Applications of...

Which one of the following curves cuts the parabola y² = 4ax at right angles :

If the line joining the points (0, 5) and (5, 3) is a tangent to the curve

Two men are walking on a path x³ + y³ = a³. When the first man arrives at a point (x₁, y₁), he finds the second man in the direction of his own instantaneous motion. If the co−ordinates of the second man are (x₂, y₂) then :

On the curve x³ = 12y, the abscissa changes at a faster rate than the ordinate. Then x belongs to the interval :

A balloon is pumped at the rate of a cm³/minute. The rate of increase of its surface area when the radius is b cm, is :

The function f(x) = | px − q| + r |x|, x ∈ (− ∞, ∞), where p > 0, q > 0, r > 0, assumes its minimum value only at one point if :

The normal to the curve y = (1 + 2x)^x + sin⁻¹ (sin³x) at x = 0 is :

The co−ordinates of the point M(x, y) of y = e^−|x| so that the area formed by the co−ordinate axes and the tangent at M is the greatest, are :