Home
Class 12
MATHS
If f(x)=k^(3)x+k^(3)-2 cuts the curve g(...

If `f(x)=k^(3)x+k^(3)-2` cuts the curve `g(x)=1/2Inx^(2)` at exactly one point `'k'` may lie in the interval

A

`(1/(sqrt(e)),e)`

B

`(1/e,1/(sqrt(e)))`

C

`(1/(e^(2)),1/e)`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
A
`(-3"In"k+2)/(1/(k^(3))+1)=k^(3)`
So, `f(x)=k^(3)+3"In"k-1`
`f(1/sqrt(e))f(e)lt0`
Promotional Banner

Topper's Solved these Questions

  • STRAIGHT LINE

    FIITJEE|Exercise NUMERICAL BASED|4 Videos

  • TIPS

    FIITJEE|Exercise NUERICAL DECIMAL BASED QUATIONS|20 Videos

Similar Questions

Explore conceptually related problems

Let f(x)=x^(3)-3x^(2)+2x. If the equation f(x)=k has exactly one positive and one negative solution then the value of k equals.-(2sqrt(3))/(9)(b)-(2)/(9)(2)/(3sqrt(3)) (d) (1)/(3sqrt(3))

If the equation sin^(4)x-(k+2)sin^(2)x=(k+3) has a solution then 'k' must lie in the interval: (-4,-2) b.[-3,2) c.(-4,-3)d[-3,-2]

Show that the curves x=y^(2) and xy=k cut at right angles; if 8k^(2)=1

If the equation x^(2)-(2k+1)x+(3k+2)=0 has exactly one root in (-1,4), then the possible interval of the values of k is

Show that the curves x=y^(2) and xy=k cut at right angles,if 8k^(2)=1

Show that the curves 2x=y^(2) and 2xy=k cut at right angles,if k^(2)=8.

Prove that the curves y=x^(3) and xy-k cut each other orthogonally, if 3k= 1.

Show that the curves 2x=y^2 and 2x y=k cut at right angles, if k^2=8 .

The value of k for which the equation 3x^(2) + 2x (k^(2) + 1) + k^(2) - 3k + 2 = 0 has roots of opposite signs, lies in the interval

If the equation x^(log_(a)x^(2))=(x^(k-2))/a^(k),a ne 0 has exactly one solution for x, then the value of k is/are

FIITJEE-TEST PAPERS-MATHEMATICS
  1. If int(-20)^(-10)((x^(2)-x)/(x^(3)-3x+1))^(2)+dx+int(1/21)^(1/11)((x^(...

    Text Solution

    |

  2. Solution of the differential equation x^(2)dy-2xydx=x^(3)y^(3)dx+x^(4)...

    Text Solution

    |

  3. If f(x)=k^(3)x+k^(3)-2 cuts the curve g(x)=1/2Inx^(2) at exactly one p...

    Text Solution

    |

  4. Let =f(x) be the solution of the diferential equation y^(')=(3y^(2)+x)...

    Text Solution

    |

  5. The solution of the differential equation (x^(2)+4y^(2)-5)xd=(4x^(2)-3...

    Text Solution

    |

  6. Let functions are defined from set A to set B where B={alpha,beta} and...

    Text Solution

    |

  7. If f(x) is a twice differentiable function and given that f(1)=2,f(2)=...

    Text Solution

    |

  8. Let f(x)={(0 , x "is irrational"),(2/(2q^(3)-q^(2)+q+sin^(2)q+5) , if ...

    Text Solution

    |

  9. Let y=f(x) be the solution of the differential equation (dy)/(dx)+k/7 ...

    Text Solution

    |

  10. Let y=f(x) be the solution of the differential equation (dy)/(dx)+k/7 ...

    Text Solution

    |

  11. Let f(x)={(|x-1|+|x-2|, ,, 2ge1),(x, ,, xlt1):} and g(x)={("max"{f(t):...

    Text Solution

    |

  12. Let Q(x) be a function defined for xepsilon [e^(3), e^(6)] be a real v...

    Text Solution

    |

  13. If lim(xtoI^(-)) prod(n=0)^(oo)((1+x^(n+1))/(1+x^(n))^(x^n))=l then [1...

    Text Solution

    |

  14. If the least bounded by the curves y=x^(2) and y=lamdax+12 is equal to...

    Text Solution

    |

  15. The range of real constant t for which (1-tan^2 t)sin theta^2+tan^2 t...

    Text Solution

    |

  16. The complete set of non-zero values of 'k' such that the equation |x^(...

    Text Solution

    |

  17. Let f be the real valued differentiable function on R such that e^(-x)...

    Text Solution

    |

  18. Let f(x)=[x]+{x}^(3) then the area of the figure bounded by y=f^(-1)(x...

    Text Solution

    |

  19. Total number of distinct x epsilon [0,1] for which int(0)^(x) (t^(8)+1...

    Text Solution

    |

  20. Let f(x)=ax^(17)+bsinx.sin2x.sin3x+cx^(2) sgn(sin x)+d log (x+sqrt(1+x...

    Text Solution

    |