Home
Class 12
MATHS
If the determinant |(a ,b,2aalpha+3b),(b...

If the determinant `|(a ,b,2aalpha+3b),(b, c,2balpha+3c),(2aalpha+3b,2balpha+3c,0)|=0` then (a)`a , b , c` are in H.P. (b)`alpha` is root of `4a x^2+12 b x+9c=0` or(c) `a , b , c` are in G.P. (d)`a , b , c ,` are in G.P. only `a , b ,c` are in A.P.

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • DERIVATIVES AS A RATE MEASURER

    RD SHARMA ENGLISH|Exercise All Questions|168 Videos

  • DIFFERENTIABILITY

    RD SHARMA ENGLISH|Exercise All Questions|135 Videos

Similar Questions

Explore conceptually related problems

If the determinant |[a,b,2aalpha+3b],[b,c,2balpha+3c],[2aalpha+3b,2balpha+3c,0]|=0 then (a) a , b , c are in H.P. alpha is root of 4a x^2+12 b x+9c=0 or a , b , c are in G.P. a , b , c , are in G.P. only a , b ,c are in A.P.

the determinant |{:(a,,b,,aalpha+b),(b,,c,,balpha+c),(aalpha+b,,balpha+c,,0):}|=0 is equal to zero if

If a, b, c are in A.P and a, b, d are in G.P, prove that a, a -b, d -c are in G.P.

If a, b, c are in A.P and a, b, d are in G.P, prove that a, a -b, d -c are in G.P.

If a, b, c are in A.P and a, b, d are in G.P, prove that a, a -b, d -c are in G.P.

If a, b, c are in A.P. and b-a, c-b, a are in G.P. then a:b:c=?

If |{:(a,b,aalpha-b),(b,c,balpha-c),(2,1,0):}|=0 , then

If a,b, and c are in G.P then a+b,2b and b+ c are in

If a,b,c, are in A.P., b,c,d are in G.P. and c,d,e, are in H.P., then a,c,e are in

If a, b, c are in G.P. and also a, b, c are in A.P. Prove that: 1/a+1/c=2/b

RD SHARMA ENGLISH-DETERMINANTS-All Questions
  1. Using the factor theorem it is found that a+b , b+c and c+a are three ...

    Text Solution

    |

  2. If a ,b ,c are different, then the value of |[0,x^2-a, x^3-b], [x^2+a,...

    Text Solution

    |

  3. If the determinant |(a ,b,2aalpha+3b),(b, c,2balpha+3c),(2aalpha+3b,2b...

    Text Solution

    |

  4. If 1.omega, omega^2 are the roots of unity, then Delta=|(1,omega^n,ome...

    Text Solution

    |

  5. If Ar=|(1,r,2^r),(2,n,n^2),(n,(n(n+1))/2 ,2^(n+1))| , then the value o...

    Text Solution

    |

  6. If a >0 and discriminant of a x^2+2b x+c is negative, then |[a,b,ax+b]...

    Text Solution

    |

  7. The value of |[5^2 ,5^3, 5^4], [5^3, 5^4, 5^5], [5^4, 5^5, 5^6]| is (a...

    Text Solution

    |

  8. |[(log)3 512,(log)4 3],[(log)3 8,(log)4 9]|xx|[(log)2 3,(log)8 3],[(lo...

    Text Solution

    |

  9. If a, b, c, are in A.P, then the determinant|[x+2,x+3,x+2a], [x+3,x+4,...

    Text Solution

    |

  10. If A+B+C=pi, then the value of |"sin"(A+B+C)sin(A+C)cosC-sinB0tanCcos...

    Text Solution

    |

  11. The number of distinct real roots of |{:(cosec x, secx, secx), (secx...

    Text Solution

    |

  12. Let A=|[1,sintheta,1],[-sintheta,1,sintheta],[-1,-sintheta,1]|, where ...

    Text Solution

    |

  13. If |[2x,5], [8,x]|=|[6,-2], [7, 3]| , then x= (a) 3 (b) +-3 (c) +-6 (...

    Text Solution

    |

  14. If f(x)=|[0,x-a, x-b], [x+a,0,x-c], [x+b, x+c,0]|,t h e n (a)f(a)=0 ...

    Text Solution

    |

  15. The value of the determinant |[a-b,b+c, a], [b-a, c+a, b], [c-a, a+b...

    Text Solution

    |

  16. If x , y , z are different from zero and |[1+x,1 ,1], [1, 1+y,1], [1, ...

    Text Solution

    |

  17. The determinant |{:(b^2-ab, b-c, bc-ac), (a b-a^2, a-b, b^2-ab) ,(b c-...

    Text Solution

    |

  18. If x , y in R , then the determinant =|[cosx,-sinx,1],[sinx,cosx,1],[...

    Text Solution

    |

  19. The maximum value of =|[1, 1, 1], [1, 1+sintheta,1], [1+costheta,1, 1]...

    Text Solution

    |

  20. The value of the determinant |[x,x+y, x+2y], [x+2y, x,x+y], [x+y, x+2y...

    Text Solution

    |