CUET · MATHS · PYQ PAPER 2023

A matrix which is symmetric as well as skew symmetric is:

A Row matrix
B Column matrix
C Square matrix
D Square null matrix

Verified Solution

Answer & Solution

Correct Answer

(D) Square null matrix

Step-by-step Solution

Detailed explanation

If symmetric, \(A = A^T\). If skew-symmetric, \(A = -A^T\). \(A = -A \implies 2A = 0 \implies A = 0\). The matrix must be a square null matrix.

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 the Matrix in List - I with its Adjoint's Determinant in List - II.
List - I (Matrix A) :

LIST 1	LIST 2
(A) \(\left[\begin{array}{ll}3 & 1 \\ 4 & 2\end{array}\right]\)	(I) 9
(B) \(\left[\begin{array}{cc}5 & -1 \\ 4 & 2\end{array}\right]\)	(II) 8
(C) \(\left[\begin{array}{cc}6 & -1 \\ 2 & 1\end{array}\right]\)	(III) 14
(D) \(\left[\begin{array}{ll}4 & 1 \\ 3 & 3\end{array}\right]\)	(IV) 2

Choose the correct answer from the options given below:

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From CUET

Match List-I with List-II

List-I	List-II
(A) Maximum kinetic energy of photoelectron	(I) No emission of electrons
(B) Photoelectric current	(II) slope of kinetic energy of electron-frequency graph
(C) Frequency of radiation < threshold frequency	(III) independent of intensity
(D) Plank's constant	(IV) independent of frequency

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