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`

Promotional Banner

Topper's Solved these Questions

  • SAMPLE PAPER 2019

    XII BOARDS PREVIOUS YEAR|Exercise Section D 35 B|1 Videos

Similar Questions

Explore conceptually related problems

If x,y,z are different and Delta=det[[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]|

If x,y,z are different and Delta=det[[x,x^(2),1+x^(3)y,y^(2),1+y^(3)z,z^(2),1+z^(3)]]=0, then prove that 1+xyz=0,

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 , show that : (i) 1+xyz=0 (ii) xyz=-1

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

If |{:(x,x^2,1+x^3),(y,y^2,1+y^3),(z, z^2,1+z^3):}|=0 then relation of x,y and z is

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

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)

Prove that [[x, x^2 , 1+px^3], [y, y^2, 1+py^3] ,[z, z^2, 1+pz^3]] = (1+pxyz)(x-y)(y-z)(z-x)

If x,y,z are distinct and |(x, x(x^2+1), x+1),(y,y(y^2+1), y+1),(z, z(z^2+1), z+1)|=0 then (A) xyz=0 (B) x+y+z=0 (C) xy+yz+zx=0 (D) x^2+y^2+z^2=1

XII BOARDS PREVIOUS YEAR-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 3 such that A^2=3A ...

    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. Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  15. If y=e^acos^((-1)x),-1lt=xlt=1,show that (1-x^2)(d^2y)/(dx^2)-x(dy)/(d...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  19. Find the area lying above x-axis and included between the circle x^2+...

    Text Solution

    |

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

    Text Solution

    |