CUET · MATHS · PYQ PAPER 2023

Determinant is unaltered if :

A Elements of any two rows are interchanged
B Elements of any two columns are interchanged
C Every diagonal element is changed to zero
D All the rows and columns are interchanged

Verified Solution

Answer & Solution

Correct Answer

(D) All the rows and columns are interchanged

Step-by-step Solution

Detailed explanation

This operation represents taking the transpose of a matrix \(\left(A^T\right)\). One of the fundamental properties of determinants is that the determinant of a matrix is equal to the determinant of its transpose, or \(\operatorname{det}(A)=\operatorname{det} \left(A^T\right)\).…

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 \(List - I\) with \(List - II\)

\(List - I\)	\(List - II\)
General solution	Differential Equation
(A) \(y=c x\)	(I) \(y^{\prime}=\frac{1}{2 \sqrt{x}}-1\)
(B) \(y=e^{-3 x}+c\)	(II) \(y^{\prime}+3 y=0\)
(C) \(x+y=\sqrt{x}+c\)	(III) \(y^{\prime}=\frac{y^2}{1-x y}(x y \neq 1)\)
(D) \(x y=\log y+c\)	(IV) \(x y^{\prime}=y\)

(c is an arbitrary constant and \(y^{\prime}=\frac{d y}{d x}\) )
Choose the correct answer from the options given below:

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