Home
Class 12
MATHS
If the gradient of the tangent at any po...

If the gradient of the tangent at any point `(x,y)` of a curve which passes through the point `(1, (pi)/(4))` is `{(y)/(x)-sin^(2)((y)/(x))}`, then the equation of the curve is-

A

`y= cot^(-1) (logx)`

B

`y= cot^(-1) {log((x)/(e))}`

C

`y= x cot^(-1){log(xe)} `

D

`y= cot^(-1){log((e)/(x))} `

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Topper's Solved these Questions

  • MCQ ZONE 3

    CHHAYA PUBLICATION|Exercise Question Paper 4|30 Videos

  • MCQ ZONE 3

    CHHAYA PUBLICATION|Exercise Question Paper 5|30 Videos

  • MCQ ZONE 3

    CHHAYA PUBLICATION|Exercise Question Paper 2|30 Videos

  • MCQ ZONE

    CHHAYA PUBLICATION|Exercise Question Paper 7|80 Videos

  • MCQ's

    CHHAYA PUBLICATION|Exercise QUESTION PAPER 9|66 Videos

Similar Questions

Explore conceptually related problems

The slope of the tangent at (x, y) to a curve passing through (1, (pi)/(4) ) is given by (y)/(x) - cos^(2) ((y)/(x)) , then the equation of the curve is-

If the slope of the tangent at (x,y) to a curve passing through the point (2,1) is (x^(2)+y^(2))/(2xy) , then the equation of the curve is-

The slope of the tangent at (x , y) to a curve passing through a point (2,1) is (x^2+y^2)/(2x y) , then the equation of the curve is

The slope of the tangent at (x , y) to a curve passing through (1,pi/4) is given by y/x-cos^2(y/x), then the equation of the curve is

Find the equation of the normal to curve x^(2) = 4y which passes through the point (1, 2).

Find the equation of the normal to the curve x^(2) = 4y which passes through the point (1, 2).

Find the equation of the normal to the curve x^(2)=4y, which passes through the point (1,2).

A curve passes through the point (1,(pi)/(6)) . Let, the slope of the curve at each point (x,y)" be "(y)/(x)+sec((y)/(x)),x gt0 . Then the equation of the curve is

Find the equation of the curve whose slope at any point (x,y) is (-y) and which through the point (2,1)

The tangent to the curve y=xe^(x^2) passing through the point (1,e) also passes through the point

CHHAYA PUBLICATION-MCQ ZONE 3 -Question Paper 3
  1. Two perpendicular tangents to y^(2)=4ax always intersect on the line-

    Text Solution

    |

  2. If the gradient of the tangent at any point (x,y) of a curve which pas...

    Text Solution

    |

  3. The number of tangents that can be drawn from the point (6, 2) on the ...

    Text Solution

    |

  4. The equation of the tangent to the curve x^((2)/(3))+y^((2)/(3))= a^((...

    Text Solution

    |

  5. If the area enclosed by the parabola x^(2)=72y and the line y=k be 64 ...

    Text Solution

    |

  6. Two intersecting circles have their radii 1 metre and sqrt(3) metre. T...

    Text Solution

    |

  7. The equation of the tangent to the curve y= be^(-(x)/(a)) at the poin...

    Text Solution

    |

  8. The equations of the two common tangents to the circle x^(2) +y^(2)=2a...

    Text Solution

    |

  9. If the curve y= a sqrt(x) + bx passes through the point (1, 2) and t...

    Text Solution

    |

  10. The area (in square unit ) bounded by the curve y= sinx between the o...

    Text Solution

    |

  11. The equation of the normal to the ellipse (x^(2))/(a^(2)) + (y^(2))/(b...

    Text Solution

    |

  12. The point on the curve sqrt(x) + sqrt(y) = sqrt(a), the normal at whic...

    Text Solution

    |

  13. The slope of the tangent to the curve x= 3t^(2) +1, y=t^(3)-1 at x=1...

    Text Solution

    |

  14. If the area above the x-axis bounded by the curve y=2^(kx) and the lin...

    Text Solution

    |

  15. If the line x+y =1 is a tangent to the parabola y^(2)-y +x=0, then th...

    Text Solution

    |

  16. The angle between the curves y= sin x and y= cos x is-

    Text Solution

    |

  17. The function f(x)=cos x - 2ax is monotonically decreasing when-

    Text Solution

    |

  18. If PQ and PR are the two sides of a triangle, then the angle between ...

    Text Solution

    |

  19. The function f(x)=x^(3) +3x^(2) +4x+7 is increasing for-

    Text Solution

    |

  20. If x+y=60, x, y gt 0, then the maximum value of xy^(3) is-

    Text Solution

    |