Let P(h, k) be a point on the curve
y = x² + 7x + 2, nearest to the line, y = 3x – 3.
Then the equation of the normal to the curve at P is :

A spherical iron ball of 10 cm radius is coated with a layer of ice of uniform thickness the melts at a rate of 50 cm³/min. When the thickness of ice is 5 cm, then the rate (in cm/min.) at which of the thickness of ice decreases, is :

The length of the perpendicular from the origin, on the normal to the curve,
x² + 2xy – 3y² = 0 at the point (2,2) is

Let ƒ(x) = xcos^–1(–sin|x|), $$x \in \left[ { - {\pi \over 2},{\pi \over 2}} \right]$$, then which of the following is true?