Home
Class 12
MATHS
If x, y, z are different and Delta=|[x,...

If x, y, z are different and `Delta=|[x, x^2, 1+x^3],[y, y^2, 1+y^3],[z, z^2, 1+z^3]|=0` then show that `1+xyz=0`

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • SAMPLE PAPER 2019

    XII BOARD PREVIOUS YEAR PAPER ENGLISH|Exercise Section D|2 Videos

Similar Questions

Explore conceptually related problems

If x, y, z are different and Delta=|xx^2 1+x^3y y^2 1+y^3z z^2 1+z^3|=0 , then

If x,y,z are different and Delta=|[x,x^2,x^3-1],[y,y^2,y^3-1],[z,z^2,z^3-1]|=0 , then using properties of determinants, show that xyz=1

If x!=y!=z and |x x^2 1+x^3 y y^2 1+y^3 z z^2 1+z^3|=0 , then prove that x y z=-1 .

If x,y,z are dinstinct and |[x,x^3,x^4-1],[y,y^3,y^4-1],[z,z^3,z^4-1]|=0 then prove that (xyz)(xy+yz+zx)=(x+y+z)

Prove that : Det[[x,x^2,x^3],[y,y^2,y^3],[z,z^2,z^3]]=xyz(x-y)(y-z)(z-x)

If x!=y!=za n d|[x,x^2, 1+x^3],[y ,y^2 ,1+y^3],[z, z^2, 1+z^3]|=0, then the value of x y z is a. 1 b. 2 c. -1 d. 2

For any scalar p prove that =|[x,x^2, 1+p x^3],[y, y^2, 1+p y^3],[z, z^2 ,1+p z^3]|=(1+p x y z)(x-y)(y-z)(z-x) .

If xneynez" and " |{:(x,x^(2),1+x^(3)),(y,y^(2),1+y^(3)),(z,z^(2),1+z^(3)):}|=0, then xyz =

Let delta=|A x x^2 1 B y y^2 1 C z z^2 1|a n d_1=|A B C x y z y z z xx y|, then show that delta = delta1

If 2^x = 3^y =12^z show that 1/z= 1/y+2/x

XII BOARD PREVIOUS YEAR PAPER ENGLISH-XII Boards-All Questions
  1. Find the principal value of: cos^(-1)(-1/2)

    Text Solution

    |

  2. Show that the plane x-5y-2z =1 contains the line (x-5)/3 = y = 2- z

    Text Solution

    |

  3. If x, y, z are different and Delta=|[x, x^2, 1+x^3],[y, y^2, 1+y^3],[...

    Text Solution

    |

  4. If | (2x, -9), (-2, x) | = |(-4,8) , (1, -2)|, then value of x is

    Text Solution

    |

  5. If A is a non- singular square matrix of the order 3xx3 such that A^2=...

    Text Solution

    |

  6. If P(1,0,-3) is the foot of the perpendicular from the origin to the p...

    Text Solution

    |

  7. If A = [ (-3 , 2) , (1, -1)] and I = [(1,0) , (0, 1)], find the scalar...

    Text Solution

    |

  8. Evaluate: int0^(pi/2) (sin2x tan^(-1)(sinx))dx

    Text Solution

    |

  9. Solve the following differential equation: (1+ e ^(y/x)) dy + e^(y...

    Text Solution

    |

  10. If f(x) = sqrt ((sec x -1)/(sec x + 1)) , find f'( pi /3)

    Text Solution

    |

  11. A cottage industry manufactures pedestal lamps and wooden shades.Both ...

    Text Solution

    |

  12. Amongst all open (from the top) right circular cylindrical boxes of vo...

    Text Solution

    |

  13. If tan^(-1) (y/x) = log sqrt(x^(2) + y^(2)), prove that dy/dx = (x+y)/...

    Text Solution

    |

  14. If y=e^{a\cos ^{-1}x},-1lt=xlt=1,show that (1-x^2)(d^2y)/(dx^2)-x(dy)/...

    Text Solution

    |

  15. Find f'(x) if f(x) = tan x^(tan x)

    Text Solution

    |

  16. Amongst all open (from the top) right circular cylindrical boxes of vo...

    Text Solution

    |

  17. the domain of the function f(x) = sin^(-1) (2x) is (a) [0,1] (b) ...

    Text Solution

    |

  18. Using the method of integration find the area of the triangle ABC, ...

    Text Solution

    |

  19. Find the angle between unit vector veca and vecb so that sqrt(3) veca ...

    Text Solution

    |

  20. If A = [ (-3 , 2) , (1, -1)] and I = [(1,0) , (0, 1)], find the scalar...

    Text Solution

    |