CBSE  /  Class 11  /  Maths  /  Principle of Mathematical Induction

  • 1. 
    For any natural number n, 7n – 2n is divisible by

  • 3
  • 4
  • 5
  • 7

  • 2. 
    (n² + n) is ____ for all n ∈ N.

  • Even
  • odd
  • Either even or odd
  • None of these

  • 3. 
    For all n ∈ N, 3×52n+1 + 23n+1 is divisible by

  • 19
  • 17
  • 23
  • 25

  • 4. 
    Find the number of shots arranged in a complete pyramid the base of which is an equilateral triangle, each side containing n shots.

  • n(n+1)(n+2)/3
  • n(n+1)(n+2)/6
  • n(n+2)/6
  • (n+1)(n+2)/6

  • 5. 
    {1 – (1/2)}{1 – (1/3)}{1 – (1/4)} ……. {1 – 1/(n + 1)} =

  • 1/(n + 1) for all n ∈ N.
  • 1/(n + 1) for all n ∈ R
  • n/(n + 1) for all n ∈ N.
  • n/(n + 1) for all n ∈ R

  • 6. 
    (1 + x)n ≥ ____ for all n ∈ N,where x > -1

  • 1 + nx
  • 1 – nx
  • 1 + nx/2
  • 1 – nx/2

  • 7. 
    102n-1 + 1 is divisible by ____ for all N ∈ N

  • 9
  • 10
  • 11
  • 13

  • 8. 
    For all n∈N, 72n − 48n−1 is divisible by :

  • 25
  • 2304
  • 1234
  • 26

  • 9. 
    The sum of the series 1² + 2² + 3² + ………..n² is

  • n(n + 1)(2n + 1)
  • n(n + 1)(2n + 1)/2
  • n(n + 1)(2n + 1)/3
  • n(n + 1)(2n + 1)/6

  • 10. 
    {1/(3 ∙ 5)} + {1/(5 ∙ 7)} + {1/(7 ∙ 9)} + ……. + 1/{(2n + 1)(2n + 3)} =

  • n/(2n + 3)
  • n/{2(2n + 3)}
  • n/{3(2n + 3)}
  • n/{4(2n + 3)}
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