Objective Questions On Class 11 Maths Chapter 4 Principle Of Mathematical Induction

Questions

1 FFor any natural number n, 7n - 2n is divisible by

A 3

B 4

C 5

D 7

View Answer

Answer:5

2 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

View Answer

Answer:{n(n + 1)/2}²

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3 (n² + n) is ____ for all n ∈ N.

A Even

B odd

C Either even or odd

D None of these

View Answer

Answer:Even

4 The sum of n terms of the series 1² + 3² + 5² +......... is

A n(4n² - 1)/3

B n²(2n²+1)/6

C none of these.

D n²(n²+1)/3

View Answer

Answer:n(4n² - 1)/3

5 (1 + x)ⁿ ≥ ____ for all n ∈ N,where x > - 1

A 1 + nx

B 1 - nx

C 1 + nx/2

D 1 - nx/2

View Answer

Answer:1 + nx

6 (1² + 2² + …... + n² ) _____ for all values of n ∈ N

A = n³ /3

B < n³ /3

C > n³ /3

D None of these

View Answer

Answer:> n³ /3

7 The nth term of the series 1 + 4 + 10 + 22 + ….. is

A 2n²+2

B 3*2^n-1 - 2

C 2n²+2n

D 5n-1

View Answer

Answer:3*2^n-1 - 2

8 n < 2ⁿ for all

A n ∈ R

B n ∈ N

C n may be any number

D None of these

View Answer

Answer:n ∈ N

9 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

View Answer

Answer:n(n+1)(n+2)/6

10 (2 ∙ 7^N + 3 ∙ 5^N - 5) is Divisible by ___ for all N ∈ N

A 6

B 12

C 18

D 24

View Answer

Answer:24

11 The nth term of the series 1 + 4 + 10 + 22 + ….. is

A 2n²+2

B 3*2^n-1 - 2

C 2n²+2n

D 5n-1

View Answer

Answer:3*2^n-1 - 2

12 A + AR + AR² + ....... + AR^{N – 1} = (AR^{N – 1})/(R - 1) for

A r ≥ 1 and n ∈ N

B r ≤ 1 and n ∈ N

C r > 1 and n ∈ N

D r < 1 and n ∈ N

View Answer

Answer:r > 1 and n ∈ N

13 The sum of n terms of the series 1²+ 3²+ 5²+......... is

A n(4n² - 1)/3

B n²(2n²+1)/6

C none of these.

D n²(n²+1)/3

View Answer

Answer:n(4n² - 1)/3

14 For all n∈N, 5²ⁿ − 1 is divisible by :

A 26

B 24

C 11

D 25

View Answer

Answer:24

15 What is the base case for the inequality 7n > n3, where n = 3?

A 652 > 189

B 42 < 132

C 343 > 27

D 42 <= 431

View Answer

Answer:343 > 27

16 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

View Answer

Answer:induction hypothesis

17 For m = 1, 2, …, 4m+2 is a multiple of ________

A 3

B 5

C 6

D 2

View Answer

Answer:2

18 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

View Answer

Answer:m²+3

19 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

View Answer

Answer:64 > 9

20 For any positive integer m ______ is divisible by 4.

A 5m² + 2

B 3m + 1

C m² + 3

D m³ + 3m

View Answer

Answer:m³ + 3m

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