Home
Class 12
MATHS
Without expanding,show that abs((x+1,x+2...

Without expanding,show that `abs((x+1,x+2,x+a),(x+2,x+3,x+b),(x+3,x+4,x+c))` =0,Where a ,b,c are in A.P

Promotional Banner

Topper's Solved these Questions

  • DEFINITE INTEGRATION

    PATHFINDER|Exercise QUESTION BANK|246 Videos

  • INDEFINITE INTEGRAL

    PATHFINDER|Exercise QUESTION BANK|39 Videos

Similar Questions

Explore conceptually related problems

If a ,b ,c are in A.P , show that , |{:(x+1,x+2,x+a),(x+2,x+3,x+b),(x+3,x+4,x+c):}|=0

Show that abs((a,b,c),(a+2x,b+2y,c+2z),(x,y,z)) =0

Without expanding show that the determinant |(1,a,a^2),(-1,2,4),(1,x,x^2)| has a factor (X-a)

Show that |{:(x-3,x-4,x-alpha),(x-2,x-3,x-beta),(x-1,x-2,x-gamma):}|=0,where" "alpha,beta,gamma are in A.P

Without expanding a determinant at any stage, show that abs((x^2+x ,x+1 , x-2),(2x^2+3x-1 ,3x , 3x-3) , (x^2+2x+3, 2x-1 ,2x-1))=xA+B ,where A and B are determinant of order 3 not involving xdot

|{:(0,x-a,x-b),(x+a,0,x-c),(x+b,x+c,0):}|=0[where" "a neb nec]

If |(0,x-a,x-b),(x+a,0,x-c),(x+b,x+c,0)|=0 then the value of x is -

Solve the equation |[a-x, c, b], [ c, b-x, a], [b, a, c-x]|=0 where a+b+c!=0.

Show that the roots of (b+c)x^2-(a+b+c)x+a=0 are rational .where a,b,c are rational.

PATHFINDER-DETERMINATES-QUESTION BANK
  1. If abs((x-2,-3),(3x,2x))=3, Find the integral value of x.

    Text Solution

    |

  2. Without expanding,show that abs((x+1,x+2,x+a),(x+2,x+3,x+b),(x+3,x+4,x...

    Text Solution

    |

  3. Solve fox x: abs((x,3),(5,2x))=abs((x,-4),(5,3))

    Text Solution

    |

  4. Evaluateabs((1,omega,omega^2),(omega^2,1,omega),(omega^2,omega,1)) wer...

    Text Solution

    |

  5. Using determainant find the area of the triangle formed by joining the...

    Text Solution

    |

  6. If x+y+z=0 then show that abs((1,1,1),(x,y,z),(x^3,y^3,z^3)) = 0.

    Text Solution

    |

  7. Evaluate the following determinantabs((x+lamda,x,x),(x,x+lamda,x),(x,x...

    Text Solution

    |

  8. Without expanding prove that,abs((1,ab,1/a+1/b),(1,bc,1/b+1/c),(1,ca,1...

    Text Solution

    |

  9. Show that abs((a,b,c),(a-b,b-c,c-a),(b+c,c+a,a+b)) = a^3+b^3+c^3-3abc.

    Text Solution

    |

  10. If a,b c(all positive)are the p th,q thand r th terms repectively of a...

    Text Solution

    |

  11. If p+-a, q+- b, r+-c and abs((p,b,c),(a,q,c),(a,b,r)) = 0 show that p...

    Text Solution

    |

  12. find the value of :- (101)^2

    Text Solution

    |

  13. Given that x =-9 is a root of abs((x,3,7),(2,x,2),(7,6,x))= 0 .Find th...

    Text Solution

    |

  14. Show that abs(((a-x)^2,(a-y)^2,(a-z)^2) , ((b-x)^2,(b-y)^2,(b-z)^2) ...

    Text Solution

    |

  15. Find the ratio in which the line joining the pts (-3,4,8) and (5,-6,4)...

    Text Solution

    |

  16. Show that: abs(((b+c)^2,a^2,bc) , ((c+a)^2,b^2,ca) , ((a+b)^2,c^2,ab)...

    Text Solution

    |

  17. If A,B,C be the angles of a triangle, then prove that ,abs((-1,cosC,co...

    Text Solution

    |

  18. int(sinx)/(1+cosx)dx= ?

    Text Solution

    |

  19. If x,y,z are all distinct and if abs((x,x^2,1+x^3),(y,y^2,1+y^3),(z,z^...

    Text Solution

    |

  20. Prove that,abs((a^2+1,ab,ac),(ab,b^2+1,bc),(ca,cb,c^2+1))=1+a^2+b^2+c^...

    Text Solution

    |