Home
Class 12
MATHS
Let the three-digit numbers A28,3B9 and ...

Let the three-digit numbers A28,3B9 and 62C, where A,B and C are integers between 0 and 9, be divisible by fixed integer K. Show that the determinant `{:|(A,3,6),(8,9,C),(2,B,2)|` is divisible by k.

Promotional Banner

Topper's Solved these Questions

  • DETERMINANTS

    MODERN PUBLICATION|Exercise EXERCISE|326 Videos

  • CONTINUITY AND DIFFERENTIABILITY

    MODERN PUBLICATION|Exercise EXERCISE|588 Videos

  • EXCLUSIVELY FOR JEE(ADVANCED)

    MODERN PUBLICATION|Exercise EXERCISE|38 Videos

Similar Questions

Explore conceptually related problems

The digits A,B,C are such that the three digit numbers A88, 6B8, 86 C are divisible by 72 the determinant |{:(A,6,8),(8,B,6),(8,8,C):}| is divisible by

The digits A,B,C are such that the three digit numbers A88, 6B8, 86 C are divisible by 72 the determinant |{:(A,6,8),(8,B,6),(8,8,C):}| is divisible by

Compute |(2,a,3),(4,b,6),(6,c,9)|

How many 6-digit numbers can be formed from the digits 0, 1, 3, 5, 7 and 9 which are divisible by 10 and no digit is repeated ?

If a,b and c are integers and age1,bge2 and c ge 3 . If a+b+c=15 , the number of possible solutions of the equation is

If a,b, and c are positive integers such that a+b+c le8 , the number of possible values of the ordered triplet (a,b,c) is

Nine digit numbers are formed using 1, 2, 3, ..., 9 without repetition. The probability that the number is divisible by 4 is :

The digits 1, 2, 3, 4, 5, 6, 7, 8, and 9 are written in random order to form a nine digit number.Let p be the probability that this number is divisible by 36, find 9p.

Let n be a fixed positive integer. Define a relation R on Z as follows: (a ,\ b) in RhArra-b is divisible by ndot Show that R is an equivalence relation on Zdot

MODERN PUBLICATION-DETERMINANTS-EXERCISE
  1. Let the three-digit numbers A28,3B9 and 62C, where A,B and C are integ...

    Text Solution

    |

  2. Let A be a square matrix of order 3xx3, then prove that |kA|=k|A|.

    Text Solution

    |

  3. If any two rows (or columns) of a determinant are identical, the value...

    Text Solution

    |

  4. Answer in one word. {:|(3,1,6),(5,2,10),(7,4,14)|

    Text Solution

    |

  5. If A is a square matrix of order 3 and |3A| = k|A|, then write the val...

    Text Solution

    |

  6. Write the value of the following determinant abs{:(a-b, b-c, c-a),(b-c...

    Text Solution

    |

  7. Use properties of determinants ot evaluate: {:|(2,a,abc),(2,b,bca),(...

    Text Solution

    |

  8. Use properties of determinants ot evaluate: {:|(x+y,y+z,z+x),(z,x,y)...

    Text Solution

    |

  9. Evaluate |[102,18,36],[1,3,4],[17,3,6]|

    Text Solution

    |

  10. Use properties of determinants ot evaluate: {:|(2,3,1),(4,6,2),(1,3,...

    Text Solution

    |

  11. Use properties of determinants ot evaluate: {:|(2,3,5),(261,592,127)...

    Text Solution

    |

  12. Show that x=1 is a root of the equation: {:|(x+1,2x,-11),(2x,x+1,-4...

    Text Solution

    |

  13. If p,q,r ar in A.P. write the value of : {:|(x+1,x+2,x+2p),(x+2,x+3,...

    Text Solution

    |

  14. Without expanding, prove that the following determinant vanishes. |...

    Text Solution

    |

  15. Without actual expansion, prove that the following determinants vanish...

    Text Solution

    |

  16. Without actual expansion, prove that the following determinants vanish...

    Text Solution

    |

  17. Without actual expansion, prove that the following determinants vanish...

    Text Solution

    |

  18. Without actual expansion, prove that the following determinants vanish...

    Text Solution

    |

  19. Without actual expansion, prove that the following determinants vanish...

    Text Solution

    |

  20. Without expanding, prove that Delta = abs{:(x+y, y + z, z+ x),(z, x ,...

    Text Solution

    |

  21. Without expanding, prove that : |{:(1, bc, a(b+ c) ),(1, ca, b ( c+ a)...

    Text Solution

    |