The length of the sub tangent of the curve 2x²+3xy-2y²=8 at (2, 3) is

The equation of the tangent to the curve y(x+1) =4 at the point (2, 4/3) is

The value of a such that x³+3ax²+3a²x+b is increasing on R-{-a} are

The equation of the tangent to the curve y=x³+3x²-5 and which is perpendicular  to y=2x-6y+1=0  is

The circumfernce of a circle is measured as 56 cm with error 0.02 cm. the percentage error in its area is

The difference of two positive numbers is 10. If the square of the greater exceeds twice the square of the smaller by maximum value then they are

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