Match List-I with List-IIList-I (Physical quantity)List-II (Unit)(A) Electric flux(I) V m−1(B) Polarisation(II) kg m−1⁢ s−2(C) Electric field(III) V m(D) Energy density(IV) C m−2 Choose the correct answer from the options given below:

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

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

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

CUET · PHYSICS · PYQ PAPER 2025

Match List-I with List-II
List-I (Physical quantity) List-II (Unit)
(A) Electric flux (I) V m⁻¹
(B) Polarisation (II) kg m⁻¹⁢ s⁻²
(C) Electric field (III) V m
(D) Energy density (IV) C m⁻²

Choose the correct answer from the options given below:

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

Verified Solution

Answer & Solution

Correct Answer

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

Step-by-step Solution

Detailed explanation

(A) Electric flux: \(E \cdot A \Rightarrow (\text{V m}^{-1})(\text{m}^2) = \text{V m}\) (B) Polarisation: \(\frac{\text{Dipole moment}}{\text{Volume}} \Rightarrow \frac{\text{C m}}{\text{m}^3} = \text{C m}^{-2}\) (C) Electric field:…

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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(A) \(A=\left[a_{i j}\right]_{n \times n}\) is a diagonal matrix if \(a_{i j}=0\) when \(i=j\)
(B) A square matrix \(A=\left[a_{i j}\right]\) is called a symmetric matrix if \(a_{i j}=a_{j i}\) for all \(i, j\)
(C) A square matrix \(A=\left[a_{i j}\right]\) is called a skew-symmetric matrix if \(a_{i j}=-a_{j i}\) for all \(i, j\)
(D) For every square matrix A, there exist an identity matrix of the same order such that \(I A=A I=I\)
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Match List-I with List-II (Given that \(c\) is an arbitrary constant)

List-I	List-II
(A) \(\int \frac{d x}{\sqrt{a^2-x^2}}\)	(I) \(\log _e\left\|x+\sqrt{x^2-a^2}\right\|+c\)
(B) \(\int \sqrt{a^2-x^2} d x\)	(II) \(\sin ^{-1} \frac{x}{a}+c\)
(C) \(\int \sqrt{x^2-a^2} d x\)	(III) \(\frac{x}{2} \sqrt{a^2-x^2}+\frac{a^2}{2} \sin ^{-1} \frac{x}{a}+c\)
(D) \(\int \frac{d x}{\sqrt{x^2-a^2}}\)	(IV) \(\frac{x}{2} \sqrt{x^2-a^2}-\frac{a^2}{2} \log _e\left\|x+\sqrt{x^2-a^2}\right\|+c\)

Choose the correct answer from the options given below :

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List-I (Physical quantity)	List-II (Unit)
(A) Electric flux	(I) V m⁻¹
(B) Polarisation	(II) kg m⁻¹⁢ s⁻²
(C) Electric field	(III) V m
(D) Energy density	(IV) C m⁻²

Match List-I with List-IIList-I (Physical quantity)List-II (Unit)(A) Electric flux(I) V m−1(B) Polarisation(II) kg m−1⁢ s−2(C) Electric field(III) V m(D) Energy density(IV) C m−2Choose the correct answer from the options given below:

Step-by-step Solution

Match List-I with List-II
List-I (Physical quantity) List-II (Unit)
(A) Electric flux (I) V m⁻¹
(B) Polarisation (II) kg m⁻¹⁢ s⁻²
(C) Electric field (III) V m
(D) Energy density (IV) C m⁻²

Choose the correct answer from the options given below: