CUET · MATHS · PYQ PAPER 2025

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 :

A (A) - (I), (B) - (IV), (C) - (II), (D) - (III)
B (A) - (III), (B) - (II), (C) - (I), (D) - (IV)
C (A) - (II), (B) - (III), (C) - (I), (D) - (IV)
D (A) - (IV), (B) - (I), (C) - (II), (D) - (III)

Verified Solution

Answer & Solution

Correct Answer

(C) (A) - (II), (B) - (III), (C) - (I), (D) - (IV)

Step-by-step Solution

Detailed explanation

(A) \(C(x) = 50x^{-1/2}\) \(AC(x) = \frac{C(x)}{x} = 50x^{-3/2}\) \(MAC(x) = \frac{d}{dx}(AC(x)) = -\frac{75}{x^{5/2}} = -\frac{75}{x^2 \sqrt{x}}\) (II) (B) \(C(x) = 50x^{1/2}\) \(AC(x) = \frac{C(x)}{x} = 50x^{-1/2}\)…

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

Same subject

The value of integral \(\int_0^1 \sqrt{1-x^2} d x\) is :

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Match List - I with List - II. Evaluate the integrals.

\(List - I\)	\(List - II\)
(A) \(\int_0^{\pi / 2} \frac{\sin x-\cos x}{1+\sin x \cos x} d x\)	\((I)\) \(2 \pi\)
(B) \(\int_0^{1 / 2} \frac{d x}{\sqrt{x-x^2}}\)	\((II)\) \(\frac{\pi}{4}\)
(C) \(\int_{-\pi}^\pi x \sin x d x\)	\((III)\) \(0\)
(D) \(\int_0^1 \frac{1}{1+x^2} d x\)	\((IV)\) \(\frac{\pi}{2}\)

CUET 2023 Easy

For the objective function \(Z = 4x + 6y\) subject to the constraints
\(3x + 2y ≥ 5, 7x + 2y ≤ 9, x ≥ 0, y ≥ 0\),
the maximum value of Z occurs at (a, b)
and the minimum value of Z occurs at (p, q)
then the value of \(\frac{a}{p}+\frac{b}{q}\) is:

CUET 2025 Hard

Match List-I with List-II

List-I	List-II
(A) Angle between \(\hat{i}-2 \hat{j}+3 \hat{k}\) and \(2 \hat{i}+\hat{j}\)	(I) \(\cos ^{-1}\left(\frac{2}{\sqrt{18}}\right)\)
(B) Angle between \(\hat{i}+\hat{j}+2 \hat{k}\) and \(2 \hat{i}+2 \hat{j}+4 \hat{k}\)	(II) 0
(C) Angle between \(2 \hat{i}-\hat{j}+\hat{k}\) and \(\hat{i}+\hat{j}+\hat{k}\)	(III) \(90^{\circ}\)
(D) Angle between \(\hat{i}+\hat{j}-\hat{k}\) and \(\hat{i}+\hat{j}+\hat{k}\)	(IV) \(\cos ^{-1}\left(\frac{1}{3}\right)\)

Choose the correct answer from the options given below:

CUET 2023 Easy

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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) \(75 \sqrt{x}\)