The function $\mathrm{f}(x)=[x(x-2)]^2$ is increasing in the set

The minimum value of $a x+b y$ where $x y=c^2$ is

The equation of the tangent to the curve $y=\mathrm{be}^{-x / \mathrm{a}}$ at the point where it crosses the Y axis is

A manufacturer sells $x$ items at a price of rupees $\left(6-\frac{x}{40}\right)$ each. The cost price of $x$ items is ₹ $\left(\frac{x}{5}+193\right)$. The maximum profit in ₹ __________ is