Home
Class 11
MATHS
The number of divisors of 2^4 .3^3 .5^2...

The number of divisors of `2^4 .3^3 .5^2`, having two prime factors, is

A

3

B

24

C

26

D

60

Text Solution

AI Generated Solution

To find the number of divisors of the number \(2^4 \cdot 3^3 \cdot 5^2\) that have exactly two prime factors, we can follow these steps: ### Step 1: Identify the prime factors and their powers The given number is \(2^4 \cdot 3^3 \cdot 5^2\). The prime factors are: - \(2\) with power \(4\) - \(3\) with power \(3\) - \(5\) with power \(2\) ...
Promotional Banner

Topper's Solved these Questions

  • PERMUTATIONS AND COMBINATIONS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Section II - Assertion Reason Type|9 Videos
  • PERMUTATIONS AND COMBINATIONS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Exercise|136 Videos
  • PERMUTATIONS AND COMBINATIONS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|60 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

The sum of the divisors of 2^(5)xx3^(4)xx5^(2) , is

Find the number of divisors of the number N=2^3 .3^5 .5^7 .7^9 which are perfect squares.

Find the number of divisors of the number N=2^3 .3^5 .5^7 .7^9 which are perfect squares.

Total number of divisors of n = 3^5. 5^7. 7^9 that are in the form of 4lambda + 1; lamda >=0 is equal to

The number of odd divisor of the number N=2^(10). 3^5 .7^2, are a. 16 b. 17 c. 18 d. 20

The total number of divisor of 480 that are of the form 4n+2,ngeq0, is equal to a. 2 b. 3 c. 4 d. none of these

The number of divisors of 3630, which have a remainder of 1 when divided by 4, is

If N = 10800, find the(i) the number of divisors of the form 4m +2,(ii) the number of divisors which are multiple of 10(iii) the number of divisors which are multiple of 15.

The number of divisors of the form (4n+2) of the integer 240 is

The total number of divisors of the number N=2^(5).3^(4).5^(10).7^(6) that are of the form 4K+2, AAK in N is equal to

OBJECTIVE RD SHARMA ENGLISH-PERMUTATIONS AND COMBINATIONS-Section I - Solved Mcqs
  1. Find the number of odd proper divisors of 3^pxx6^mxx21^ndot

    Text Solution

    |

  2. The number of divisors of the form 4K + 2 , K ge 0 of the integers 24...

    Text Solution

    |

  3. The number of divisors of 2^4 .3^3 .5^2, having two prime factors, is

    Text Solution

    |

  4. There are five balls of different colours and five boxes of colours sa...

    Text Solution

    |

  5. The number of 5-digit numbers in which no two consecutive digits are i...

    Text Solution

    |

  6. Let A be a set of n(ge3) distinct elements. The number of triplets (x,...

    Text Solution

    |

  7. Find the number of ways to give 16 different things to three persons A...

    Text Solution

    |

  8. If P(1), P(2), P(3), ……, P(m+1) are distinct prime numbers. Then the...

    Text Solution

    |

  9. There are n different books and p copies of each in a library. The num...

    Text Solution

    |

  10. The number of ways in which one or more balls can be selected out of 1...

    Text Solution

    |

  11. The number of all three element subsets of the set {a(1),a(2),a(3).......

    Text Solution

    |

  12. If one quarter of all three element subsete of the set A={a(1),a(2),a(...

    Text Solution

    |

  13. The sum of the divisors of 2^(5)*3^(4)*5^(2) is

    Text Solution

    |

  14. The number of words that can be made by writing down the letters of th...

    Text Solution

    |

  15. Find the number of ways in which n different prizes can be distributed...

    Text Solution

    |

  16. The total number of positive integral solutions for (x, y, z) such tha...

    Text Solution

    |

  17. The total number of positive integral solutions of abc=30, is

    Text Solution

    |

  18. The total numbre of intergral solutins of abc =24, is

    Text Solution

    |

  19. A bag contains 3 black, 4 white and 2 red balls, all the balls being d...

    Text Solution

    |

  20. The number of different pairs of words (,) that can be made with the l...

    Text Solution

    |