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

Which of the following statements are true?

(A) The break-even point is the level of production where the revenue from sales is equal to the cost of production and marketing.

(B) If R is the total revenue collected by a company when it sells $x$ units of a product at a price of p per unit, then R is given by $R=px$.

(C) Let $C=C(x)$ be the total cost of producing and marketing $x$ units of a product, then marginal cost, $MC=\frac{dC}{dx}$.

(D) If AC is the average cost, then $AC=\frac{x}{C}$.

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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 $f(x)$

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If the total cost and total revenue of a company that produces and sells $x$ units of a particular product are $C(x) = 5x + 350$ and $R(x) = 50x - x^2$ respectively, then which of the following is/are the breakeven values:

(A) $x = 10$

(B) $x = 25$

(C) $x = 45$

(D) $x = 30$

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The value of the integral

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

Match the LIST-I with LIST-II

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$\int_1^4 x^3\log x\, dx$ is equal to: