CUET · PHYSICS · PYQ PAPER 2023

List I contains physical quantities related to mechanical oscillations of a block of mass m attached to spring of force constant k. List II contains physical quantities related to a LC oscillator. Match List I with List II.
List I List II
(A) Mass m (I) Charge q
(B) Force Constant k (II) Inductance L
(C) Displacement x (III) Reciprocal capacitance 1/C
(D) Velocity ( \(v=\frac{d x}{d t}\) ) (IV) Current \(\left(i=\frac{d q}{d t}\right)\)
On the basis of analogies between mechanical and electrical quantities;
Choose the correct answer from the options given below:

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

Verified Solution

Answer & Solution

Correct Answer

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

Step-by-step Solution

Detailed explanation

(A) Mass m \( \leftrightarrow \) (II) Inductance L (B) Force Constant k \( \leftrightarrow \) (III) Reciprocal capacitance 1/C (C) Displacement x \( \leftrightarrow \) (I) Charge q (D) Velocity \( \left(v=\frac{d x}{d t}\right) \) \( \leftrightarrow \) (IV) Current…

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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Let X be a random variable. Let E(X) and Var(X) denote the mean and the variance of X respectively.
Match List - I with List - II

List - I	List - II
(A) If \(\operatorname{Var}( X )=\alpha\), then \(\operatorname{Var}(2 X +3)\) is	(I) \(11 \alpha\)
(B) If \(E ( X )=\alpha\), then \(E (2 X )\) is	(II) \(6 \alpha\)
(C) If \(\operatorname{Var}( X )=\alpha\), then \(\operatorname{Var}(3 X -\alpha)+\operatorname{Var}(\sqrt{2} X +\beta)\) is	(III) \(4 \alpha\)
(D) If \(E(X) = 3\) \(\frac{5\alpha}{12}, \text{ then E(12X + } \alpha)\) is	(IV) \(2 \alpha\)

Choose the correct answer from the options given below:

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List I	List II
(A) Mass m	(I) Charge q
(B) Force Constant k	(II) Inductance L
(C) Displacement x	(III) Reciprocal capacitance 1/C
(D) Velocity ( \(v=\frac{d x}{d t}\) )	(IV) Current \(\left(i=\frac{d q}{d t}\right)\)