Home
Class 12
MATHS
If a , b ,c in Ra n da(a+b)+b(b+c)+c(c+...

If `a , b ,c in Ra n da(a+b)+b(b+c)+c(c+a)=0` then a.`a=b=c=0` b. `a+b+c+=0` c. `(a-b)^2+(b-c)^2+(c-a)^2=0` d. `a^3+b^3+c^3+3a b c=0`

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • INVERSE TRIGONOMETRIC FUNCTIONS

    RESONANCE DPP ENGLISH|Exercise All Questions|15 Videos

  • MATRICES

    RESONANCE DPP ENGLISH|Exercise All Questions|7 Videos

Similar Questions

Explore conceptually related problems

If a!=b!=c\ a n d\ |{:(a, b, c), (a^2,b^2,c^2), (b+c, c+a, a+b):}|=0 then a+b+c=0 b. a b+b c+c a=0 c. a^2+b^2+c^2=a b+b c+c a d. a b c=0

If a+b+c!=0 and |a b c b c a c a b|=0 , then prove that a=b=cdot

If a b+b c+c a=0, then solve a(b-2c)x^2+b(c-2a)x+c(a-2b)=0.

Prove that : a^3+b^3+c^3-3a b c=1/2(a+b+c)"{"a-b")"^2+(b-c)^2+(c-a)^2}

Prove that : a^3+b^3+c^3-3a b c=1/2(a+b+c)"{"a-b")"^2+(b-c)^2+(c-a)^2}

Prove: \ |(a, b, c),( a-b,b-c,c-a),( b+c,c+a, a+b)|=a^3+b^3+c^3-3a b c

If a^2+b^2+c^2=20 and a+b+c=0 , find a b+b c+c a

If a^(1/3)+\ b^(1/3)+\ c^(1/3)=0 , then+? (a) a+b+c=0 (b) (a+b+c)^3=27\ a b c (c) a+b+c=3a b c (d) a^3+b^3+c^3=0

If a^2+b^2+c^2-a b-b c-c a=0, then (a) a+b=c (b) b+c=a (c) c+a=b (d) a=b=c

The area of the triangle formed by (a , b+c),(b , c+a)a n d(c , a+b) is (a) a+b+c (b) a b c (c) (a+b+c)^2 (d) 0

RESONANCE DPP ENGLISH-JEE MAINS-All Questions
  1. If p is a constant and f(x) =|(x^2,x^3,x^4),(2,3,6),(p,p^2,p^3)| if ...

    Text Solution

    |

  2. In any triangle ABC, if (cos A + 2 cos C)/(cos A + 2 cos B) = (sin B)/...

    Text Solution

    |

  3. If a , b ,c in Ra n da(a+b)+b(b+c)+c(c+a)=0 then a.a=b=c=0 b. a+...

    Text Solution

    |

  4. Number of ways in which 5 colours be selected out of 8 different colou...

    Text Solution

    |

  5. The number of right inverse of the matrix is [(1,-1, 2),( 2,-1, 1)]

    Text Solution

    |

  6. If R is a relation on the set A={1,2,3,4,5,6,7,8,9} given by x R y⇔y =...

    Text Solution

    |

  7. There are two groups of subjects, one of which consists of 5 science ...

    Text Solution

    |

  8. Let f(x)= 4x^2-4ax+a^2-2a+2 be a quadratic polynomial in x , a in R. I...

    Text Solution

    |

  9. Let A be an mxxn matrix. If there exists a matrix L of type nxxm such ...

    Text Solution

    |

  10. about to only mathematics

    Text Solution

    |

  11. 50^(th) term of the squence 3+12+25+42+…… is

    Text Solution

    |

  12. If a cricket team of 11 players is to be selected from 8 batsmen, 6 bo...

    Text Solution

    |

  13. If log(10)(x-1)3-3log(10)(x-3)=log(10)8,then log(x)625 has the value e...

    Text Solution

    |

  14. If points A and B are (1, 0) and (0, 1), respectively, and point C is ...

    Text Solution

    |

  15. If the roots of the equation x^3-12 x^2+39 x-28=0 are in A.P. th...

    Text Solution

    |

  16. The expression (n^3 - n), where n is any odd natural number is divisib...

    Text Solution

    |

  17. There are N + 1 identical boxes each containing N wall clocks. r^(th) ...

    Text Solution

    |

  18. If f(theta) = (sin theta + cossec theta)^(2) + (cos theta + sec theta)...

    Text Solution

    |

  19. Write of the following statements as true and false:- The set of rats...

    Text Solution

    |

  20. If x=(7+5sqrt(2))^(1/3)-1/((7+5sqrt(2))^(1/3)) , then the value of x^3...

    Text Solution

    |