CUET · PHYSICS · PYQ PAPER 2025

A 10 cm long air-core solenoid of cross-sectional area \( 1.0 \, \text{cm}^2 \) contains 300 turns. Its inductance is:

A \( 36\pi \times 10^{-6} \, \text{H} \)
B \( 4\pi \times 10^{-6} \, \text{H} \)
C \( 4\pi \times 10^{-5} \, \text{H} \)
D \( 36 \times 10^{-6} \, \text{H} \)

Verified Solution

Answer & Solution

Correct Answer

(A) \( 36\pi \times 10^{-6} \, \text{H} \)

Step-by-step Solution

Detailed explanation

\( L = \mu_0 \frac{N^2 A}{l} \) \( L = (4\pi \times 10^{-7} \, \text{H/m}) \frac{(300)^2 (1.0 \times 10^{-4} \, \text{m}^2)}{0.1 \, \text{m}} \) \( L = 36\pi \times 10^{-6} \, \text{H} \)

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-I with List-II

List-I	List-II
(A) Williamson's synthesis.	\((I)\) \(C _6 H _5 Cl + NaOH \xrightarrow[\text { High pressure }]{350^{\circ} C }\)
(B) Reimer Tiemann reaction.	\((II)\) \(C _6 H _5 OH + C _6 H _5 COCl \xrightarrow{\text { aq. } NaOH }\)
(C) Dow's process	\((II)I\) \(CH_3 CH_2 ONa+CH_3 Cl \xrightarrow{\text { heat }}\)
(D) Schotten Baumann reaction	\((IV)\) \(C _6 H _5 OH + CHCl _3+ NaOH \xrightarrow{\text { heat }}\)

Choose the correct answer from the options given below:

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