CUET · MATHS · PYQ PAPER 2025

Match List-I with List-II
List-I List-II
(A) \(\int_0^1 \frac{x^2}{1+x^3} d x\) (I) 0
(B) \(\int_0^\pi 3 \sin x d x\) (II) \(2 \log _e\left(\frac{3}{2}\right)\)
(C) \(\int_{-1}^1 \sin ^5 x \cos ^6 x d x\) (III) 6
(D) \(\int_2^3 \frac{4}{x^2-1} d x\) (IV) \(\frac{1}{3} \log _e 2\)
Choose the correct answer from the options given below:

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

Verified Solution

Answer & Solution

Correct Answer

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

Step-by-step Solution

Detailed explanation

(A) \(\int_0^1 \frac{x^2}{1+x^3} d x = \frac{1}{3} [\log_e |1+x^3|]_0^1\) \(= \frac{1}{3} (\log_e 2 - \log_e 1)\) \(= \frac{1}{3} \log_e 2\) (B) \(\int_0^\pi 3 \sin x d x = 3 [-\cos x]_0^\pi\) \(= 3 (-\cos \pi - (-\cos 0))\) \(= 3 (1+1)\) \(= 6\) (C) \(f(x) = \sin^5 x \cos^6 x\)…

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

Let \(P\) and \(Q\) be any two invertible matrices of the same order. Then Match List-I with List-II

List - I (Matrix)	List - II (Equivalent matrix)
(A) \((P Q)^{-1}\)	(I) \(Q^{-1} P\)
(B) \(\left(P^{-1} Q\right)^{-1}\)	(II) \(Q P^{-1}\)
(C) \(\left(P Q^{-1}\right)^{-1}\)	(III) \(Q^{-1} P^{-1}\)
(D) \(\left(P^{-1} Q^{-1}\right)^{-1}\)	(IV) \(Q P\)

Choose the Correct answer from the options given below :

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Year		Commodities
	A	B	C
2011	32	80	100
2015	40	120	180

List-I	List-II
(A) \(\int_0^1 \frac{x^2}{1+x^3} d x\)	(I) 0
(B) \(\int_0^\pi 3 \sin x d x\)	(II) \(2 \log _e\left(\frac{3}{2}\right)\)
(C) \(\int_{-1}^1 \sin ^5 x \cos ^6 x d x\)	(III) 6
(D) \(\int_2^3 \frac{4}{x^2-1} d x\)	(IV) \(\frac{1}{3} \log _e 2\)