Home
Class 12
MATHS
If Delta=|(1,bc,bc(b+c)),(1,ca,ca(c+a))...

If `Delta=|(1,bc,bc(b+c)),(1,ca,ca(c+a)),(1,ab,ab(a+b))|=` , then its value is equal to

A

`a^3 +b^3+c^3 -3abc`

B

`abc(a+b+c)`

C

independent of a,b,c

D

zero

Text Solution

Verified by Experts

The correct Answer is:
C, D
Promotional Banner

Topper's Solved these Questions

  • DETERMINANTS

    ML KHANNA|Exercise Problem Set (1) (TRUE AND FALSE) |7 Videos

  • DETERMINANTS

    ML KHANNA|Exercise Problem Set (2) (MULTIPLE CHOICE QUESTIONS) |21 Videos

  • DEFINITE INTEGRAL

    ML KHANNA|Exercise Miscellaneous Questions (Assertion/Reason)|1 Videos

  • DIFFERENTIAL EQUATIONS

    ML KHANNA|Exercise MISCELLANEOUS EXERCISE (Matching Entries) |2 Videos

Similar Questions

Explore conceptually related problems

det[[1,bc,bc(b+c)1,ca,ca(c+a)1,ab,ab(a+b)]]=0

|[1,bc,a(b+c)],[1,ca,b(c+a)],[1,ab,c(a+b)]|=0

If Delta=|{:(1,bc,a),(1,ca,b),(1,ab,c):}| , then minor of element ab is :

Delta = |(1//a,1,bc),(1//b,1,ca),(1//c,1,ab)|=

The value of the determinant |{:(1,bc,a(b+c)),(1,ca,b(a+c)),(1, ab,c(a+b)):}| doesn't depend on

Delta=det[[1,a,bc1,b,ca1,c,ab]]

Value of the D=|(1/a,bc,a^(3)),(1/b,ca,b^(3)),(1/c,ab,c^(3))| is

ML KHANNA-DETERMINANTS -Self Assessment Test
  1. If Delta=|(1,bc,bc(b+c)),(1,ca,ca(c+a)),(1,ab,ab(a+b))|= , then its ...

    Text Solution

    |

  2. If a != b != c, are value of x which satisfies the equation |(0,x -a...

    Text Solution

    |

  3. |(b+c,a,a),(b,c+a,b),(c,c,a+b)|=

    Text Solution

    |

  4. |(1,1,1),(a,b,c),(a^3,b^3,c^3)|=

    Text Solution

    |

  5. |(1/a,a^2,bc),(1/b,b^2,ca),(1/c,c^2,ab)|=

    Text Solution

    |

  6. If x=-9 is a root of |(x,3,7),(2,x,2),(7,6,x)|=0 then other two roots ...

    Text Solution

    |

  7. The solution of the equation |(x,2,-1),(2,5,x),(-1,2,x)| = 0 are

    Text Solution

    |

  8. The roots of the equation |(0,x,16),(x,5,7),(0,9,x)| = 0 are

    Text Solution

    |

  9. |(a+b,b+c,c+a),(b+c,c+a,a+b),(c+a,a+b,b+c)|=k|(a,b,c),(b,c,a),(c,a,b)|...

    Text Solution

    |

  10. A root of the equation |(3-x,-6,3),(-6,3-x,3),(3,3,-6-x)| = 0

    Text Solution

    |

  11. If |(-a^2,ab,ac),(ab,-b^2,bc),(ac,bc,-c^2)|=ka^2b^2c^2 , then k =

    Text Solution

    |

  12. If omega!=1 is a cube root of unity and Delta=|(x+omega^(2),omega,1)...

    Text Solution

    |

  13. |((a^x+a^(-x))^2,(a^x-a^(-x))^(2),1),((b^x+b^(-x))^2,(b^x-b^(-x))^(2),...

    Text Solution

    |

  14. The number of values of k which the linear equations 4x+ky+2z=0 kx...

    Text Solution

    |

  15. The value of k for which the set of equationsx + ky + 3z=0, 3x + ky – ...

    Text Solution

    |

  16. If x + y +z=0, 4x+3y -z=0 and 3x + 5y +3z=0 is the given system of equ...

    Text Solution

    |

  17. The system of equations x + y + z=2, 3x – y +2z=6 and 3x + y +z=-18 ha...

    Text Solution

    |

  18. The system of equations x+y+z=6, x+2y + 3z= 10, x+2y + lamdaz=mu has n...

    Text Solution

    |

  19. The system of linear equations x1 + 2x2 + x3 = 3, 2x1 + 3x2 + x3 = 3...

    Text Solution

    |

  20. Let a,b,c be such that b(a+c) ne 0 . If |(a,a+1,a-1),(-b,b+1,b-1),(c...

    Text Solution

    |