Principle Of Mathematical Induction CBSE Questions & Answers

Principle Of Mathematical Induction

This is Mathematics Class 11 Principle of Mathematical Induction CBSE Questions & Answers. There are 15 questions in this test with each question having around four answer choices.

Questions & Answers

1
The statement \({2^{n + 2}} < {3^n}\) is true for all
  • A
    for all n \( \in \) N
  • B
    none of these.
  • C
    all n \(>\) 2
  • D
    all n \(>\) 3
    Correct
2
The smallest positive integer for which The statement \({3^{n + 1}} < {4^n}\) is true for
  • A
    1
  • B
    3
  • C
    4
    Correct
  • D
    2
3
For all n \( \in \) N , \({49^n} + 16n - 1\)is divisible by
  • A
    64
    Correct
  • B
    29
  • C
    19
  • D
    3
4
The digit in the unit’s place of the number \(183! + {3^{183}}\) is
  • A
    6
  • B
    3
  • C
    7
    Correct
  • D
    none of these
5
\({7^{2n}} + {3^{n - 1}}{.2^{3n - 3}}\) is divisible by
  • A
    none of these
  • B
    9
  • C
    24
  • D
    25
    Correct
6
If n \( \in \) N then \({n^3} + 2n\) is divisible by
  • A
    4
  • B
    3
    Correct
  • C
    2
  • D
    6
7
If n is a positive integer , then \({2.7^n} + {3.5^n} - 5\) is divisible by
  • A
    17
  • B
    24
    Correct
  • C
    64
  • D
    676
8
If n is a +ve integer, then \({4^n} - 3n - 5\) is divisible by
  • A
    none of these
  • B
    9
    Correct
  • C
    27
  • D
    3
9
If n is a +ve integer, then \({2.4^{2n + 1}} + {3^{3n + 1}}\) is divisible by
  • A
    11
    Correct
  • B
    9
  • C
    2
  • D
    none of these
10
If n is a +ve integer, then \({10^n} + {3.4^{n + 2}} + 5\) is divisible by
  • A
    15
  • B
    4
  • C
    9
    Correct
  • D
    3
11
If n is a +ve integer, then \({3^{3n}} - 26n - 1\) is divisible by
  • A
    547
  • B
    627
  • C
    239
  • D
    676
    Correct
12
If n is a +ve integer, then \({2^{3n}} - 7n - 1\) is divisible by
  • A
    36
  • B
    64
  • C
    none of these
  • D
    49
    Correct
13
If n is a +ve integer, then \({3.5^{2n + 1}} + {2^{3n + 1}}\) is divisible by
  • A
    64
  • B
    none of these
  • C
    17
    Correct
  • D
    24
14
If n is a +ve integer, then \({7^{2n}} - 4\) is divisible by
  • A
    26
  • B
    25
  • C
    2309
    Correct
  • D
    none of these
15
Let P ( k ) = 1 + 3 + 5 + …………….+ ( 2k – 1 ) =\(\left( {3 + {k^2}} \right)\).Then which of the following is true ?
  • A
    P ( k ) \( \Rightarrow \)P ( k + 2 )
  • B
    P ( k ) \( \Rightarrow \) P ( k+1 )
    Correct
  • C
    Principal of mathematical induction can be used to prove the formula
  • D
    P ( 1 ) is correct