CUET · MATHS · PYQ PAPER 2023

Match List - I with List - II.
LIST I LIST II
A. \(\left[1+\left(\frac{d y}{d x}\right)^2\right]=\left(\frac{d^2 y}{d x^2}\right)^2\) I. order \(=2\), degree \(=2\)
B. \(\frac{d^3 y}{d x^3}-3 \frac{d^2 y}{d x^2}+2\left(\frac{d y}{d x}\right)^4=y^4\) II. order \(=3\), degree \(=2\)
C. \(\left(1+\frac{d y}{d x}\right)^3=\left(\frac{d^3 y}{d x^3}\right)^2\) III. order \(=2\), degree \(=1\)
D. \(\left[1+\left(\frac{d y}{d x}\right)^2\right]^?=\frac{d^2 y}{d x^2}\) IV. order \(=3\), degree \(=1\)
Choose the correct answer from the option given below:

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

Verified Solution

Answer & Solution

Correct Answer

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

Step-by-step Solution

Detailed explanation

A. \(\left[1+\left(\frac{d y}{d x}\right)^2\right]=\left(\frac{d^2 y}{d x^2}\right)^2\): Order \(=2\), Degree \(=2\). (Matches I) B. \(\frac{d^3 y}{d x^3}-3 \frac{d^2 y}{d x^2}+2\left(\frac{d y}{d x}\right)^4=y^4\): Order \(=3\), Degree \(=1\). (Matches IV) C.…

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

Match List - I with List - II

List - I	List - II
(A) The degree of the differential equation \(\left(\frac{d^2 y}{d x^2}\right)^2+\left(\frac{d y}{d x}\right)=x \sin \left(\frac{d y}{d x}\right)\)	(I) 4
(B) The degree of differential equation \(\frac{d^2 y}{d x^2}+\left(\frac{d y}{d x}\right)^{1 / 4}+x^{1 / 5}=0\)	(II) 1
(C) The degree of differential equation \(\frac{d^2 y}{d x^2}+\left(\frac{d y}{d x}\right)^3+6 y^5=0\)	(III) Not defined
(D) The degree of differential equation \(1+\left(\frac{d y}{d x}\right)^4=7\left(\frac{d^2 y}{d x^2}\right)^3\)	(IV) 3

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Match List-I with List-II

List-I	List-II
(A) The current lags behind the emf by \( \pi/4 \) in phase	(I) A.C. circuit containing only an inductor
(B) The e.m.f. lags behind the current by \( \pi/4 \) in phase	(II) A.C. circuit with resistance and inductances in series
(C) The current lags behind the e.m.f. in phase by \( \pi/2 \)	(III) A.C. circuit containing only as capacitor
(D) The e.m.f. lags behind the current in phase by \( \pi/2 \)	(IV) A.C. circuit with resistance and capacitor in series

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LIST I	LIST II
A. \(\left[1+\left(\frac{d y}{d x}\right)^2\right]=\left(\frac{d^2 y}{d x^2}\right)^2\)	I. order \(=2\), degree \(=2\)
B. \(\frac{d^3 y}{d x^3}-3 \frac{d^2 y}{d x^2}+2\left(\frac{d y}{d x}\right)^4=y^4\)	II. order \(=3\), degree \(=2\)
C. \(\left(1+\frac{d y}{d x}\right)^3=\left(\frac{d^3 y}{d x^3}\right)^2\)	III. order \(=2\), degree \(=1\)
D. \(\left[1+\left(\frac{d y}{d x}\right)^2\right]^?=\frac{d^2 y}{d x^2}\)	IV. order \(=3\), degree \(=1\)