Home
Class 11
MATHS
(n!)^(2) gt n^(n) is true for...

`(n!)^(2) gt n^(n)` is true for

A

`AA n in N`

B

`AA n gt 1, n in N`

C

`AA n gt 2, n in N`

D

`AA n in Z`

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Topper's Solved these Questions

  • MATHEMATICAL INDUCTION

    AAKASH SERIES|Exercise PRACTICE SHEET (EXERCISE-I) LEVEL-I (Principle of Mathematical Induction) (Straight Objective Type Questions)|55 Videos

  • LOCUS

    AAKASH SERIES|Exercise PRACTICE EXERCISE|37 Videos

  • MATRICES

    AAKASH SERIES|Exercise LINEAR EQUATIONS - PRACTICE EXERCISE|15 Videos

Similar Questions

Explore conceptually related problems

Let P(n) : 1+ (1)/(4) + (1)/(9) + …. + (1)/(n^2) lt 2 - (1)/( n) is true for

Let P(n) denote the statement that n^(2) +n is odd. It is seen that P(n) rArr P(n+1), P(n) is true for all

log ( x )^(n) = n .log x is true for n .

lim_(ntooo)(((n+1)(n+2)....3n)/(n^(2n)))^(1//n) is equal to

Statement-1: If A = (300)^( 600) , B =600!, C= (200)^(600) , then A gt B gt C . Statement-2: ((n)/(2) )^(n) gt n! gt ((n)/(3) )^(n) for n gt 6 .

The least positive intergral value of n which satisfies the inequality ""^(n-1) C_(3) + ^(n-1) C_(4) gt ^(n) C_(3) is

If for n gt 1, P_(n)=int_(1)^(e ) ( logx)^(n)dx , then P_(10)-90P_(8) is equal to:

AAKASH SERIES-MATHEMATICAL INDUCTION-PRACTICE SHEET (EXERCISE-I) LEVEL-I (Principle of Mathematical Induction) (Straight Objective Type Questions)
  1. (n!)^(2) gt n^(n) is true for

    Text Solution

    |

  2. Let P(n) denote the statement that n^(2) +n is odd. It is seen that P(...

    Text Solution

    |

  3. The statement P(n) (1xx1!) + (2 xx2!) + (3 xx 3!) + … …. + (nxx n!) = ...

    Text Solution

    |

  4. If P(n) be the statement n (n+1)+1 is an integer, then which of the fo...

    Text Solution

    |

  5. n gt 1, n even rArr digit in the units place of 2^(2n)+1

    Text Solution

    |

  6. log ( x )^(n) = n .log x is true for n.

    Text Solution

    |

  7. If 2^(3) + 4^(3) + 6^(3) + … + (2n)^(3) = kn^(2) ( n+1)^(2) then k=

    Text Solution

    |

  8. 4^(3) + 5^(3) + 6^(3) + … + 10^(3)

    Text Solution

    |

  9. Sum of the series S=t^(2) - 2^(2) + 3^(2) - 4^(2) + …... - 2002^(2) + ...

    Text Solution

    |

  10. (sumn^(3) ) ( sumn) = (sumn^2) ^2 if

    Text Solution

    |

  11. n^( th) term of the series 4+14+ 30 + 52+ …..

    Text Solution

    |

  12. If 1+ 5+ 12+ 22 + 35+ ….. + to n terms = ( n^(2) (n+1) )/(2) then n^...

    Text Solution

    |

  13. 1+ 3+ 7 + 15…n terms =

    Text Solution

    |

  14. 1^(2) + 3^(2) + 5^(2) + …. upto n terms =

    Text Solution

    |

  15. 2+ 3.2 + 4.2^(2) + …... upto n terms =

    Text Solution

    |

  16. (1^(2) )/( 1) + (1^(2) + 2^(2) )/(1+2) + (1^(2) + 2^(2) + 3^(2) )/( 1...

    Text Solution

    |

  17. Sum of first 'n' terms of the series = (3)/(2) + (5)/(4) + (9)/(8) + (...

    Text Solution

    |

  18. 0.2 + 0.22 + 0.222+ …. upto n terms is equal to

    Text Solution

    |

  19. 2+7+14+…..+ (n^(2) + 2n-1)=

    Text Solution

    |

  20. 1.6 + 2.9+ 3.12+ ….. + n ( 3n+3)=

    Text Solution

    |

  21. 2.4 + 4.7 + 6.10+ …. upto (n-1) terms=

    Text Solution

    |