Home
Class 11
MATHS
If m and n are positive integers more th...

If m and n are positive integers more than or equal to 2, `mgtn`, then (mn)! is divisible by

A

`(m!)^(n),(n!)^(m)and(m+n)!` but not by (m-n)!

B

`(m+n)!,(m-n)!,(m!)^(n)` but `(n!)^(m)`

C

`(m!)^(n),(n!)^(m),(m+n)!and(m-n)!`

D

`(m!)^(n)and(n!)^(m)` but not by (m+n)!and(m-n)!

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Topper's Solved these Questions

  • PERMUTATIONS AND COMBINATIONS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|60 Videos
  • PERMUTATIONS AND COMBINATIONS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Section II - Assertion Reason Type|9 Videos
  • PARABOLA

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|30 Videos
  • PROBABILITY

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|45 Videos

Similar Questions

Explore conceptually related problems

For each positive integer n, let S_n =sum of all positive integers less than or equal on n. Then S_(51) equals

Prove by induction that if n is a positive integer not divisible by 3 , then 3^(2n)+3^(n)+1 is divisible by 13 .

If n is a positive integer, then prove that 81^n + 20 n - 1 is divisible by 100

If m and n are positive integers, then prove that the coefficients of x^(m) " and " x^(n) are equal in the expansion of (1+x)^(m+n)

If n is positive integer show that 9^n+7 is divisible 8

If n is a positive integer, then show tha 3^(2n+1)+2^(n+2) is divisible by 7 .

Prove that if xa n dy are odd positive integers, then x^2+y^2 is even but not divisible by 4.

If m , n are positive integers and m+nsqrt(2)=sqrt(41+24sqrt(2)) , then (m+n) is equal to (a) 5 (b) 6 (c) 7 (d) 8

If n is any positive integer , show that 2^(3n +3) -7n - 8 is divisible by 49 .

Find the number of positive integers greater than 6000 and less than 7000 which are divisible by 5, provided that no digit is to be repeated.

OBJECTIVE RD SHARMA ENGLISH-PERMUTATIONS AND COMBINATIONS-Exercise
  1. How many different words of 4 letters can be formed with the letters o...

    Text Solution

    |

  2. ""sum(r=1)^(4)""^(21-r)C(4)+ 17C(5), is

    Text Solution

    |

  3. Given that .^(n)C(n-r)+3^(n)C(n-r+1)+3. .^(n)C(n-r+2)+.^(n)C(n-r+3)=...

    Text Solution

    |

  4. If n is even and ""^(n)C(0)lt""^(n)C(1) lt ""^(n)C(2) lt ....lt ""^(...

    Text Solution

    |

  5. Find the number of ways in which one can post 5 letters in 7letter ...

    Text Solution

    |

  6. What is the total number of 2xx2 matrices with each entry 0 or 1...

    Text Solution

    |

  7. Three dice are rolled. Find the number of possible outcomes in which a...

    Text Solution

    |

  8. The numbers of four different digits number that can be formed from th...

    Text Solution

    |

  9. If m and n are positive integers more than or equal to 2, mgtn, then (...

    Text Solution

    |

  10. Find the number of integers which lie between 1 and 10^6 and which hav...

    Text Solution

    |

  11. A man invites a party to (m+n) friends to dinner and places m at one r...

    Text Solution

    |

  12. The number of ways of arranging m positive and n(lt m+1) negative si...

    Text Solution

    |

  13. Out of 10 consonants four vowels, the number of words that can be form...

    Text Solution

    |

  14. Four couples (husband and wife) decide to form a committee of four mem...

    Text Solution

    |

  15. N a certain test, there are n question. In the test, 2^(n-i) students ...

    Text Solution

    |

  16. The number of nine nonzero digits such that all the digits in the f...

    Text Solution

    |

  17. The number of ways in which 20 different pearls of two colours can be ...

    Text Solution

    |

  18. There are n seats round a table numbered 1,2, 3,..., n. The number of...

    Text Solution

    |

  19. A shopkeeper sells three varieties of perfumes and he has a large numb...

    Text Solution

    |

  20. If rgtpgtq, the number of different selections of p+q things taking r ...

    Text Solution

    |