Home
Class 12
MATHS
Let a curve y = f(x) pass through the po...

Let a curve y = f(x) pass through the point ` (2, (log_e 2)^2)` and have slope ` (2y)/(x log_e x)` for all positive real value of x. Then the value of f(e) is equal to_______.

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • JEE MAINS 2021

    JEE MAINS PREVIOUS YEAR|Exercise Mathematics Section A|40 Videos

  • JEE MAINS 2021

    JEE MAINS PREVIOUS YEAR|Exercise Mathematics Section B|20 Videos

  • JEE MAINS 2021

    JEE MAINS PREVIOUS YEAR|Exercise MATHEMATICS (SECTION-A)|80 Videos

  • JEE MAINS 2020

    JEE MAINS PREVIOUS YEAR|Exercise MATHEMATICS|250 Videos

  • JEE MAINS 2022

    JEE MAINS PREVIOUS YEAR|Exercise MATHEMATICS (SECTION - B)|10 Videos

Similar Questions

Explore conceptually related problems

A curve passes through the point "(2,0)" and the slope of tangent at any point (x,y) on the curve is x^(2)-2x for all values of x ,then the maximum value of y is equal to _____________

If y=e^(1+log_(e)x) , then the value of (dy)/(dx) is equal to

Let us consider a curve, y=f(x) passing through the point (-2,2) and the slope of the tangent to the curve at any point (x,f(x)) is given by f(x)+xf'(x)=x^(2) . Then :

f(x)=log_(e)x, find value of f(1)

Let f(x)=log_(e)|x-1|, x ne 1 , then the value of f'((1)/(2)) is

if f(x)=log_(5)log_(3)x then f'(e) is equal to

If f(x)=log_(e)[log_(e)x] . then what is f (e) equal to ?

JEE MAINS PREVIOUS YEAR-JEE MAINS 2021-MATHEMATICS (SECTION-B)
  1. If a rectangle is inscribed in an equilateral triangle of side length ...

    Text Solution

    |

  2. If (veca + 3 vecb) is perpendicular to ( 7 veca - 5 vecb) and ...

    Text Solution

    |

  3. Let a curve y = f(x) pass through the point (2, (loge 2)^2) and have...

    Text Solution

    |

  4. If a + b + c = 1, ab + bc + ca = 2 and abc = 3, then the value of a^4...

    Text Solution

    |

  5. A coin is tossed n times, if the probability of getting at least one h...

    Text Solution

    |

  6. If the coefficients of x^(7) and x^(8) in the expansion of (2+(x)/(3))...

    Text Solution

    |

  7. If the lines (x-k)/(1) = (y-2)/(2) = (z-3)/(3) and (x+1)/(3) = (y ...

    Text Solution

    |

  8. For real numbers alpha and beta, consider the following system of line...

    Text Solution

    |

  9. Let vec(a) = hat(i) + hat(j) + hat(k), vec(b) and vec(c )= hat(j)-hat(...

    Text Solution

    |

  10. If (log)3 2,(log)3(2^x-5)a n d(log)3(2^x-7/2) are in arithmetic progre...

    Text Solution

    |

  11. Find the domain of function f(x)=(log)4[(log)5{(log)3(18 x-x^2-77}]

    Text Solution

    |

  12. Let f(x)= |(sin^(2)x,-2+cos^(2)x,cos2x),(2+sin^(2)x,cos^(2)x,cos2x),(s...

    Text Solution

    |

  13. Let F:[3,5] rarr R be a twice differentiable function on (3,5) such th...

    Text Solution

    |

  14. Let a plane p passes through the point (3,7,-7) and contain the line ,...

    Text Solution

    |

  15. Let S= {1,2,3,4 5,6, 7}. Then the number of possible functions f: S ra...

    Text Solution

    |

  16. If y= y(x), y in [0, (pi)/(2)) is the solution of the differential equ...

    Text Solution

    |

  17. Let f: [0,3] rarr R be defined by f(x)= "min" {x-[x], 1+[x]-x} where [...

    Text Solution

    |

  18. Let vec(a) = hat(i) - alpha hat(j) + beta hat(k) , vec(b) = 3 hat(i) ...

    Text Solution

    |

  19. Find the distance of the point P3,\ 4,\ 4) from the point where the li...

    Text Solution

    |

  20. If the real part of the complex number z = ( 3 + 2 i cos theta)/( 1 -...

    Text Solution

    |