A. 5/8π cm/sec
B. 1/100π cm/sec
C. 5/12π cm/sec
D. 1/120π cm/sec
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 pv1/4 =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=