Home
Class 12
MATHS
If the system of linear equations x+2ay...

If the system of linear equations `x+2ay +az =0,x+3by+bz =0 and x+4cy + cz =0` has a non-zero solution, then `a, b, c`

A

A. `A.P.`

B

B. `G.P.`

C

C. `H.P.`

D

D. satisfies `a+2b+3c=0`

Text Solution

Verified by Experts

The correct Answer is:
C
`(c )` The system of linear equation has a non zero solution.
`Delta=|{:(1,2a,a),(1,3b,b),(1,4c,c):}|=0`
`:.(3bc-4bc)-(2ac-4ac)+(2ab-3ab)=0`
`:.bc+ab=2ac`
`:. (1)/(a)+(1)/(c )=(2)/(b)`
`impliesa,b,c` are in `H.P.`
Promotional Banner

Topper's Solved these Questions

  • DETERMINANT

    CENGAGE PUBLICATION|Exercise Multiple Correct Answer|5 Videos

  • DETERMINANT

    CENGAGE PUBLICATION|Exercise Multiple Correct Answer|5 Videos

  • DEFINITE INTEGRATION

    CENGAGE PUBLICATION|Exercise JEE ADVANCED|38 Videos

  • DETERMINANTS

    CENGAGE PUBLICATION|Exercise All Questions|262 Videos

Similar Questions

Explore conceptually related problems

If the system of linear equations x+ky+3z=0; 3x+ky-2z=0; 2x+4y-3z=0 has a non-zero solution (x,y,z) then (xz)/(y^2) is equal to

If a system of three linear equations x+4a y+a=0,x+3b y+b=0, and x+2c y+c=0 is consistent, then prove that a ,b , c are in H.P.

If the system of equations x-k y-z=0, k x-y-z=0,x+y-z=0 has a nonzero solution, then the possible value of k are a. -1,2 b. 1,2 c. 0,1 d. -1,1

If the system of equations x+a y=0,a z+y=0,a n da x+z=0 has infinite solutions, then the value of a is, a. -3 b. -1 c. 0 d. 3

The system of linear equations x+lambday-z=0 , lambdax-y-z=0 , x+y-lambdaz=0 has a non-trivial solution for : (1) infinitely many values of lambda . (2) exactly one value of lambda . (3) exactly two values of lambda . (4) exactly three values of lambda .

Find the real values of a for which the system of equations a^3x+(a+1)^3y+(a+2)^3z=0, ax+(a+1)y+(a+2)z=0 x+y+z=0 has a non -zero solution.

The product of all values of t , for which the system of equations (a-t)x+b y+c z=0,b x+(c-t)y+a z=0,c x+a y+(b-t)z=0 has non-trivial solution, is (a) |[a, -c, -b], [-c, b, -a], [-b, -a, c]| (b) |[a, b, c], [b, c, a], [c, a, b]| (c) |[a, c, b], [b, a, c], [c, b, a]| (d) |[a, a+b, b+c], [b, b+c, c+a], [c, c+a, a+b]|

If a inRR and the system of equations x+ay=0, az+y=0 , ax+z=0 has infinite number of solution then the value of a is

If the system of linear equations 2x+2y+3z=a 3x-y+5z=b x-3y+2z=c where a,b and c are non-zero real numbers, has more than one solution, then

The value of k for which the system of equations x+ky-3z=0 , 3x+ky-2z=0, 2x+3y-4z=0 has a non -trivial solution is

CENGAGE PUBLICATION-DETERMINANT-Single correct Answer
  1. |[1/c,1/c,-(a+b)/c^2],[-(b+c)/a^2,1/a,1/a],[(-b(b+c))/(a^2c),(a+2b+c)/...

    Text Solution

    |

  2. The equation |((1+x)^2,(1-x)^2,-(2+x^2)),(2x+1,3x,1-5x),(x+1,2x,2-3x)...

    Text Solution

    |

  3. Let Delta(1)=|{:(ap^(2),2ap,1),(aq^(2),2aq,1),(ar^(2),2ar,1):}| and De...

    Text Solution

    |

  4. Area of triangle whose vertices are (a,a^2),(b,b^2),(c,c^2) is 1/2 . a...

    Text Solution

    |

  5. Prove that |{:(betagamma,betagamma'+beta'gamma,beta'gamma'),(gammaalph...

    Text Solution

    |

  6. If |{:(a,b,1),(b,c,1),(c,a,1):}|=2010 and if |{:(c-a,c-b,ab),(a-b,a-c,...

    Text Solution

    |

  7. Let |(a,l,m),(l,b,n),(m,n,c)||(bc-n^2,mn-lc,ln-bm),(mn-lc,ac-m^2,ml-an...

    Text Solution

    |

  8. The value of |{:(x^(2)+y^(2),ax+by,x+y),(ax+by,a^(2)+b^(2),a+b),(x+y,a...

    Text Solution

    |

  9. If u=ax+by+cz, v=ay+bz+cx, w=az+bx+cy, then the value of |{:(a,b,c),(b...

    Text Solution

    |

  10. If the number of positive integral solutions of u+v+w=n be denoted by ...

    Text Solution

    |

  11. If f(x), h(x) are polynomials of degree 4 and |(f(x), g(x),h(x)),(a, b...

    Text Solution

    |

  12. If f(x)=|[x-2, (x-1)^2, x^3] , [(x-1), x^2, (x+1)^3] , [x,(x+1)^2, (x+...

    Text Solution

    |

  13. If f(x)=|{:(sinx,cosx,tanx),(x^(3),x^(2),x),(2x,1,x):}|, then lim(xto0...

    Text Solution

    |

  14. If the system of linear equations x+2ay +az =0,x+3by+bz =0 and x+4cy ...

    Text Solution

    |

  15. Find all values of lambda for which the (lambda-1)x+(3lambda+1)y+2lamb...

    Text Solution

    |

  16. The system of homogenous equations tx+(t+1)y+(t-1)z=0, (t+1)x+ty+(t+...

    Text Solution

    |

  17. If a , b , c are non-zero, then the system of equations (alpha+a)x+alp...

    Text Solution

    |

  18. The values of theta, lambda for which the following equations sintheta...

    Text Solution

    |

  19. If the system of equation {:(,x-2y+z=a),(2x+y-2z=b),and,(x+3y-3z=c):} ...

    Text Solution

    |

  20. If A,B,C are the angles of a triangle, the system of equations (sinA...

    Text Solution

    |