Home
Class 11
MATHS
If bc+ca+ab=18, and |(1,a^(2),a^(3)),(1,...

If `bc+ca+ab=18`, and `|(1,a^(2),a^(3)),(1,b^(2),b^(3)),(1,c^(2),c^(3))|=lambda|(1,1,1),(a,b,c),(a^(2),b^(2),c^(2))|` the value of `lambda` is

A

abc

B

`a+b+c`

C

`ab+bc+ca`

D

0

Text Solution

Verified by Experts

The correct Answer is:
A
Promotional Banner

Topper's Solved these Questions

  • MATRICES

    AAKASH SERIES|Exercise DETERMINANTS-PRACTICE EXERCISE|39 Videos
  • MATRICES

    AAKASH SERIES|Exercise INVERSE OF A MATRIX- EXERCISE - I|21 Videos
  • MATRICES

    AAKASH SERIES|Exercise DETERMINANTS- EXERCISE - I|15 Videos
  • MATHEMATICAL INDUCTION

    AAKASH SERIES|Exercise PRACTICE SHEET (EXERCISE-I) LEVEL-I (Principle of Mathematical Induction) (Straight Objective Type Questions)|55 Videos
  • MAXIMA & MINIMA

    AAKASH SERIES|Exercise EXERCISE-III|35 Videos

Similar Questions

Explore conceptually related problems

|(1,1,1),(a,b,c),(a^(2)-bc,b^(2)-ca,c^(2)-ab)|=

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

|(1,a,a^(2)),(1,b,b^(2)),(1,c,c^(2))|=

|(1,1,1),(a^(2),b^(2),c^(2)),(a^(3),b^(3),c^(3))|=

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

|(a,b,c),(a^(2),b^(2),c^(2)),(bc,ca,ab)|=

If a,b,c are different and |(a,a^(2),a^(3)-1),(b,b^(2),b^(3)-1),(c,c^(2),c^(3)-1)|=0 then

|(a^(2)+1,ab,ac),(ab,b^(2)+1,bc),(ac,bc,c^(2)+1)|=

Show that |{:(1,a^2,a^3),(1,b^2,b^3),(1,c^2,c^3):}| =(a-b)(b-c)(c-a)(ab+bc+ca)

AAKASH SERIES-MATRICES -DETERMINANTS- EXERCISE - II
  1. Let A=[(5,5 alpha, alpha),(0, alpha, 5 alpha),(0,0,5)] If |A|^(2)=25 t...

    Text Solution

    |

  2. If k gt1, and the determinant of the matrix A^(2), where A=[(k,kalpha,...

    Text Solution

    |

  3. If bc+ca+ab=18, and |(1,a^(2),a^(3)),(1,b^(2),b^(3)),(1,c^(2),c^(3))|=...

    Text Solution

    |

  4. If a,b,c are positive and not all equal then |(a,b,c),(b,c,a),(c,a,b)|

    Text Solution

    |

  5. |(a^(2)+x,ab,ac),(ab,b^(2)+x,bc),(ac,bc,c^(2)+x)|

    Text Solution

    |

  6. Show that A=|{:(-2a,a+b,c+a),(a+b,-2b,b+c),(c+a,c+b,-2c):}|=4(a+b)(b+c...

    Text Solution

    |

  7. If a+b+c=0 and |(a-x,c,b),(c,b-x,a),(b,a,c-x)|=0 then x=

    Text Solution

    |

  8. If |(lamda^(2)+3lamda, lamda-1, lamda+3),(lamda+1, 2-lamda,lamda-4),(l...

    Text Solution

    |

  9. Let |{:(x^(2)+x+1,x+1,2x-3),(3x^(2)-1,x+2,x-1),(x^(2)+5x+1,2x+3,x+4):}...

    Text Solution

    |

  10. If |(a,b,a alpha+b),(b,c, b alpha+c),(a alpha+b, b alpha+c,0)|=0 then

    Text Solution

    |

  11. If a,b,c are the p^(th),q^(th),r^(th) terms in H.P. then |{:(bc,p,1),(...

    Text Solution

    |

  12. If |(3x-8,3,3),(3,3x-8,3),(3,3,3x-8)|=0 then x=0

    Text Solution

    |

  13. If a,b,c are different and |(0,x-a,x-b),(x+a,0,x-c),(x+b,x+c,0)|=0 the...

    Text Solution

    |

  14. If x=-1 is a root of the equation |{:(2-x,3,3),(3,4-x,5),(3,5,4-x):}|=...

    Text Solution

    |

  15. If one of the roots of |(3,5,x),(7,x,7),(x,5,3)|=0 is -10, then the ot...

    Text Solution

    |

  16. If |(x,x+y,x+y+z),(2x,3x+2y,4x+3y+2z),(3x,6x+3y,10x+6y+3z)|=64 then x=

    Text Solution

    |

  17. If a,b,c, are in A.P. then |(x+1,x+2,x+a),(x+2,x+3,x+b),(x+3,x+4,x+c)|...

    Text Solution

    |

  18. If a,b,c are pth, qth rth terms respectivelyy of a G.P then |(loga, p,...

    Text Solution

    |

  19. If |{:(0,sinalpha,sinbeta),(sinalpha,0,singamma),(sinbeta,singamma,0):...

    Text Solution

    |

  20. With the usual notation in DeltaABC det|(1,1,1),(sinA,sinB,sinC),(sin^...

    Text Solution

    |