Home
Class 12
MATHS
a, b, c, d are integers such that ad + b...

a, b, c, d are integers such that ad + bc divides each of a, b, c and d.Prove that `ad + bc = pm1`

Promotional Banner

Topper's Solved these Questions

  • NUMBER THEORY

    RESONANCE ENGLISH|Exercise Exercise -2 (PART - II)|4 Videos

  • NUMBER THEORY

    RESONANCE ENGLISH|Exercise Exercise -1 (PART - II)|5 Videos

  • MATRICES & DETERMINANT

    RESONANCE ENGLISH|Exercise HLP|34 Videos

  • RELATION, FUNCTION & ITF

    RESONANCE ENGLISH|Exercise SSP|55 Videos

Similar Questions

Explore conceptually related problems

If a,b,c ,d are in H.P., then show that ab + bc + cd =3ad

If (a + b + c + d) (a - b - c + d) = (a + b - c - d) (a - b + c - d) , prove that: a : b = c : d .

If a,b,c,d are in H.P., then ab+bc+cd is equal to

If {:A=[(a,b),(c,d)]:} such that ad - bc ne 0 , then A^(-1) , is

DeltaABC is a right triangle right angled at A such that AB = AC and bisector of /_C intersects the side AB at D . Prove that AC + AD = BC .

ABCD is a parallelogram. A circle through A, B is so drawn that it intersects AD at P and BC at Q. Prove that P, Q, C and D are concyclic.

In the given figures, AB > AC and D is any point on BC. Prove that : AB >AD.

A B C is a triangle. D is a point on A B such that AD=1/4A B\ a n d\ E is a point on A C such that A E=1/4A C . Prove that D E=1/4B C

ABCD is a trapezium with A B|| D C . A line parallel to AC intersects AB at X and BC at Y. Prove that a r\ (A D X)\ =\ a r\ (A C Y) .

If the four consecutive coefficients in any binomial expansion be a, b, c, d, then prove that (i) (a+b)/a , (b+c)/b , (c+d)/c are in H.P. (ii) (bc + ad) (b-c) = 2(ac^2 - b^2d)

RESONANCE ENGLISH-NUMBER THEORY-Exercise -2 (PART - I)
  1. How many non-negative integral values of x satisfy the equation [x/5]=...

    Text Solution

    |

  2. What is the sum of the squares of the roots of the equation x^(2)-7[x]...

    Text Solution

    |

  3. Let S(M) denote the sum of the digits of a positive integer M written ...

    Text Solution

    |

  4. To each element of the set S = {1, 2, 3.....1000}, a colour is assigne...

    Text Solution

    |

  5. What is the smallest positive integer k such that k(3^(3) + 4^(3)+ 5^(...

    Text Solution

    |

  6. One morning, each member of manjul's family drank an 8-ounce mixture o...

    Text Solution

    |

  7. For how many natural numbers n between 1 and 2014 (both inclusive) is ...

    Text Solution

    |

  8. What is the greatest possible perimeter of a right angled triangle wit...

    Text Solution

    |

  9. Positive integers a and b are such that a+b=a/b+b/a What is the value...

    Text Solution

    |

  10. Let n be the largest integer that is the product of exactly 3 distinct...

    Text Solution

    |

  11. The digits of a positive integer n are four consecutive integers in de...

    Text Solution

    |

  12. Find the total number of solutions to the equation x^2 + y^2 = 2015 wh...

    Text Solution

    |

  13. a, b, c, d are integers such that ad + bc divides each of a, b, c and ...

    Text Solution

    |

  14. Suppose an integer, a natural number n and a prime number p satisfy th...

    Text Solution

    |

  15. Let p, q be prime numbers such that non n^(3pq)-n is a multiple of 3p...

    Text Solution

    |

  16. For each positive integer n, consider the highest common factor hn of ...

    Text Solution

    |

  17. If a,b,c ge 4 are integers, not all equal, and 4abc = (a + 3) (b + 3)...

    Text Solution

    |

  18. Let a and b natural numbers such that 2a - b, a - 2b and a + b are all...

    Text Solution

    |

  19. Let N = 6 + 66 + 666 + ... + 666....66, where there are hundred 6's in...

    Text Solution

    |

  20. Determine the sum of all possible positive integers n, the product of ...

    Text Solution

    |