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Free download in PDF Class 11 Maths Chapter 4 Principles of Mathematical Induction Multiple Choice Questions and Answers for Board, JEE, NEET, AIIMS, JIPMER, IIT-JEE, AIEE and other competitive exams. MCQ Questions for Class 11 Maths with Answers were prepared based on the latest exam pattern. These short solved questions or quizzes are provided by Gkseries./p>
(1)
FFor any natural number n, 7n - 2n is divisible by
(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
(3)
(n² + n) is ____ for all n ∈ N.
[A]
Even
[B]
odd
[C]
Either even or odd
[D]
None of these
(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
(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
(6)
(12 + 22 + …... + n2 ) _____ for all values of n ∈ N
[A]
= n3 /3
[B]
< n3 /3
[C]
> n3 /3
[D]
None of these
(7)
The nth term of the series 1 + 4 + 10 + 22 + ….. is
[A]
2n2+2
[B]
3*2n-1 - 2
[C]
2n2+2n
[D]
5n-1
(8)
n < 2n for all
[A]
n ∈ R
[B]
n ∈ N
[C]
n may be any number
[D]
None of these
(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
(10)
(2 ∙ 7N + 3 ∙ 5N - 5) is Divisible by ___ for all N ∈ N
[A]
6
[B]
12
[C]
18
[D]
24
(11)
The nth term of the series 1 + 4 + 10 + 22 + ….. is
[A]
2n2+2
[B]
3*2n-1 - 2
[C]
2n2+2n
[D]
5n-1
(12)
A + AR + AR2 + ....... + ARN – 1 = (ARN – 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
(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
(14)
For all n∈N, 52n − 1 is divisible by :
[A]
26
[B]
24
[C]
11
[D]
25
(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
(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
Answer: induction hypothesis
(17)
For m = 1, 2, …, 4m+2 is a multiple of ________
(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
(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
(20)
For any positive integer m ______ is divisible by 4.
[A]
5m2 + 2
[B]
3m + 1
[C]
m2 + 3
[D]
m3 + 3m
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