If the radius of a spherical balloon increases by 0.1%, then its volume increases approximately by

The law of motion of a body moving along a straight line is x = $${1 \over 2}$$ vt. x being its distance from a fixed point on the line at time t and v is its velocity there. Then

A ladder 20 ft long leans against a vertical wall. The top end slides downwards at the rate of 2 ft per second. The rate at which the lower end moves on a horizontal floor when it is 12 ft from the wall is

The normal to the curve $$y = {x^2} - x + 1$$, drawn at the points with the abscissa $${x_1} = 0$$, $${x_2} = - 1$$ and $${x_3} = {5 \over 2}$$