The base radius of a cylindrical vessel full of oil is 30 cm. Oil is drawn at the rate of 27000 cubic cm per minute. The rate at which the level of oil is falling in the vessel is

The length of the sub tangent of the curve 2x²+3xy-2y²=8 at (2, 3) is

The equation of the tangent to the curve y(x+1) =4 at the point (2, 4/3) is

The value of a such that x³+3ax²+3a²x+b is increasing on R-{-a} are

The equation of the tangent to the curve y=x³+3x²-5 and which is perpendicular  to y=2x-6y+1=0  is

The circumfernce of a circle is measured as 56 cm with error 0.02 cm. the percentage error in its area is

The difference of two positive numbers is 10. If the square of the greater exceeds twice the square of the smaller by maximum value then they are

The radius of the base of certain cone is increasing at the rate of 3 cm per minute and the altitude is decreasing at the rate of 4 cm per minute. The rate of change of the total surface of the cone when the radius is 7 cm and the altitude is 24 cm is

A cylindrical gas container is closed at the top and open at the bottom. If the iron plate of the top is 5/4 times as thick as the plate forming the cylindrical sides, the ratio of the radius to the height of the cylinder using minimum material for the same capacity is

The function f(x) =√25-4x² is decreasing in