The radius and height of a cylinder are measured as 5cm and 10 cm respectively and there is an error of 0.02 cm in both the measurements. The approximate error in the volume is

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