Home
Class 11
MATHS
Prove that (n !+1) is not divisible by ...

Prove that `(n !+1)` is not divisible by any natural number between `2` and `n`

Promotional Banner

Topper's Solved these Questions

  • PARABOLA

    RD SHARMA ENGLISH|Exercise All Questions|86 Videos
  • PROBABILITY

    RD SHARMA ENGLISH|Exercise All Questions|290 Videos

Similar Questions

Explore conceptually related problems

Prove that (n !+1) is not divisible by any natural number between 2a n dndot

Prove that (n !)! is divisible by (n !)^((n-1)!)

prove that 4^(n)-1 is divisible by 3, for each natural number n.

prove that 3^(2n)-1 is divisible by 8, for all natural numbers n.

prove that n(n^(2)+5) is divisible by 6, for each natural number n.

Prove that 3^(2n)+24n-1 is divisible by 32 .

Using principle of mathematical induction, prove that 7^(4^(n)) -1 is divisible by 2^(2n+3) for any natural number n.

Show that n^3+(n+1)^3+(n+2)^3 is divisible by 9 for every natural number n .

Prove that (mn)! Is divisible by (n!)^(m) " and" (m!)^(n)

((n+2)!)/((n-1)!) is divisible by

RD SHARMA ENGLISH-PERMUTATIONS-All Questions
  1. Prove that 33! is divisible by " 2^15. what is the largest integer n s...

    Text Solution

    |

  2. Find the number of arrangements of the letters of the MISS.

    Text Solution

    |

  3. Prove that (n !+1) is not divisible by any natural number between 2 a...

    Text Solution

    |

  4. Prove that: ((2n)!)/(n !)={1. 3. 5 (2n-1)}2^ndot

    Text Solution

    |

  5. If (n !)/(2!(n-2)!) and (n !)/(4!(n-4)!) are in the ratio 2:1 , find t...

    Text Solution

    |

  6. Find n , if (n+2)! =2550xxn !

    Text Solution

    |

  7. If 1/(9!)+1/(10 !)=x/(11 !) , find xdot

    Text Solution

    |

  8. Prove that: n(n-1)(n-2)....(n-r+1)=(n !)/((n-r)!)

    Text Solution

    |

  9. If w(1).w(2),w(3) and w(4) are work done in isothermal, adiabatic, iso...

    Text Solution

    |

  10. How many permutations of the letters of the word MADHUBANI do not b...

    Text Solution

    |

  11. Find the probability that in a random arrangement of the letters of th...

    Text Solution

    |

  12. How many numbers can be formed with the digits 1, 2, 3, 4, 3, 2, 1 so ...

    Text Solution

    |

  13. If the letters of the word ‘MOTHER’ are written in all possible orders...

    Text Solution

    |

  14. In how many ways can the letters of the word PERMUTATIONS be arrange...

    Text Solution

    |

  15. In how many ways can the letters of the word PERMUTATIONS be arrang...

    Text Solution

    |

  16. (i) How many different words can be formed with letters of the word ‘S...

    Text Solution

    |

  17. How many words can be formed using the letter A thrice, the letter B ...

    Text Solution

    |

  18. How many 5 letters words can be formed using the letters of the words ...

    Text Solution

    |

  19. m men and n women ae to be seated in a row so that no two women sit...

    Text Solution

    |

  20. A gentle man wants to invite six friends. In how many ways he can send...

    Text Solution

    |