Home
Class 12
MATHS
For how many positive integral values of...

For how many positive integral values of n does n! end with precisely 25 zeros?

Text Solution

Verified by Experts

`because`Number of zeroes at the end of n!=25 [given]
`impliesE_(5)(x!)=25`
`implies[n/5]+[n/25]+[n/125]+ . . . .=25`
It's easy to see that n=105 is the smallest satisfactory value of n. the next four values of n will also work (i.e., n=106,107,108,109). hence, the answer is 5.
Promotional Banner

Topper's Solved these Questions

  • PERMUTATIONS AND COMBINATIONS

    ARIHANT MATHS|Exercise JEE Type Solved Examples: Single Matching Type Questions|1 Videos

  • PERMUTATIONS AND COMBINATIONS

    ARIHANT MATHS|Exercise Exercise For Session 1|11 Videos

  • PARABOLA

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|35 Videos

  • PROBABILITY

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|55 Videos

Similar Questions

Explore conceptually related problems

If n is a positive integer, then find int x^n dx

Use proof by contradition to show that there is no value of n for which 6^n ends with the digit zero.

Find the least positive integral value of n, for which ((1-i)/(1+i))^n , where i=sqrt(-1), is purely imaginary with positive imaginary part.

The smallest positive integral value of ‘n’ such that [(1+sin frac (pi)(8)+i cos frac (pi)(8))/(1+sin frac (pi)(8)-i cos frac (pi)(8))]^n is purely imaginary is n =

For how many days does the proliferative phase extend?

State true or false : A perfect cube does not end with two zeros.

For every positive integer n, prove that 7^n-3^n is divisible by 4.

ARIHANT MATHS-PERMUTATIONS AND COMBINATIONS -Exercise (Questions Asked In Previous 13 Years Exam)
  1. For how many positive integral values of n does n! end with precisely ...

    Text Solution

    |

  2. There is a rectangular sheet of dimension (2m-1)xx(2n-1), (where m > 0...

    Text Solution

    |

  3. If the letters of the word SACHIN are arranged in all possible ways ...

    Text Solution

    |

  4. lf r, s, t are prime numbers and p, q are the positive integers such t...

    Text Solution

    |

  5. At an election, a voter may vote for any number of candidates not grea...

    Text Solution

    |

  6. The letters of the word COCHIN are permuted and all the permutation...

    Text Solution

    |

  7. The set S""=""{1,""2,""3,""........ ,""12) is to be partitioned into...

    Text Solution

    |

  8. Consider all possible permutations of the letters of the word ENDEANOE...

    Text Solution

    |

  9. The number of words can be formed with the letters of the word 'MATHEM...

    Text Solution

    |

  10. In a shop, there are five types of ice-creams available. A child buys ...

    Text Solution

    |

  11. The number of seven digit integers, with sum of the digits equal to 10...

    Text Solution

    |

  12. Three boys and two girls stand in a queue. The probability that the nu...

    Text Solution

    |

  13. There are two urns. Urn A has 3 distinct red balls and urn B has 9 ...

    Text Solution

    |

  14. In how many ways 5 different balls can be distributed into 3 boxes so ...

    Text Solution

    |

  15. There are 10 points in a plane, out of these 6 are collinear. The numb...

    Text Solution

    |

  16. The total number of ways in which 5 balls of differert colours can be ...

    Text Solution

    |

  17. Let n denote the number of all n-digit positive integers formed by the...

    Text Solution

    |

  18. Let a(n) denote the number of all n-digit numbers formed by the digits...

    Text Solution

    |

  19. Assuming the balls to be identical except for difference in colours, t...

    Text Solution

    |

  20. Let Tn be the number of all possible triangles formed by joining ve...

    Text Solution

    |

  21. Consider the set of eight vector V={a hat i+b hat j+c hat k ; a ,bc in...

    Text Solution

    |