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

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 50 mt, the rate increase in the circumference of the wave ring is

The angle A ofABC is found by measurement to be 63⁰ an the area is calculated by the formula 1/2bc sin A. the percentage error in the calculated value of the area due to an error of 15 minutes in the measured value of A is

A line segment of length 10 cm is divided into two parts and a rectangle is formed with these as adjacent sides, then the dimensions of the rectangle in order that its area is maximum is

If the tangent at any point on the curve x⁴+y⁴=a⁴ cuts off intercepts  p and q on the coordinates axes then p^-4/3+q^-4/3=

If the rate of change of the side of a square is 0.05 cm/sec, then the rate of change in the area of the square when the side is 10 cm is