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

In measuring the circumfrence of a circle, there in an error of 0.05 cm. if with this error the cir cumfence of the circle is measured of the circle is measured as c cm, and then the error in area is

A stone is dropped into a quiet pond and waves move in circles outward from the place where it strikes, at a speed of 30 cm per second. At the instant when the radius of the wave ring is 50mt, the rate of increase in the area of the wave ring is

f(x) = |x| has

A man 6 feet height walks at a uniform of 20 above the floor. An object falls freely under gravity, starting from rest at the same height as the lamp, put at a horizontal distance of 5 ft from it. The speed of the shadow of the object on the floor when it has fallen through 15 ft is