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

If the function f(x)=9ax²+12a²x+1 where a>0 attains its maximum and minimum at p and q respectively such that p²=q then a=

The equation of the normal to the curve 2y=3-x² at (1, 1) is

Oil is being filled in a cylindrical tank of diameter 12mt. the rate of increase in the height of oil corresponding to the rate of increase 1800π cubic cm per minute in its volume is

Two parallel sides of a rectangle are being lengthened at the rate of 2 cm/sec while the other two sides are shortened in such a way that the area of the rectangle is 50sq. cm. the rate of change of the perimeter when the length of an increasing side 5 cm is

The diameter and altitude of a right circular cylinder are found at a certain instant to be 10 cm and 20 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