The function f(x)=cot^-1 x+x increases in the interval

The point P in the first quadrant of the ellipse x²/8+y²/18=1 so that the area of the triangle formed by the tangent at P and the coordinate axes is least

A rectangular sheet of dimensions 30 cm * 80 cm four equal squares of side x cm are removed at the corners, and the sides are then turned up so as to form an open rectangle box. The value of x, so that the value of the box is the greatest is

The displacement of a body of mass 100kg in a rectilinear motion is given by the formula s=2t²+3t+1. The K.E of the body 5 sec after the start is

If the slope of the tangent to the curve xy+ax=by at (1, 1) is 2, then (a, b)

The function f(x)=a sin x+1/3x has maximum value at x =π/3. The value of a is

The portion of the tangent drawn at any point on x^2/3+y^2/3=a^2/3 (a>0), except the points on the coordinate axes, included between the coordinate axes is

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

The stationary point of f(x)=2x³-9x²+12x-3 is

The length of the sub tangent   of the curve y²=x³/2a-x at (a, a) is