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
A student was asked to prove a statement P ( n ) by method of induction . He proved P ( k + 1 ) is true whenever P ( k ) Is true for all k ≥ 5 , \(k \in N\) and P ( 5 ) is true . On the basis of this he could conclude that P ( n ) is true
  • A
    for all n \(≥\) 5
    Correct
  • B
    for all n \(<\) 5
  • C
    none of these
  • D
    for all n \(>\) 5
2
If \(a,b,c \in N,{a^n} + {b^n}\) is divisible by c , when n is odd but not when n is even , then the value of c is :
  • A
    a+b
    Correct
  • B
    a - b
  • C
    none of these
  • D
    \({a^3} + {b^3}\)
3
1.2.3 + 2.3.4 + 3.4.5 + ………..up to n terms is equal to :
  • A
    none of these
  • B
    1/4 ( n + 1 ) ( n + 2 ) ( n + 3 )
  • C
    1/4 n ( n + 1 ) ( n + 2 ) ( n + 3 )
    Correct
  • D
    1/4 ( n + 1 ) ( n -1 ) ( n + 2 ) ( n + 3 )
4
The number of terms in the expansion of \({\left( {x + y + z} \right)^n}\) is
  • A
    \({1 \over 2}\) (n) ( n + 2 )
  • B
    none of these
  • C
    \({1 \over 2}\) (n + 1 ) ( n + 2 )
    Correct
  • D
    \({1 \over 2}\) (n + 1 ) ( n + 3 )
5
The sum of the terms in the nth bracket of the series 1 + (2+3+4) + (5+6+7+8+9) ….is
  • A
    \({\left( {n - 1} \right)^3} + {n^3}\)
    Correct
  • B
    none of these
  • C
    \({{\left( {n + 1} \right)\left( {n + 2} \right)} \over {6n}}\)
  • D
    \({\left( {n + 1} \right)^3} + 8{n^2}\)
6
For all \(n \in N,{2.4^{2n + 1}} + {3^{3n + 1}}\) is divisible by :
  • A
    11
    Correct
  • B
    7
  • C
    5
  • D
    209
7
If \({49^n} + 16n + \lambda \) is divisible by 64 for all n \( \in \) N , then the least negative integral value of \(\lambda \) is
  • A
    -1
    Correct
  • B
    -4
  • C
    -3
  • D
    -2
8
\({3 \over 4} + {{15} \over {16}} + {{63} \over {64}} + ...........\) to n terms is equal to
  • A
    \(n + {{{4^{ - n}}} \over 3} - {1 \over 3}\)
    Correct
  • B
    \(n + {{{4^{ - n}}} \over 3} + {1 \over 3}\)
  • C
    \(n + {{{4^n}} \over 3} - {1 \over 3}\)
  • D
    \(n - {{{4^n}} \over 3} - {1 \over 3}\)
9
\({10^{2n - 1}} + 1\forall n \in N\) is divisible by :
  • A
    11
    Correct
  • B
    2
  • C
    7
  • D
    3
10
For all odd positive integers n , the number \(n({n^2} - 1)\) is divisible by :
  • A
    36
  • B
    24
    Correct
  • C
    16
  • D
    9
11
\({{{1 \over 2}.{2 \over 2}} \over {{1^3}}} + {{{2 \over 2}.{3 \over 2}} \over {{1^3} + {2^3}}} + {{{3 \over 2}.{4 \over 2}} \over {{1^3} + {2^3} + {3^3}}} + ........\) upto n terms is equal to
  • A
    \({n \over {n + 2}}\)
  • B
    \({n \over {n + 1}}\)
    Correct
  • C
    none of these
  • D
    \({{n + 1} \over {n + 2}}\)
12
\({1 \over {3.5}} + {1 \over {5.7}} + {1 \over {7.9}} + .......\) up to n terms is equal to
  • A
    \({n \over {3\left( {2n + 3} \right)}}\)
    Correct
  • B
    \({n \over {\left( {2n + 3} \right)}}\)
  • C
    none of these.
  • D
    \({1 \over {\left( {n + 2} \right)\left( {n + 4} \right)}}\)
13
The nth terms of the series 4+14+30+52+80+114+….. is =
  • A
    \(3{n^2} + n\)
    Correct
  • B
    \(2{n^{2}} + 2n\)
  • C
    5n-1
  • D
    \(2{n^{2}} + 2\)
14
The product of three consecutive natural numbers is divisible by
  • A
    3
  • B
    11
  • C
    6
    Correct
  • D
    8
15
For \(n \in N,{3^{2n + 2}} - {2^3}n - 9\) is divisible by
  • A
    9
  • B
    64
    Correct
  • C
    3
  • D
    81