The two positive numbers whose sum is 40 and the product of the cube of one number and the other number is maximum, are

Let $C(x)$ and $R(x)$ be the cost function and the revenue function for $x$ units of a commodity such that marginal cost of producing 2 units is equal to marginal revenue of selling 1 unit. If $C(x) = ax^3 + bx^2 - 12x + 6$ and $R(x) = 100 + 6ax - bx^2$, then which one of the following is TRUE?

The function $f(x)=x^2-x\sqrt{2}$ is strictly decreasing in the interval :

The position of Sumit when Amit will hit the paper ball is :

The rate of change in area of a triangle having sides 10cm and 12cm when the variable angle between them at an angle $60°$, is:

The largest open interval in which the function $f(x) = 4x^3 - 5x^2 - 8x + 12$ increases, is:

The function $f(x) = x^2e^{-2x}$ increases on