Water flows into a conical  vessel is at the rate of 5 cubic cm per sec. if the semi vertical angle of the vessel is 30⁰, then the rate of increase of water level when the water level in the vessel is 6 cm is

The volume of a metal hollow sphere is constant. If the outer radius is increasing at the rate of ¼ cm per sec. the rate at which the inner radius is increasing when the radii are 8 cm and 4 cm respectively is

f(x)=(sin^-1x)²+(cos^-1x)² is stationary at

On the interval [0, 1] the function x²⁵(1-x)⁷⁵ takes its maximum value at the point

The diameter x of a circle is found by measurements to be 5 cm with maximum error of 0.05 cm. the relevant error in the area is

The pressure P and the volume v of a gas are connected by the relation pv^1/4 =a constant. The percentage increase in the pressure corresponding to a diminutions of ½% in the volume is

The diameter and altitude of a right circular cylinder are found at a certain instant to be 20 cm and 40 cm respectively. If the diameter is increasing at the rate of 2 cm/sec then the rate of the change in the altitude will keep the volume constant is

The shortest distance between the line y-x=1 and the curve x=y² is

The radius of the circular disc increases at a uniform rate of 0.025 cm per sec. the rate at which the area of the disc increases, when the radius is 15 cm is

A straight line through the point (3, 4) in the first quadrant meets the axes at A and B. the minimum area of the triangle OAB is