If the number of five digit numbers with distinct digits and 2 at the 10^th place is 336 k, then k is equal to :

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 number of real roots of the equation,
e^4x + e^3x – 4e^2x + e^x + 1 = 0 is :

Let C be the centroid of the triangle with vertices (3, –1), (1, 3) and (2, 4). Let P be the point of intersection of the lines x + 3y – 1 = 0 and 3x – y + 1 = 0. Then the line passing through the points C and P also passes through the point :