Home
Class 12
MATHS
P=n(n^(2)-1)(n^(2)-4)(n^(2)-9)…(n^(2)-10...

`P=n(n^(2)-1)(n^(2)-4)(n^(2)-9)…(n^(2)-100)` is always divisible by , `(n in I)` (a) `2!3!4!5!6!` (b) `(5!)^(4)` (c) `(10!)^(2)` (d) `10!11!`

A

`(2r+2)!`

B

`(2r-1)!`

C

`(2r+1)!`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
B, C
Promotional Banner

Topper's Solved these Questions

  • PERMUTATION & COMBINATION

    VMC MODULES ENGLISH|Exercise JEE ARCHIVE|50 Videos

  • PERMUTATION & COMBINATION

    VMC MODULES ENGLISH|Exercise LEVEL-1|125 Videos

  • MOCK TEST 9

    VMC MODULES ENGLISH|Exercise MATHEMATICS (SECTION 2)|5 Videos

  • PROBABILITY

    VMC MODULES ENGLISH|Exercise JEE ADVANCED (ARCHIVE)|102 Videos

Similar Questions

Explore conceptually related problems

10^n+3(4^(n+2))+5 is divisible by (n in N)

For all n inN,3*5^(2n+1)+2^(3n+1) is divisible by (A) 19 (B) 17 (C) 23 (D) 25

If n is a natural number, then 9^(2n)-4^(2n) is always divisible by (a) 5 (b) 13 (c) both 5 and 13 (d) none of these

If P(n) stands for the statement n(n+1)(n+2) is divisible by 3, then what is P(4).

Prove that for n in N ,10^n+3. 4^(n+2)+5 is divisible by 9 .

If the mean of first n natural numbers is (5n)/9 , then n= (a) 5 (b) 4 (c) 9 (d) 10

If S_(n) = sum_(n=1)^(n) (2n + 1)/(n^(4) + 2n^(3) + n^(2)) then S_(10) is less then

If .^(n)P_(3)+.^(n)C_(n-2)=14n , the value of n is (a) 5 (b) 6 (c) 8 (d) 10

If 2(2n+5)=3\ (3n-10), then n= (a)5 (b) 3 (c)7 (d) 8

Using Mathematical induction, prove that 10 ^(n)+3.4^(n+2)+5 is divisible by 9 for all ninN .

VMC MODULES ENGLISH-PERMUTATION & COMBINATION-LEVEL-2
  1. The combinatorial coefficients ""^(n – 1)C(p) denotes

    Text Solution

    |

  2. Which of the following statements are correct?

    Text Solution

    |

  3. P=n(n^(2)-1)(n^(2)-4)(n^(2)-9)…(n^(2)-100) is always divisible by , (...

    Text Solution

    |

  4. Let n be a positive integer and define f(n)=1!+2!+3!+…+n!. Find polyno...

    Text Solution

    |

  5. Consider seven digit number x1,x2,...,x7, where x1,x2,..,x7 != 0 havin...

    Text Solution

    |

  6. A woman has 11 close friends. Number of ways in which she can invite 5...

    Text Solution

    |

  7. On the normal chess board as shown, I1, & I2, are two insects whic...

    Text Solution

    |

  8. There are 12 points in a plane of which 5 are collinear. The maximum n...

    Text Solution

    |

  9. There are 10 seats in the first row of a theatre of which 4 are to be ...

    Text Solution

    |

  10. A man is at the origin on the x-axis and takes a unit step either to t...

    Text Solution

    |

  11. For the equation x + y + z +omega= 19, the number of positive integral...

    Text Solution

    |

  12. Find the number of non-negative integral solutions of x1+x2+x3+4x4=20.

    Text Solution

    |

  13. 10 persons are to be arranged in a circular fashion so that in no two ...

    Text Solution

    |

  14. The Number of ways in which five different books to be distributed amo...

    Text Solution

    |

  15. Number of ways in which the letters of the word ‘B U L B U L’ can be a...

    Text Solution

    |

  16. Number of ways in which 200 people can be divided in 100 couples is -

    Text Solution

    |

  17. If letters of the word “THING” are arranged in all possible manner and...

    Text Solution

    |

  18. You are given 8 balls of different colour (black,white ......). The nu...

    Text Solution

    |

  19. Kanchan has 10 friends among whom two are married to each other. Sh...

    Text Solution

    |

  20. Number of quadrilaterals which can be constructed by joining the verti...

    Text Solution

    |