The two curves y=x^-3, y=e^3(1-x) at (1, 1)

The distance between the origin and the normal to the curve y=e^2x+x² at x=0 is

The angle between the curves x²=4y, x²+y²=5 at (-2, 1) is

The equation of the tangent to the curve x²+2y=8 and which is perpendicular to x-2y+1=0 is

The condition for f(x)= x³+px²+qx+r(x R) to have no extreme value, is

When a circular oil drop expands on water, its area increases at the uniform rate of 40sq. cm per minute. The rate of increase in the radius when the radius 5 cm is

The two curves x²+y²=25, 2x²-9y+18=0

The minimum value of x³-9x²+24x-12 is

The maximum value of x²-x+1/ x²+x+1 is

If y=x³-ax²+12x+5 is increasing for all real values of x, then a lies between