Home
Class 12
MATHS
If N is the number of positive integral ...

If N is the number of positive integral solutions of `x_1x_2x_3x_4 = 770`, then N =

A

`256`

B

`729`

C

`900`

D

`770`

Text Solution

Verified by Experts

The correct Answer is:
A
`(a)` `770=2xx5xx7xx11`
We can assign `2` to `x_(1)`, or `x_(2)` or `x_(3)` or `x_(4)`.
Thus `2` can be assigned in `4` ways similarly each of `5,7,11` can be assigned in `4` ways
No. of solutions `=4xx4xx4xx4=256`
Promotional Banner

Topper's Solved these Questions

  • PERMUTATION AND COMBINATION

    CENGAGE|Exercise Multiple Correct Answer|2 Videos

  • PERMUTATION AND COMBINATION

    CENGAGE|Exercise Comprehension|8 Videos

  • PARABOLA

    CENGAGE|Exercise Question Bank|21 Videos

  • PRINCIPLE OF MATHEMATICAL INDUCTION

    CENGAGE|Exercise Exercise|9 Videos

Similar Questions

Explore conceptually related problems

If N is the number of positive integral solutions of x_(1)x_(2)x_(3)x_(4)=770, then N=

If N is the number of positive integral solutions of x_(1)x_(2)x_(3)x_(4)=770, then N=(A)1800(B)1600(C)1400(D) None

Statement-1: If N the number of positive integral solutions of x_(1)x_(2)x_(3)x_(4)=770 , then N is divisible by 4 distinct prime numbers. Statement-2: Prime numbers are 2,3,5,7,11,13, . .

If n is the number of positive integral solutions of x_(1)x_(2)x_(3)x_(4)=210. Then

If n is the number of positive integral solution of x_(1), x_(2)x_(3)x_(4) = 210 , then which of the following is incorrect ?

The number of positive integral solutions of x_(1)*x_(2)*x_(3)=30 is

Total number of positive integral solution of x_1.x_2.x_3=60 is equal to

If N is the number of positive integral solutions of the equation x_(1)x_(2)x_(3)x_(4)=770 , then the value of N is

CENGAGE-PERMUTATION AND COMBINATION-Question Bank
  1. If N is the number of positive integral solutions of x1x2x3x4 = 770, t...

    Text Solution

    |

  2. If the number of ways in which a selection of 100 balls can be made ou...

    Text Solution

    |

  3. If the number of circular permutations of 20 letters P, Q, R, S, T , A...

    Text Solution

    |

  4. Let N be the number of points (x, y, z) in space such that x+y+z=12, w...

    Text Solution

    |

  5. On the sides A B, B C, C A of a triangle A B C, 3,4,5 distinct points ...

    Text Solution

    |

  6. The number of ways in which the letters of the word 'LONDON' can be re...

    Text Solution

    |

  7. We have 19 identical gems available with us which are needed 'to be di...

    Text Solution

    |

  8. If ' N ' denotes the number of ways in which 8 different mobilès can b...

    Text Solution

    |

  9. If the number of arrangements of 4 alike apples, 5 alike mangoes, 1 ba...

    Text Solution

    |

  10. Duronto express bound from Jaipur to Mumbai stops at 7 intermediate st...

    Text Solution

    |

  11. There are 6 different balls and 6 different boxes of the colour same a...

    Text Solution

    |

  12. Consider M=2^(4) 3^(4) 5^(2) 7^(2) 11^(2) and number of ways in which ...

    Text Solution

    |

  13. Consider the word 'HALEAKALA'. The number of ways the letters of this ...

    Text Solution

    |

  14. Consider the word 'CARCASSONNE'. Words are formed' using all the lette...

    Text Solution

    |

  15. If (201) ! is divided by 24^(k) then the largest value of k is

    Text Solution

    |

  16. If there are 10 stations on a route and the train has to be stopped at...

    Text Solution

    |

  17. Let A={1,2,3,4] . The number of different ordered pairs (B, C) that ca...

    Text Solution

    |

  18. Number of ways in which three distinct numbers can be selected between...

    Text Solution

    |

  19. Matrices are formed using four given distinct real numbers, taking all...

    Text Solution

    |

  20. If n is a factor of 72 , such that x y=n, then number of ordered pairs...

    Text Solution

    |