CUET · MATHS · PYQ PAPER 2025

If \(A\) and \(B\) are invertible matrices of same order, then which one of the following is NOT true?

A \((A B)^{-1}=B^{-1} A^{-1}\)
B \(\operatorname{adj}(A B)=(\operatorname{adj} A)(\operatorname{adj} B)\)
C \(\operatorname{adj} A^T=(\operatorname{adj} A)^T\)
D \(\left|A^{-1}\right|=(|A|)^{-1}\)

Verified Solution

Answer & Solution

Correct Answer

(B) \(\operatorname{adj}(A B)=(\operatorname{adj} A)(\operatorname{adj} B)\)

Step-by-step Solution

Detailed explanation

The statement \(\operatorname{adj}(A B)=(\operatorname{adj} A)(\operatorname{adj} B)\) is not true.

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.

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A. aq \(N a C l\) solution with \(P t\) electrodes	I.oxygen gas evolution at the anode
B. Dilute solution of \(H _2 SO _4\) with Pt electrode	II. Metal loss at anode.
C. aq \(CuCl _2\) with Pt electrode	III. Hydrogen gas evolved at cathode
D. aq \(CuCl _2\) with Cu electrode	IV. Metal deposited at cathode.

Choose the correct answer from the options given below:

CUET 2023 Hard

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