Refer to Class 11 Mathematics Principle of Mathematical Induction Functions MCQs provided below. CBSE Class 11 Mathematics MCQs with answers available in Pdf for free download. The MCQ Questions for Class 11 Mathematics with answers have been prepared as per the latest syllabus, CBSE books and examination pattern suggested in Class 11 by CBSE, NCERT and KVS. Multiple Choice Questions for Chapter 4 Principle of Mathematical Induction are an important part of exams for Class 11 Mathematics and if practiced properly can help you to get higher marks. Refer to more Chapter-wise MCQs for CBSE Class 11 Mathematics and also download more latest study material for all subjects
MCQ for Class 11 Mathematics Chapter 4 Principle of Mathematical Induction
Class 11 Mathematics students should refer to the following multiple-choice questions with answers for Chapter 4 Principle of Mathematical Induction in Class 11. These MCQ questions with answers for Class 11 Mathematics will come in exams and help you to score good marks
Chapter 4 Principle of Mathematical Induction MCQ Questions Class 11 Mathematics with Answers
Question. If P(n) = 2 + 4 + 6 + .....+ 2n, nÎN , then P(k) =k(k +1) + 2
⇒ P(k +1) = (k +1)(k + 2) + 2 for all k ÎN . So we can conclude that P(n) = n(n +1) + 2 for D
(a) all nεN
(b) n > 1
(c) n > 2
(d) nothing can be said
Answer : D
Question. Let P(n) be statement 2n < n!. Where n is a natural number, then P(n) is true for:
(a) all n
(b) all n > 2
(c) all n > 3
(d) none of these
Answer : C
Question. What is the sum of 12 + 22 + 32 + ... + n2?
(a) n(n+1)(2n+1) /6
(b) n(n+1)/6
(c) n(n+1+2n+1) /6
(d) n(n+1)(n+2) /3
Answer : A
Question. Let T(k) be the statement 1 + 3 + 5 + .... + (2k – 1) = k2 +10
Which of the following is correct?
(a) T(1) is true
(b) T(k) is true ⇒ T(k + 1) is true
(c) T(n) is true for all n ÎN
(d) All above are correct
Answer : B
Question. Let P(n) : n2 + n + 1 is an even integer. If P(k) is assumed true then P(k + 1) is true. Therefore P(n) is true.
(a) for n > 1
(b) for all n Î N
(c) for n > 2
(d) none of these
Answer : D
Question. If n is a positive integer, then 2 . 42n + 1 + 33n + 1 is divisible by :
(a) 2
(b) 7
(c) 11
(d) 27
Answer : C
Question. If P(n) : 2 + 4 + 6 +... + (2n), n Î N, then P(k) =k (k + 1) + 2 implies P (k + 1) = (k + 1) (k + 2) + 2 is true for all k Î N.
So statement P(n) = n (n + 1) + 2 is true for:
(a) n ≥ 1
(b) n ≥ 2
(c) n ≥ 3
(d) none of these
Answer : D
Question. The smallest +ve integer n for which n! (n+1/2) holds is
(a) 1
(b) 2
(c) 3
(d) 4
Answer : B
Question. Let S(K) = 1+ 3+ 5...+ (2K -1) = 3 + K2 then which of the following is true?
(a) Principle of mathematical induction can be used to prove the formula
(b) S(K)ÞS(K +1)
(c) S(K)Þ/ S(K +1)
(d) S(1) is correct
Answer : B
Question. Let P(n) : “2n < (1 × 2 × 3 × ... × n)”. Then the smallest positive integer for which P(n) is true is
(a) 1
(b) 2
(c) 3
(d) 4
Answer : D
Question. For all n Î N, 3.52n +1 + 23n + 1 is divisible by
(a) 19
(b) 17
(c) 23
(d) 25
Answer : B
Question. What is the sum of 13 + 23 + 33 + ........ + n3 ?
(a) [n(n+1)/3]2
(b) [n(n+1)/2]2
(c) [n(n+2)/3]2
(d) [n(n+1)/2]3
Answer : B
Question. What is the sum of 1 + 2 + 3 + ... n ?
(a) n+1/2
(b) n/2
(c) n(n+1)/2
(d) n(n+2)/2
Answer : C
Question. If P(n) = 2 + 4 + 6 + .....+ 2n, n ÎN, then P(k) = k(k +1) + 2
⇒ P(k +1) = (k +1)(k + 2) + 2 for all k ÎN.
So we can conclude that P(n) = n(n +1) + 2 for
(a) all n ÎN
(b) n > 1
(c) n > 2
(d) nothing can be said
Answer : D
Question. The greatest positive integer, which divides n(n +1)(n + 2)(n + 3) for all n ÎN, is
(a) 2
(b) 6
(c) 24
(d) 120
Answer : C
Question. 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.
(a) – 1
(b) 1
(c) 2
(d) – 2
Answer : A
Question. If an = √7 + √7 + √7 +... ... having n radical signs then by methods of mathematical induction which is true
(a) an > 7 " n ≥ 1
(b) an < 7 " n ≥ 1
(c) an < 4 " n ≥ 1
(d) an < 3 " n ≥ 1
Answer : B
Question. Let T(k) be the statement 1 + 3 + 5 + .... + (2k – 1)= k2 +10
Which of the following is correct
(a) T(1) is true
(b) T(k) is true ⇒ T(k + 1) is true
(c) T(n) is true for all nεN
(d) All above are correct
Answer : B
Question. 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
Answer : A
Question. A student was asked to prove a statement P(n) by induction. He proved that P(k + 1) is true whenever P(k) is true for all k > 5 Î N and also that P (5) is true. On the basis of this he could conclude that P(n) is true
(a) for all n Î N
(b) for all n > 5
(c) for all n ³ 5
(d) for all n < 5
Answer : C
Question. If 10n + 3.4n+2 k is divisible by 9 for all n ÎN, then the least positive integral value of k is
(a) 5
(b) 3
(c) 7
(d) 1
Answer : A
Question. What is the sum of 2 + 4 + 6 + 8 + ....+ 2n ? A
(a) n (n + 1)
(b) n(n + 2)
(c) n (n + 3)
(d) n(n + 4)
Answer : A
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CBSE Class 11 Mathematics Chapter 4 Principle of Mathematical Induction MCQs
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MCQs for Mathematics CBSE Class 11 Chapter 4 Principle of Mathematical Induction
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Chapter 4 Principle of Mathematical Induction MCQs Mathematics CBSE Class 11
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Chapter 4 Principle of Mathematical Induction CBSE Class 11 MCQs Mathematics
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CBSE MCQs Mathematics Class 11 Chapter 4 Principle of Mathematical Induction
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