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

A stone is projected vertically upwards with an initial velocity 112 ft/sec and moves such that s=112t-16t² where s is the distance from the starting point and t is the time. The greatest height reached by the stone is

The angle between the curves y²=8, x²=4y-12 at (2, 4) is

The radius of a sphere is 3 cm. If an error of 0.03 cm is made in measuring the radius of the sphere, then the percentage error in its surface area is

If p and q are the lengths of the perpendiculars from the origin on the tangent and the normal to the curve x^2/3+y^2/3=a^2/3, then 4p²+q² =

A box is made from a piece of sheet of metal 12 inch square by cutting equal small squares from each corner and tuning up the edge. The dimensions of the box of largest volume which can be made in this way are

If the rate of change in the radius of a circle is 0.02 cm/sec, then the rate of change in the area of the circle when the radius is 5 cm is

A particle moves on a line according to the law s=at²+bt+c. if the displacement after one second is 16 cm, the velocity after 2 second is 24 cm/sec and the acceleration is 8 cm /sec², then (a, b, c)=

A rectangular vessel is of 2mt long 0.5mt breadth and 1mt deep. If water flows in at the rate of 900 cubic cm per sec, than the rate of increase of water level when 25 cm deep is

The sum of the length of the sub tangents and subnormal at θ=π/3 on the cycloid x=a(θ-sinθ), y=a(1-cosθ) is