Home
Class 12
MATHS
If Delta=|{:(a(11),a(12),a(13)),(a(21),a...

`If Delta=|{:(a_(11),a_(12),a_(13)),(a_(21),a_(22),a_(23)),(a_(31),a_(32),a_(33)):}|` and `C_(ij)=(-1)^(i+j) M_(ij), "where " M_(ij)` is a determinant obtained by deleting ith row and jth column then then `|{:(C_(11),C_(12),C_(13)),(C_(21),C_(22),C_(23)),(C_(31),C_(32),C_(33)):}|=Delta^(2).`
Suppose a,b,c,`in R, a+b+c gt 0, A =bc -a^(2),B =ca-b^(2)` and `c=ab-c^(2)` and `|{:(A,B,C),(B,C,A),(C,A,B):}|` =49 then the valu of `a^(3)+b^(3)+c^(3)`-3abc is

A

-3

B

3

C

-9

D

9

Text Solution

Verified by Experts

The correct Answer is:
B
Promotional Banner

Topper's Solved these Questions

  • DETERMINANTS

    ARIHANT MATHS|Exercise Exercise (Single Integer Answer Type Questions)|10 Videos

  • DETERMINANTS

    ARIHANT MATHS|Exercise Exercise (Statement I And Ii Type Questions)|7 Videos

  • DETERMINANTS

    ARIHANT MATHS|Exercise Exercise (More Than One Correct Option Type Questions)|15 Videos

  • DEFINITE INTEGRAL

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|38 Videos

  • DIFFERENTIAL EQUATION

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|26 Videos

Similar Questions

Explore conceptually related problems

If A=[{:(a_(11),a_(12),a_(13)),(a_(21),a_(22),a_(23)),(a_(31),a_(32),a_(33)):}] and A_(ij) is co-factos of a_(ij) , then A is given by :

if quad /_=[[a_(1),b_(1),c_(1)a_(2),b_(2),c_(2)a_(3),b_(3),c_(3)]]

if Delta=det[[a_(1),b_(1),c_(1)a_(2),b_(2),c_(2)a_(3),b_(3),c_(3)]]

Find the minors and cofactors of the elements of the determinant Delta = |{:(a_(11), a_(12), a_(13)), (a_(21), a_(22), a_(23)), (a_(31), a_(32), a_(33)):}|

If A=[{:(a_(11),a_(12),a_(13)),(a_(21),a_(22),a_(23)):}]" and "B=[{:(b_(11),b_(12)),(b_(21),b_(22)),(b_(31),b_(32)):}] then show that AB and BA both exist. Find AB and BA.

If, in D={:[(a_(1),b_(1),c_(1)),(a_(2),b_(2),c_(2)),(a_(3),b_(3),c_(3))]:}, the co-factor of a_(r)" is "A_(r), then , c_(1)A_(1)+c_(2)A_(2)+c_(3)A_(3)=

If A=[[a_(11), a_(12), a_(13)], [a_(21), a_(22), a_(23)], [a_(31), a_(32), a_(33)]] and A_(ij) denote the cofactor of element a_(ij) , then a_(11)A_(21)+a_(12)A_(22)+a_(13)A_(23)=

If A=[[a_(11), a_(12), a_(13)], [a_(21), a_(22), a_(23)], [a_(31), a_(32), a_(33)]] and a_(ij) denote the cofactor of element A_(ij) , then a_(11)A_(11)+a_(12)A_(12)+a_(13)A_(13)=

If Delta=|[a_(11),a_(12),a_(13)],[a_(21),a_(22),a_(23)],[a_(31),a_(32),a_(33)]| and A_(i j) is cofactors of a_(i j) , then value of Delta is given by A. a_(11)A_(31)+a_(12)A_(32)+a_(13)A_(33) B. a_(11)A_(11)+a_(12)A_(21)+a_(13)A_(31) C. a_(21)A_(11) + a_(22)A_(12) + a_(23)A_(13) D. a_(11)A_(11) + a_(21)A_(21) + a_(31)A_(31)

ARIHANT MATHS-DETERMINANTS -Exercise (Passage Based Questions)
  1. Consider the system of equations x+y+z=5, x+2y+3z=9, x+3y+lambda z=m...

    Text Solution

    |

  2. Consider the system of equations x+y+z=5, x+2y+3z=9, x+3y+lambda z=m...

    Text Solution

    |

  3. If Delta=|{:(a(11),a(12),a(13)),(a(21),a(22),a(23)),(a(31),a(32),a(33)...

    Text Solution

    |

  4. If Delta=|{:(a(11),a(12),a(13)),(a(21),a(22),a(23)),(a(31),a(32),a(33)...

    Text Solution

    |

  5. If Delta=|{:(a(11),a(12),a(13)),(a(21),a(22),a(23)),(a(31),a(32),a(33)...

    Text Solution

    |

  6. If alpha,beta,gamma are the roots of x^(3)+2x^(2)-x-3=0 The value of ...

    Text Solution

    |

  7. If alpha,beta,gamma are the roots of x^(3)+2x^(2)-x-3=0. If the abso...

    Text Solution

    |

  8. If alpha,beta,gamma are the roots of x^(3)+2x^(2)-x-3=0. If a = al...

    Text Solution

    |

  9. Suppose f(x) is a function satisfying the folowing conditions: (i)f(...

    Text Solution

    |

  10. Suppose f(x) is a function satisfying the folowing conditions: (i)f(...

    Text Solution

    |

  11. Suppose f(x) is a function satisfying the folowing conditions: (i)f(...

    Text Solution

    |

  12. If |{:(x,e^(x-1),(x-1)^(3)),(x-lx,cos(x-1),(x-1)^(2)),(tanx,sin^(2)x,c...

    Text Solution

    |

  13. If |{:(x,e^(x-1),(x-1)^(3)),(x-lx,cos(x-1),(x-1)^(2)),(tanx,sin^(2)x,c...

    Text Solution

    |

  14. If |{:(x,e^(x-1),(x-1)^(3)),(x-lx,cos(x-1),(x-1)^(2)),(tanx,sin^(2)x,c...

    Text Solution

    |

  15. Let Delta =|{:(-bc,b^(2)+bc,c^(2)+bc),(a^(2)+ac,-ac,c^(2)+ac),(a^(2)+a...

    Text Solution

    |

  16. Let Delta =|{:(-bc,b^(2)+bc,c^(2)+bc),(a^(2)+ac,-ac,c^(2)+ac),(a^(2)+a...

    Text Solution

    |

  17. Let Delta =|{:(-bc,b^(2)+bc,c^(2)+bc),(a^(2)+ac,-ac,c^(2)+ac),(a^(2)+a...

    Text Solution

    |

  18. If Deltan=|{:(a^(2)+n,ab,ac),(ab,b^(2)+n,bc),(ac,bc,c^(2)+n):}|,n in ...

    Text Solution

    |

  19. If Deltan=|{:(a^(2)+n,ab,ac),(ab,b^(2)+n,bc),(ac,bc,c^(2)+n):}|,n in ...

    Text Solution

    |

  20. If Deltan=|{:(a^(2)+n,ab,ac),(ab,b^(2)+n,bc),(ac,bc,c^(2)+n):}|,n in ...

    Text Solution

    |