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:

The minimum value of $f(x) = 4x^3 - 48x + 105$ in the interval [1,3] is :

For a manufacturer, total cost function is given by $C = \frac{x^2}{25} + 2x$. Which of the following are correct ?

A. 2.6 is the marginal cost when 5 units are produced.

B. $\frac{2x}{25} + 2$ is the marginal cost function.

C. $\frac{x}{25} + 2$ is the average cost function.

D. 2.4 is the marginal cost when 5 units are produced.

E. $\frac{x}{25} + 1$ is the average cost function.

Choose the correct answer from the options given below:

Let $f : R \to R$ be defined such that $f(x) = 16x^2 - 16x + 12$

(A) Maximum value of $f(x)$ is 8

(B) Minimum value of $f(x)$ is 8

(C) Minimum value of $f(x)$ is 16

(D) No maximum value of $f(x)$

Choose the correct answer from the options given below :

A monopolist's Demand function is $x = 70 - \frac{P}{2}$, the revenue at $x = 5$ will be :

The degree of the differential equation $\left(1 - \left(\frac{dy}{dx}\right)^2\right)^{3/2} = k \frac{d^2 y}{dx^2}$ is :

Match List - I with List - II.

Choose the correct answer from the options given below :