CUET · PHYSICS · PYQ PAPER 2023

The mutual inductance \( M_{12} \) of coil 1 with respect to coil 2:

A depends on the current passing through the coil
B increases when the coils are brought nearer
C \( M_{21} \) of coil 2 with respect to coil 1 is not same
D increases when any one coil is rotated about its axis

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Answer & Solution

Correct Answer

(B) increases when the coils are brought nearer

Step-by-step Solution

Detailed explanation

Mutual inductance depends on the geometric factors and relative orientation of the coils. Bringing the coils closer increases the magnetic flux linkage between them, which directly increases the mutual inductance M. B) increases when the coils are brought nearer.

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.

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Match List-l with List-ll

List-l (Statement)	List-ll (Its value)
(A) Degree of the differential equation \(\frac{d^2 y}{d x^2}=e^{d y / d x}\) is	(I) 2
(B) Order of the differential equation \(\left(\frac{d y}{d x}\right)^2+\frac{d^3 y}{d x^3}=0\) is	(II) not defined
(C) Degree of the differential equation \(\frac{d^2 y}{d x^2}+\left(\frac{d y}{d x}\right)^2-5 x^2=0\)	(III) 3
(D) If \(p\) is the order and \(q\) is the degree of the differential equation \(\frac{d y}{d x}+3 y=e^x\), then \(p+q\) is	(IV) 1

Choose the correct answer from the options given below :

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