CUET · MATHS · PYQ PAPER 2025

Let \(A=\left[a_{i j}\right]_{n \times n}\) and \(B=\left[b_{i j}\right]_{n \times n}\).
Then which of the following is/are true?
(A) \(A B=B A\)
(B) \((A B)^{-1}=B^{-1} A^{-1}\)
(C) \((A B)^T=B^T A^T\)
(D) \(A B=0 \Rightarrow A=0\) or \(B=0\)
Choose the correct answer from the options given below :

A (A) and (D) only
B (B) and (C) only
C (B), (C) and (D) only
D (A) only

Verified Solution

Answer & Solution

Correct Answer

(B) (B) and (C) only

Step-by-step Solution

Detailed explanation

(A) False. (B) True. (C) True. (D) False. True statements: (B) and (C).

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-l with List-ll
Let A and B be any two events

List-l	List-ll
(A) \(P \left( A ^{\prime}\right)\)	(I) \(\frac{P(A \cap B)}{P(A)} ; P(A) \neq 0\)
(B) \(P (\Phi)\)	(II) \(\frac{P(A \cap B)}{P(B)} ; P(B) \neq 0\)
(C) \(P ( A \mid B )\)	(III) \(1-P(A)\)
(D) \(P ( B \mid A )\)	(IV) \(0\)

Choose the correct answer from the options given below :

CUET 2025 Medium

Match List-I with List-II
[.] denotes the greatest integer function.
List-I List-II
(A) \(\int_0^3[x] d x\) (I) \(\frac{1}{2}\)
(B) \(\int_0^1[2 x] d x\) (II) 1
(C) \(\int_0^1[3 x] d x\) (III) \(\frac{3}{2}\)
(D) \(\int_0^1[4 x] d x\) (IV) 3
Choose the correct answer from the options given below :

CUET 2025 Easy

Match List-I with List-II

List-I	List-II
(A) Marginal average cost if cost function \(C ( x )=\frac{50}{\sqrt{x}}\)	(I) \(50 \sqrt{x}\)
(B) Marginal average cost if cost function \(C ( x )=50 \sqrt{x}\)	(II) \(-\frac{75}{x^2 \sqrt{x}}\)
(C) Revenue function if demand function \(P =\frac{50}{\sqrt{x}}\)	(III) \(\frac{-25}{x \sqrt{x}}\)
(D) Marginal revenue if demand function \(P =50 \sqrt{x}\)	(IV) \(75 \sqrt{x}\)

Choose the correct answer from the options given below :

CUET 2025 Hard

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List-I	List-II
(A) \(\int_0^3[x] d x\)	(I) \(\frac{1}{2}\)
(B) \(\int_0^1[2 x] d x\)	(II) 1
(C) \(\int_0^1[3 x] d x\)	(III) \(\frac{3}{2}\)
(D) \(\int_0^1[4 x] d x\)	(IV) 3

Let \(A=\left[a_{i j}\right]_{n \times n}\) and \(B=\left[b_{i j}\right]_{n \times n}\).Then which of the following is/are true?(A) \(A B=B A\)(B) \((A B)^{-1}=B^{-1} A^{-1}\)(C) \((A B)^T=B^T A^T\)(D) \(A B=0 \Rightarrow A=0\) or \(B=0\)Choose the correct answer from the options given below :

Step-by-step Solution