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

If θ is the angle of intersection of the curves y²=x³ and y=2x²-1 at (1, 1), then tanθ=

If θ is the angle between the curves xy=2, y² =4x at (1, 2) then tan θ=

At a given instant the legs of a right angled triangle are 8 inch and 6 inch respectively. The first leg decreases at 1 inch per minute and second increases at 2 inch per minute. The rate of increasing of the area after 2 minutes is

If an error of 0.01 cm is made while measuring the radius 5 cm of a circle, then the relative error in the area is

A particle is moving along a straight line according to the law s=16+48+t-t^3. Then distance travelled by the particle before coming to rest at an instant is

The base radius of a cylindrical vessel full of oil is 30 cm. Oil is drawn at the rate of 27000 cubic cm per minute. The rate at which the level of oil is falling in the vessel is

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