Home
Class 14
MATHS
When a certain positive integer P is div...

When a certain positive integer `P` is divided by another positive integer, the remainder is `r_1` When a second positive integer Q is divided by the same integer, the remainder is `r_2` and when (P + Q) is divided by the same divisor, the remainder is `r_3dot` Then the divsor may be `r_1\ r_2\ r_3` (b) `r_1+r_2+r_3` (c) `r_1-r_2+r_3` (d) `r_1\ +r_2-r_3` (e) `C a nnot\ b e\ d e t e r m in e d`

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • LOGARITHMS

    RS AGGARWAL|Exercise All Questions|105 Videos

  • ODD MAN OUT AND SERIES

    RS AGGARWAL|Exercise All Questions|81 Videos

Similar Questions

Explore conceptually related problems

What are the possible values of remainder r, when a positive integer a is divided by 3?

What are the possible values of remainder r, when a positive integer is divided by 2

When product of r consecutive positive integers is divided by r! then the quotient is:

For natural numbers,when p is divided by d, the quotient is q and the remainder is r .When q is divided by d,the quotient is q and the remainder is r'. Then if p is divided by dd' the remainder is

When f(x) is divided by (x-2), the quotient is Q(x) and the remainder is zero.And when f(x) is divided by [Q(x)-1], the quotient is (x-2) and the remainder is R(x). Find the remainder R(x).

When f(x) is divided by (x-2) , the qoutient is Q (x) and the remainder is zero . And when f(x) is divided by [Q(x)-1] , the qoutient is (x-2) and the remainder is R (x) . Find the remainder R (x).

When a polynomial p(x) is divided by x-1, the remainder is 3. When p(x) is divided by x-3, the remainder is 5. If r(x) isthe remainder when p(x) is divided by (x-1)(x-3), then thevalue of r(-2) is

Suppose p(x) is a polynomial with integer coefficients.The remainder when p(x) is divided by x-1 is 1 and the remainder when p(x) is divided cby x-4 is 10. If r(x) is the remainder when p(x) is divided by (x-1)(x-4) then find the value of r(2006)

Suppose p(x) is a polynomial with integer coefficients.The remainder when p(x) is divided by x-1 is 1 and the remainder when p(x) is divided cby x-4 is 10. If r(x) is the remainder when p(x) is divided by (x-1)(x-4) then find the value of r(2006)

Prove the questions a(r r_(1) + r_(2)r_(3)) = b(r r_(2) + r_(3) r_(1)) = c (r r_(3) + r_(1) r_(2))

RS AGGARWAL-NUMBER SYSTEM-All Questions
  1. When a number is divided by 13, the remainder is 11. When the same ...

    Text Solution

    |

  2. In a division sum, the remainder was 71. With the same divisor but ...

    Text Solution

    |

  3. When a certain positive integer P is divided by another positive integ...

    Text Solution

    |

  4. Two numbers when divided by a certain divisor leave the remainders ...

    Text Solution

    |

  5. A number divided by 13 leaves a remainder 1 and if the quotient, th...

    Text Solution

    |

  6. The numbers 2272 and 875 are divided by a three- digit number N, gi...

    Text Solution

    |

  7. A number when divided by three consecutive numbers 9, 11, 13 leaves...

    Text Solution

    |

  8. After the division of a number successively by 3, 4 and 7, the rema...

    Text Solution

    |

  9. A number is successively divided by 8, 7 and 3 giving residues 3, 4...

    Text Solution

    |

  10. A number when divided by 3 leaves a remainder 1. When the quotient i...

    Text Solution

    |

  11. When the square of any odd number, greater than 1, is divided by 8,...

    Text Solution

    |

  12. The numbers from 1 to 29 are written side by side as follows:    1...

    Text Solution

    |

  13. If 17^(200) is divided by 18, the remainder is 1 (b) 2 (c) 16 (d) ...

    Text Solution

    |

  14. What is the remainder when 2^(31) is divided by 5? 1 (b) 2 (c) 3 (d...

    Text Solution

    |

  15. Consider the following statements: 1. a^n+b^n is divisible by a+b\ if\...

    Text Solution

    |

  16. (7^(19)+2) is divided by 6. The remainder is (a) 1 (b) 2 (c) 3 (d)...

    Text Solution

    |

  17. If (10^(12)+25)^2-\ (10^(12)-25)^2=10^n , then the value of n is 5 ...

    Text Solution

    |

  18. (3^(25)+3^(26)+3^(27)+3^(28)) is divisible by 11 (b) 16 (c) 25 (d)...

    Text Solution

    |

  19. (4^(61)+4^(62)+4^(63)+4^(64)) is divisible by (a) 3 (b) 11 (c) 1...

    Text Solution

    |

  20. (9^6+1) when divided by 8, would leave a remainder of 0 (b) 1 (c) ...

    Text Solution

    |