If the cost function and the profit function for a company is given by $C = 10 - 0.3x^2$ and $P = 0.3x^2 + 2x - 10$ respectively , where X represent units of output, then the revenue function is given by :

In a company, the cost of producing one item is ₹100, if the item is sold at ₹150 and ₹50,000 is the fixed cost of the company, then the break-even point is:

If $x = 6t^2$, $y = \frac{6}{t^2}$, then $\frac{d^2 y}{dx^2}$ is equal to :

If $y = e^{\frac{1}{2}\log(1+ \tan^2 x)}$, then $\frac{d^2y}{dx^2}$ is equal to:

The point on the straight line $3x + 4y = 8$, which is closest to the origin is:

The value of the integral

$I = \int_{-1}^{1} (x + x^3 + x^5) dx$ is :

The supply function of a commodity is P = $x^3+2x+18$. When 4 units of commodity are sold , then producer surplus is: