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
For all positive integers n, the number \(n({n^2} - 1)\) is divisible by :
  • A
    6
    Correct
  • B
    24
  • C
    36
  • D
    16
2
For all \(n \in N,{7^{2n}} - 48n - 1\) is divisible by :
  • A
    25
  • B
    2304
    Correct
  • C
    1234
  • D
    26
3
For all \(n \in N,{5^{2n}} - 1\) is divisible by :
  • A
    26
  • B
    24
    Correct
  • C
    11
  • D
    25
4
For all \(n \in N,{3^{2n}} + 7\) is divisible by :
  • A
    11
  • B
    3
  • C
    8
    Correct
  • D
    none of these
5
For all \(n \in N,3{n^5} + 5{n^3} + 7n\) is divisible by :
  • A
    5
  • B
    3
  • C
    10
  • D
    15
    Correct
6
The nth terms of the series 3+7+13+21+……….is =
  • A
    n+2
  • B
    none of these
  • C
    \({n^2} + n + 1\)
    Correct
  • D
    4n-1
7
The nth terms of the series 4+14+30+52+80+114+….. is =
  • A
    \(2{n^{2}} + 2n\)
  • B
    5n-1
  • C
    \(3{n^2} + n\)
    Correct
  • D
    \(2{n^{2}} + 2\)
8
3+13+29+51+79+………..to n terms is
  • A
    none of these
  • B
    \({n^3} + 2{n^2}\)
    Correct
  • C
    \(2{n^{2}} + 7n\)
  • D
    \({n^{2}} + 5{n^3}\)
9
The sum of n terms of the series \({1^3} + {3^3} + {5^3} + .........\) is
  • A
    \({n^2}\left( {{n^2} + 1} \right)\)
  • B
    \({n^2}\left( {2{n^2} - 1} \right)\)
    Correct
  • C
    \({n^2}\left( {2{n^2} + 1} \right)\)
  • D
    none of these.
10
If n is an odd positive integer, then \({a^n} + {b^n}\)is divisible by :
  • A
    \({a^2} + {b^2}\)
  • B
    a-b
  • C
    none of these
  • D
    a+b
    Correct
11
If n is an even positive integer, \({a^n} + {b^n}\) is divisible by :
  • A
    none of these
    Correct
  • B
    a-b
  • C
    \({a^2} + {b^2}\)
  • D
    a+b
12
For all \(n \in N,{{{n^5}} \over 5} + {{{n^3}} \over 3} + {7 \over {15n}}\) is
  • A
    an integer
  • B
    a positive fraction
  • C
    none of these
  • D
    a natural number
    Correct
13
The sum of n terms of the series \(1 + \left( {1 + a} \right) + \left( {1 + a + {a^2}} \right) + \left( {1 + a + {a^2} + {a^3}} \right) + .........,\) is
  • A
    \({n \over {1 - a}} + {{a\left( {1 + {a^n}} \right)} \over {{{\left( {1 - a} \right)}^2}}}\)
  • B
    none of these
  • C
    \( - {n \over {1 - a}} + {{a\left( {1 - {a^n}} \right)} \over {{{\left( {1 - a} \right)}^2}}}\)
  • D
    \({n \over {1 - a}} - {{a\left( {1 - {a^n}} \right)} \over {{{\left( {1 - a} \right)}^2}}}\)
    Correct
14
If 3+5+9+17+33+…….to n terms = \({2^{n + 1}} + n - 2,\) then nth term of LHS is
  • A
    \({2^n} + 1\)
    Correct
  • B
    3n-1
  • C
    none of these
  • D
    2n+1
15
\({{\left( {n + 2} \right)!} \over {\left( {n - 1} \right)!}}\) is divisible by :
  • A
    11
  • B
    6
    Correct
  • C
    24
  • D
    26