The radius of the base of certain cone is increasing at the rate of 3 cm per minute and the altitude is decreasing at the rate of 4 cm per minute. The rate of change of the total surface of the cone when the radius is 7 cm and the altitude is 24 cm is

A cylindrical gas container is closed at the top and open at the bottom. If the iron plate of the top is 5/4 times as thick as the plate forming the cylindrical sides, the ratio of the radius to the height of the cylinder using minimum material for the same capacity is

The function f(x) =√25-4x² is decreasing in

An aero plane is flying horizontally at an altitude of 3000 ft directly over an observe. If it is flying with a speed of 300 ft/sec, the rate at which it is moving away from the observe when it is at 5000 ft away from the observe is

For the curve y²=(x+a)³, then square of the sub tangent is ….subnormal

The approximate value of log (2.01), given that log 2=0.6934 is

If there is an error of 0.05 cm, while measuring the side of equilateral triangles as 5 cm, then the percentage error in area is

A man on a wharf 20mt above the water level pulls in a rope to which a boat is attached at the rate of 4mt per second. At what rate is the boat approaching the shore, when there is still 25mt rope out…?

A particle is moving along a line according to the law s=t³-3t²+5. The acceleration of the particle at the instant where the velocity is zero is

A circular plate expands when heated from a radius of 5 cm to 5.06 cm. The approximate increase area is