Students can refer to the following MCQ Questions for Class 11 Principle of Mathematical Induction with Answers provided below based on the latest curriculum and examination pattern issued by CBSE and NCERT. Our teachers have provided here collection of multiple choice questions for Principle of Mathematical Induction Class 11 covering all topics in your textbook so that students can assess themselves on all important topics and thoroughly prepare for their exams

## Class 11 Principle of Mathematical Induction MCQs Questions with Answers

We have provided below MCQs questions for Class 11 Principle of Mathematical Induction with answers which will help the students to go through the entire syllabus and practice multiple choice questions provided here with solutions. As Principle of Mathematical Induction MCQs in Class 11 pdf download can be really scoring for students, you should go through all problems provided below so that you are able to get more marks in your exams.

#### MCQ Questions for Class 11 Principle of Mathematical Induction

**Question. For positive integer n, 10 ^{n-2} > 81 , if **

(a) n

**>**5

(b) n ≥ 5

(c) n < 5

(d) n

**>**6

**Answer**

B

**Question. If x ^{2n – 1} + y^{2n – 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

**Answer**

A

**Question. If 49 ^{n} + 16^{n} 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

**Answer**

A

**Question. If n εN, 7^{2n} – 48n – 1 is divisible by **

(a) 25

(b) 26

(c) 1234

(d) 2304

**Answer**

D

**Question. For all n ≥ 2,n n^{2} (n^{4} > 1) is divisible by **

(a) 60

(b) 50

(c) 40

(d) 70

**Answer**

A

**Question. For every positive integer n, n7/7 + n5/5 + 2n ^{3}/3 – n/105 is **

(a) an integer

(b) a rational number

(c) a negative real number

(d) an odd integer

**Answer**

A

**Question. For n ∈ N, (1/5)n5 +(1/3)n ^{3} + (7/15)n is **

(a) an integer

(b) a natural number

(c) a positive fraction

(d) None of these

**Answer**

B

**Question. For all n ε N, n (n+ 1)(n + 5) is a multiple of **

(a) 4

(b) 3

(c) 5

(d) 7

**Answer**

B

**Question. 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

**Answer**

D

**Question. The smallest positive integer n for which n! < (n+1 / 2) holds, is **

(a) 1

(b) 2

(c) 3

(d) 4

**Answer**

B

**Question. The inequality n ! > 2 ^{n-1} is true for **

(a) n

**>**2

(b) n

**>**N

(c) n

**>**3

(d) None of these

**Answer**

A

**Question. 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

**Answer**

B

**Question. 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 m ^{2} – n^{ 2} is **

(a) 4

(b) 6

(c) 8

(d) 9

**Answer**

C

**Question. For all nεN ,3.5 ^{2n+1} +2^{3n+1} is divisible by **

(a) 19

(b) 17

(c) 23

(d) 25

**Answer**

B

**Question. 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

**Answer**

B

**Question. 2 ^{3n} – 7n 1 is divisible by **

(a) 64

(b) 36

(c) 49

(d) 25

**Answer**

C

**Question. For eachn n εN, 3 ^{2n}-1 is divisible by **

(a) 8

(b) 16

(c) 32

(d) None of these

**Answer**

A

**Question. Let P(n) : n ^{2}+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

**Answer**

D

**Question. If x ^{n – 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. For all n εN, 41 ^{n}-14^{n} is a multiple of **

(a) 26

(b) 27

(c) 25

(d) None of these

**Answer**

B

**Question. The product of three consecutive natural numbers is divisible by**

(a) 2

(b) 3

(c) 6

(d) 4

**Answer**

(a,b,c)

**Question. S ^{n} is divisible by the multiple of **

(a) 5

(b) 7

(c) 24

(d) None of these

**Answer**

C

**Question. For each n ε** **N, the correct statement is **

(a) 2^{n} < n

(b) n^{2} > 2n

(c) n^{4} < n^{10}

(d) 2^{3n} > 7n + 1

**Answer**

C

**Question. If n εN, then the highest positive integer which dividesn(n – 1)(n – 2) is **

(a) 3

(b) 6

(c) 9

(d) 12

**Answer**

B

**Question. For all n εN, 2,4 ^{2n+1} + 3^{3n+1} is divisible by **

(a) 2

(b) 9

(c) 3

(d) 11

**Answer**

D

**Question. For eachn n εN, 10 ^{2n}-1 is divisible by **

(a) 11

(b) 13

(c) 9

(d) None of these

**Answer**

A

**Question. x(x ^{n-1} -nα^{n-1})1 is divisible by (x – α.)^{2} for **

(a) n > 1

(b) n > 2

(c) all n ∈ N

(d) None of the above

**Answer**

C

**Question. For all positive integral values ofn n,3 ^{2n} – 2n +1 is divisible by**

(a) 2

(b) 4

(c) 8

(d) 12

**Answer**

A

**Question. If Sn is divisible for every n, then Sn is **

(a) > 0

(b) > 1

(c) > 5

(d) None of these

**Answer**

A

**Question. 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

**Answer**

D

Our teachers have developed really good **Multiple Choice Questions** covering all important topics in each chapter which are expected to come in upcoming tests and exams, as MCQs are coming in all exams now therefore practice them carefully to get full understanding of topics and get good marks. Download the latest questions with multiple choice answers for Class 11 Principle of Mathematical Induction in pdf or read online for free.

The above **NCERT based MCQs for Class 11 Principle of Mathematical Induction** have been designed by our teachers in such a way that it will help you a lot to gain an understanding of each topic. These CBSE NCERT Class 11 Principle of Mathematical Induction Multiple Choice Questions have been developed and are available free for benefit of Class 11 students.

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d) It will be easy to revise all Principle of Mathematical Induction chapters and faster revisions prior to class tests and exams.

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**I want the latest MCQs based on this years syllabus ?**The MCQs for Class 11 Principle of Mathematical Induction with Answers have been developed based on current NCERT textbook issued by CBSE.

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