These Principle Of Mathematical Induction Class 11 Question and Answers are most important for your upcoming examinations including JEE Main & JEE Advanced. These Principle Of Mathematical Induction Class 11 Question and Answers will help you to score good marks in your exams by helping you to prepare the concepts better and hence, help you to understand the concepts more clearly.
Principle Of Mathematical Induction Class 11 Question and Answers
1. In the principle of mathematical induction, which of the following steps is mandatory?
(A) induction hypothesis
(B) inductive reference
(C) induction set assumption
(D) minimal set representation
Answer: induction hypothesis
2. For m = 1, 2, …, 4m+2 is a multiple of ________
(A) 3
(B) 5
(C) 6
(D) 2
Answer: 2
3. For any integer m>=3, the series 2+4+6+…+(4m) can be equivalent to ________
(A) m2+3
(B) m+1
(C) mm
(D) 3m2+4
Answer: m2+3
4. Which of the following is the base case for 4n+1 > (n+1)2 where n = 2?
(A) 64 > 9
(B) 16 > 2
(C) 27 < 91
(D) 54 > 8
Answer: 64 > 9
5. For any positive integer m ______ is divisible by 4.
(A) 5m2 + 2
(B) 3m + 1
(C) m2 + 3
(D) m3 + 3m
Answer: m3 + 3m
6. For any natural number n, 7n – 2n is divisible by
(A) 3
(B) 4
(C) 5
(D) 7
Answer: 5
7. The sum of the series 1³ + 2³ + 3³ + ………..n³ is
(A) {(n + 1)/2}²
(B) {n/2}²
(C) n(n + 1)/2
(D) {n(n + 1)/2}²
Answer: {n(n + 1)/2}²
8. n(n + 1)(n + 5) is a multiple of ____ for all n ∈ N
(A) 2
(B) 3
(C) 5
(D) 7
Answer: 3
9. The sum of the series 1² + 2² + 3² + ………..n² is
(A) n(n + 1)(2n + 1)
(B) n(n + 1)(2n + 1)/2
(C) n(n + 1)(2n + 1)/3
(D) n(n + 1)(2n + 1)/6
Answer: n(n + 1)(2n + 1)/6
10. For all n ∈ N, 3×52n+1 + 23n+1 is divisible by
(A) 19
(B) 17
(C) 23
(D) 25
Answer: 17
11. 102n-1 + 1 is divisible by ____ for all N ∈ N
(A) 9
(B) 10
(C) 11
(D) 13
Answer: 11
12. {1/(3 ∙ 5)} + {1/(5 ∙ 7)} + {1/(7 ∙ 9)} + ……. + 1/{(2n + 1)(2n + 3)} =
(A) n/(2n + 3)
(B) n/{2(2n + 3)}
(C) n/{3(2n + 3)}
(D) n/{4(2n + 3)}
Answer: n/{3(2n + 3)}
13. If n is an odd positive integer, then an + bn is divisible by :
(A) a² + b²
(B) a + b
(C) a – b
(D) none of these
Answer: a + b
14. The sum of the series 1² + 2² + 3² + ………..n² is
(A) n(n + 1)(2n + 1)
(B) n(n + 1)(2n + 1)/2
(C) n(n + 1)(2n + 1)/3
(D) n(n + 1)(2n + 1)/6
Answer: n(n + 1)(2n + 1)/6
15. For all n∈N, 72n − 48n−1 is divisible by :
(A) 25
(B) 2304
(C) 1234
(D) 26
Answer: 2304
16. {1 – (1/2)}{1 – (1/3)}{1 – (1/4)} ……. {1 – 1/(n + 1)} =
(A) 1/(n + 1) for all n ∈ N.
(B) 1/(n + 1) for all n ∈ R
(C) n/(n + 1) for all n ∈ N.
(D) n/(n + 1) for all n ∈ R
Answer: 1/(n + 1) for all n ∈ N.
17. 1/(1 ∙ 2) + 1/(2 ∙ 3) + 1/(3 ∙ 4) + ….. + 1/{n(n + 1)}
(A) n(n + 1)
(B) n/(n + 1)
(C) 2n/(n + 1)
(D) 3n/(n + 1)
Answer: n/(n + 1)
18. {1 – (1/2)}{1 – (1/3)}{1 – (1/4)} ……. {1 – 1/(n + 1)} =
(A) 1/(n + 1) for all n ∈ N.
(B) 1/(n + 1) for all n ∈ R
(C) n/(n + 1) for all n ∈ N.
(D) n/(n + 1) for all n ∈ R
Answer: 1/(n + 1) for all n ∈ N.
19. 1/(1 ∙ 2 ∙ 3) + 1/(2 ∙ 3 ∙ 4) + …….. + 1/{n(n + 1)(n + 2)} =
(A) {n(n + 3)}/{4(n + 1)(n + 2)}
(B) (n + 3)/{4(n + 1)(n + 2)}
(C) n/{4(n + 1)(n + 2)}
(D) None of these
Answer: {n(n + 3)}/{4(n + 1)(n + 2)}
20. Find the number of shots arranged in a complete pyramid the base of which is an equilateral triangle, each side containing n shots.
(A) n(n+1)(n+2)/3
(B) n(n+1)(n+2)/6
(C) n(n+2)/6
(D) (n+1)(n+2)/6
Answer: n(n+1)(n+2)/6
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