Class 11 Mathematics Principle of Mathematical Induction Functions MCQs

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

Chapter 02 Relations and Functions
Class 11 Mathematics Relations and Functions MCQs
Chapter 03 Trigonometric Functions
Class 11 Mathematics Trigonometric Functions MCQs
Chapter 05 Complex Numbers and Quadratic Equations
Class 11 Mathematics Complex Numbers and Quadratic Equation MCQs
Chapter 06 Linear Inequalities
Class 11 Mathematics Linear Inequalities MCQs
Chapter 07 Permutations and Combinations
Class 11 Mathematics Permutations and Combinations MCQs
Chapter 08 Binomial Theorem
Class 11 Mathematics Binomial Theorem MCQs
Chapter 09 Sequences and Series
Class 11 Mathematics Sequences and Series MCQs
Chapter 12 Introduction to Three Dimensional Geometry
Class 11 Mathematics Introduction To Three-Dimensional Geometry MCQs
Chapter 13 Limits and Derivatives
Class 11 Mathematics Limits And Derivatives MCQs
Chapter 14 Mathematical Reasoning
Class 11 Mathematics Mathematical Reasoning MCQs

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CBSE Class 11 Mathematics Chapter 4 Principle of Mathematical Induction MCQs

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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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