The points on the curve y=x²+√1-x² at which the tangent is perpendicular to x-axis are

If an error of 0.02cm is made while   measuring the radius 10cm of a sphere, then the error in the volume is

The stationary points of 2x³-9x²-24x+16 are

If y= ax+b/(x-1)(x-4) has a maximum value at the point (2, -1) then

The approximate percentage reduction in the volume of a cube of ice, if each side of the ice cube to reduced by 0.7% due to melting to:

The equation of the normal to the curve 3y²=4x+1 at (1, 2) is

The angle between the curves y=x² and y=4-x² is

If the normal to the curve x³-y² =0 at (m², -m³) is y=mx-2m³, then the value of m²  is

The curves y=x²-1, y=8x-x²-9 touch each other at the point (2, 3). The equation of the common normal is

If the subnormal of the curve xyⁿ=aⁿ⁺¹ is constant, then the value of n is