

Q13. For any natural number n, 7ⁿ – 2ⁿ is divisible by

(i) 3
(ii) 4
(iii) 5
(iv) 7

(iii) 5

Q14. Let P(n) : “2n < (1 × 2 × 3 × … × n)”. Then the smallest positive integer for which P(n) is true is

(i) 1
(ii) 2
(iii) 3
(iv) 4

(iv) 4

Q15. (1² + 2² + …… + n²) _ for all values of n ∈ N

(i) = n³/3
(ii) < n³/3

(iii) > n³/3
(iv) None of these

(iii) > n³/3

Q16. 1/(1 ∙ 2 ∙ 3) + 1/(2 ∙ 3 ∙ 4) + …….. + 1/{n(n + 1)(n + 2)} =

(i) {n(n + 3)}/{4(n + 1)(n + 2)}
(ii) (n + 3)/{4(n + 1)(n + 2)}
(iii) n/{4(n + 1)(n + 2)}
(iv) None of these

(i) {n(n + 3)}/{4(n + 1)(n + 2)}

Q17. What is the sum of 1 + 2 + 3 + … n ?

(i) n+1/2
(ii) n/2
(iii) n(n+1)/2
(iv) n(n+2)/2

(iii) n(n+1)/2

Q18. For all n∈N, 5²ⁿ − 1 is divisible by

(i) 26
(ii) 24
(iii) 11
(iv) 25

(ii) 24

Q19. n(n + 1)(n + 5) is a multiple of __ for all n ∈ N

(i) 2
(ii) 3
(iii) 5
(iv) 7

(ii) 3

Q20. If P(n) : “46ⁿ + 16ⁿ + k is divisible by 64 for n Î N” is true, then the least negative integral value of k is.

(i) – 1
(ii) 1
(iii) 2
(iv) – 2

(i) – 1

Q21. 1/(1 ∙ 2 ∙ 3) + 1/(2 ∙ 3 ∙ 4) + …….. + 1/{n(n + 1)(n + 2)} =

(i) {n(n + 3)}/{4(n + 1)(n + 2)}
(ii) (n + 3)/{4(n + 1)(n + 2)}
(iii) n/{4(n + 1)(n + 2)}
(iv) None of these

(i) {n(n + 3)}/{4(n + 1)(n + 2)}

Q22. Find the number of shots arranged in a complete pyramid the base of which is an equilateral triangle, each side containing n shots.

(i) n(n+1)(n+2)/3
(ii) n(n+1)(n+2)/6
(iii) n(n+2)/6
(iv) (n+1)(n+2)/6

(ii) n(n+1)(n+2)/6

Q23. If xn – 1 is divisible by x – k, then the least positive integral value of k is

(i) 1
(ii) 2
(iii) 3
(iv) 4

(i) 1

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MCQ Questions for Class 11 Mathematics Chapter wise with Answers

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