Home
Class 12
MATHS
If a,b,c are different , then the determ...

If a,b,c are different , then the determinant
`|(1,1,1),((x-a)^2,(x-b)^2,(x-c)^2),((x-b)(x-c),(x-c)(x-a),(x-a)(x-b))|` vanishes , when

A

`a+b+c=0`

B

`x=(1)/3(a+b+c)`

C

`x=1/2(a+b+c)`

D

`x=a+b+c`

Text Solution

Verified by Experts

The correct Answer is:
B
Promotional Banner

Topper's Solved these Questions

  • DETERMINANTS

    ML KHANNA|Exercise Problem Set (2) (TRUE AND FALSE) |3 Videos

  • DETERMINANTS

    ML KHANNA|Exercise Problem Set (2) (FILL IN THE BLANKS) |1 Videos

  • DETERMINANTS

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

If |(1,1,1),(a,b,c),(a^(3),b^(3),c^(3))|= (a -b) (b -c) (c -a) (a + b+c) where a, b, c are all different, then the determinant |(1,1,1),((x-a)^(2),(x -b)^(2),(x -c)^(2)),((x -b) (x -c),(x -c) (x -a),(x -a) (x -b))| vanishes when

If |1 1 1a b c a^3b^2c^3|=(a-b)(b-c)(c-a)(a+b+c),w h e r ea ,b ,c are different, then the determinant |1 1 1(x-a)^2(x-b)^2(x-c)^2(x-b)(x-c)(x-c)(x-a)(x-a)(x-b)| vanishes when a.a+b+c=0 b. x=1/3(a+b+c) c. x=1/2(a+b+c) d. x=a+b+c

If |1 1 1a b c a^3b^3c^3|=(a-b)(b-c)(c-a)(a+b+c), then the solution of the equation |1 1 1(x-a)^2(x-b)^2(x-c)^2(x-b)(x=-c_(x-c)(x-a)(x-a)(x-b)|=0i s

(a^2/(x-a)+b^2/(x-b)+c^2/(x-c)+a+b+c)/(a/(x-a)+b/(x-b)+c/(x-c))

Prove that (ax^(2))/((x -a)(x-b)(x-c))+(bx)/((x -b)(x-c))+(c)/(x-c)+1 = (x^(3))/((x-a)(x-b)(x-c)) .

(x^(3))/((x-a)(x-b)(x-c))=1+(A)/(x-a)+(B)/(x-b)+(C)/(x-c) then A=

If y=(ax^(2))/((x-a)(x-b)(x-c))+(bx)/((x-b)(x-c))+(c)/(x-c)+1 find (dy)/(dx)

If y=(ax^(2))/((x-a)(x-b)(x-c))+(bx)/((x-b)(x-c))+(c)/(x-c)+1 then (y')/(y)=

Statement-1: If a, b, c are distinct real numbers, then a((x-b)(x-c))/((a-b)(a-c))+b((x-c)(x-a))/((b-c)(b-a))+c((x-a)(x-b))/((c-a)(c-b))=x for each real x. Statement-2: If a, b, c in R such that ax^(2) + bx + c = 0 for three distinct real values of x, then a = b = c = 0 i.e. ax^(2) + bx + c = 0 for all x in R .

ML KHANNA-DETERMINANTS -Problem Set (2) (MULTIPLE CHOICE QUESTIONS)
  1. If R be the circum radius of the triangle ABC then the value of R^3...

    Text Solution

    |

  2. If a, b, c are sides of a triangle and |(a^2,b^2,c^2),((a+1)^2,(b+1...

    Text Solution

    |

  3. If A+B+C=pi, show that |(sin^2A,sinAcosA,cos^2A),(sin^2B,sinBcosB,cos...

    Text Solution

    |

  4. If x,y,z are all distinct and |(x,x^2,1+x^3),(y,y^2,1+y^3),(z,z^2,1...

    Text Solution

    |

  5. If |(x+a,a^2,a^3),(x+b,b^2,b^3),(x+c,c^2,c^3)| = 0 , a ne b ne c then ...

    Text Solution

    |

  6. If a,b,c be all distinct and |(a^3-1,b^3-1,c^3-1),(a,b,c),(a^2,b^2,c...

    Text Solution

    |

  7. If a,b,c are different , then the determinant |(1,1,1),((x-a)^2,(x-b...

    Text Solution

    |

  8. If |(x^(lamda),x^(lamda+2),x^(lamda+3)),(y^(lamda),y^(lamda+2),y^(lamd...

    Text Solution

    |

  9. Prove that |{:(x^(2),,x^(2)-(y-z)^(2),,yz),(y^(2),,y^(2)-(z-x)^(2),,zx...

    Text Solution

    |

  10. If a,b,c are negative distinct real numbers then the determinant |(a,b...

    Text Solution

    |

  11. the value of the determinant |(b+c,a-b,a),(c+a,b-c,b),(a+b,c-a,c)| is

    Text Solution

    |

  12. If |(x,y,z),(y,z,x),(z,x,y)|=-(x+y+z)(x+yk+zk^2)(x+yk^2+zk) then k eq...

    Text Solution

    |

  13. If a,b,c are the roots of x^3+px^2+q=0 , then the value of |(a,b,c),(b...

    Text Solution

    |

  14. If a,b,c are non-zero real number such that |(bc,ca,ab),(ca,ab,bc),(ab...

    Text Solution

    |

  15. If both n and r be greater than 1 and if Delta=|(""^xCr,""^(n-1)Cr,"...

    Text Solution

    |

  16. If Delta=|(""^(10)C3,""^(10)C4,""^(11)Cn),(""^(11)C5,""^(11)C6,""^(12)...

    Text Solution

    |

  17. If Delta = |(""^(5)C0,""^(5)C3,14),(""^(5)C1,""^(5)C4,1),(""^(5)C2,""^...

    Text Solution

    |

  18. The value of the determinant |(1,1,1),(.^(m)C(1),.^(m +1)C(1),.^(m+2)C...

    Text Solution

    |

  19. The determinant |(y^(2),-xy,x^(2)),(a,b,c),(a',b',c')| is equal to

    Text Solution

    |

  20. |(bc,bc'+b'c,b'c'),(ca,ca'+ac',c'a'),(ab,ab'+a'b,a'b')| is equal to

    Text Solution

    |