Home
Class 12
MATHS
How many integral solutions are there to...

How many integral solutions are there to the systems of equations `x_(1)+x_(2)+x_(3)+x_(4)+x_(5)=20andx_(1)+x_(2)=15` where `x_(k)ge0`.

Text Solution

Verified by Experts

The correct Answer is:
336
Promotional Banner

Topper's Solved these Questions

  • PERMUTATIONS & COMBINATIONS

    AAKASH SERIES|Exercise EXERCISE -1.1 VERY SHORT ANSWER QUESTIONS|13 Videos

  • PERMUTATIONS & COMBINATIONS

    AAKASH SERIES|Exercise EXERCISE -1.1 SHORT ANSWER QUESTIONS|29 Videos

  • PERMUTATIONS & COMBINATIONS

    AAKASH SERIES|Exercise PRACTICE EXERCISE|163 Videos

  • PARTIAL FRACTIONS

    AAKASH SERIES|Exercise PRACTICE EXERCISE|31 Videos

  • PROBABILITY

    AAKASH SERIES|Exercise Practise Exercise|165 Videos

Similar Questions

Explore conceptually related problems

Consider the system of linear equations: x_(1)+2x_(2)+x_(3)=3, 2x_(1)+3x_(2)+x_(3)=3 3x_(1)+5x_(2)+2x_(3)=1 The system has

Consider the system of linear equations x_(1)+2x_(2)+x_(3)=3, 2x_(1)+3x_(2)+x_(3)=3,3x_(1)+5x_(2)+2x_(3)=1 The system has

Find the number of positive integral solutions of x_(1)x_(2)x_(3)x_(4)=1050 .

Find the number of non negative integral solutions of x_(1)+x_(2)+x_(3)+x_(4)le20

Find the number of positive integral solutions of x_(1)x_(2)x_(3)=30 .

Integrate the rational functions x/((x-1)(x-2)(x-3))

Assertion (A) : The number of positive integral solutions of x_(1)+x_(2)+x_(3)=10 is 36. Reason (R) : The number positive integral solutions of the equation x_(1)+x_(2)+x_(3)+.......+x_(k)=n is ""^(n-1)C_(k-1) , The correct answer is

AAKASH SERIES-PERMUTATIONS & COMBINATIONS-ADDITIONAL SOLVED EXAMPLES
  1. Find the number of non negative integral solutions of x(1)+x(2)+x(3)+x...

    Text Solution

    |

  2. Find the number of integral solutions of x(1)+x(2)+x(3)+x(4)=4 where e...

    Text Solution

    |

  3. How many integral solutions are there to the systems of equations x(1)...

    Text Solution

    |

  4. In how many ways can 5 post letters of which 3 are alike and two are d...

    Text Solution

    |

  5. Find the number of positive integral solutions of x(1)x(2)x(3)x(4)=105...

    Text Solution

    |

  6. Find the number of positive integral solutions of x(1)x(2)x(3)=30.

    Text Solution

    |

  7. Find the number of positive integral solutions of x(1)x(2)x(3)=54 wher...

    Text Solution

    |

  8. Find the number of non-negative solution of 3x+y+z=24

    Text Solution

    |

  9. In how many ways the number 18900 can be split in to two factors which...

    Text Solution

    |

  10. What is the largest positive integer n such that lfloor33 is divisible...

    Text Solution

    |

  11. Find the exponent of 2 in ""^(20)C(10).

    Text Solution

    |

  12. Find the number of proper divisors of lfloor15

    Text Solution

    |

  13. Find the number of zeros at the end of (100)!

    Text Solution

    |

  14. In how many ways can 100 persons can be arranged along a row so that t...

    Text Solution

    |

  15. In how many ways can 10 men and 10 women be divided into 10 couples, e...

    Text Solution

    |

  16. Find the number of onto functions that can be defined from a set A={a(...

    Text Solution

    |

  17. How many on-to functions can be defined from a set A={a(1),a(2),.........

    Text Solution

    |

  18. In a class room there are 10 rows and in each row there are 2 chairs. ...

    Text Solution

    |

  19. How many different 5-digited numbers can be made, the sum of whose dig...

    Text Solution

    |

  20. How many 5 digited numbers can be made with odd digits so that no two ...

    Text Solution

    |