CUET Mathematics 2025 29 May Shift 2 PYQs

Match List-I with List-II

List-I	List-II
(A) Marginal average cost if cost function $C(x) = \frac{50}{\sqrt{x}}$	(I) $50\sqrt{x}$
(B) Marginal average cost if cost function $C(x) = 50\sqrt{x}$	(II) $-\frac{75}{x^2\sqrt{x}}$
(C) Revenue function if demand function $P=\frac{50}{\sqrt{x}}$	(III) $\frac{-25}{x\sqrt{x}}$
(D) Marginal revenue if demand function $P=50\sqrt{x}$	(IV) $75\sqrt{x}$

Choose the correct answer from the options given below:

Let $f(x) = 4x^3 - 18x^2 + 27x - 5$, $x \in R$. Then which of the following statements are TRUE?

(A) $f''(x) = 24x - 36$

(B) f has local maxima at $x = \frac{3}{2}$ but no minima

(C) f has neither maxima nor minima

(D) f has both maxima and minima

Choose the correct answer from the options given below:

A cylindrical drum of radius 7 cm and height 2 m is being kept in a vertical position filled with milk. If the milk is leaking at 14 cm³/sec from its lower base, then the rate of decrease in the level of milk is:

[Take $\pi = \frac{22}{7}$]