A Solid Cylinder Of Height H Has A Conical Portion Of Same Height And Radius 1/3rd of Height Removed From It. Rain Water Is Falling In The Cylinder With Rate Equal To π times The Instantaneous Radius Of The Water Surface Inside Hole, The Time After Which Hole Will Fill Up With Water Is:

Discuss maxima and minima.

A cubic f (x) vanishes at x = –2 and has relative maximum/minimum x = –1 and   Find the cubic f (x). 

Find the maximum and minimum value of  

Use the function f (x) = x^1/x, x > 0 to determine the bigger of the two numbers.

The maximum value of 

 then the maximum value of f (θ), is:

The values of ‘K’ for which the point of minimum of the function f (x) = 1 + K²x – x³ satisfy the inequality  belongs to:

The values of a and b for which all the extrema of the function;  is positive and the minimum is at the point  are:

 be the differential equation of a curve and let P be the point of maxima then number of tangents which can be drawn from P to x² – y²= a² is/are:

Find the value of n, for which f (x) = (x² – 4)ⁿ(x² – x + 1), n Ïµ N assumes a local minima at x = 2.