CUET · MATHS · PYQ PAPER 2025

If A and B are independent events, then which of the following is/are true?
(A) \(\bar{A}\) and B are independent events
(B) \(P(A \cap B)=0\)
(C) \(\bar{A}\) and \(\bar{B}\) are independent events
(D) \(P(A \cap B)=P(A)+P(B)\)
Choose the correct answer from the options given below:

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

Verified Solution

Answer & Solution

Correct Answer

(A) (A) and (C) only

Step-by-step Solution

Detailed explanation

(A) is true. (B) is false. (C) is true. (D) is false. The correct statements are (A) 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.

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(A) If A is a non singular matrix of order n, then \(\| A (\operatorname{adjA})\|\) is equal to	(I) \(\|A\|^{n-1}\)
(B) If A is a non singular matrix of order n, then \|adj(adj A)\| is equal to	(II) \(\|A\|^{n-2} A\)
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Choose the correct answer from the options given below :

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List-I	List-II
(A) If A is a non singular matrix of order n, then \(\| A (\operatorname{adjA})\|\) is equal to	(I) \(\|A\|^{n-1}\)
(B) If A is a non singular matrix of order n, then \|adj(adj A)\| is equal to	(II) \(\|A\|^{n-2} A\)
(C) If A is a non singular matrix of order n, then \(\operatorname{adj}(\operatorname{adj} A )\) is equal to	(III) \(\|A\|^n\)
(D) if A is a non singular matrix of order n, then \(\|(\operatorname{adj} A)\|\) is equal to	(IV) \(\|A\|^{(n-1)^2}\)

List-I	List-II
(A) Resonant frequency	(I) \( \frac{\omega L}{R} \)
(B) Quality factor	(II) \( 2\pi f L \)
(C) \( X_L \)	(III) \( \frac{1}{2\pi\sqrt{LC}} \)
(D) \( X_C \)	(IV) \( 1/2\pi f c \)

If A and B are independent events, then which of the following is/are true?(A) \(\bar{A}\) and B are independent events(B) \(P(A \cap B)=0\)(C) \(\bar{A}\) and \(\bar{B}\) are independent events (D) \(P(A \cap B)=P(A)+P(B)\)Choose the correct answer from the options given below:

Step-by-step Solution

If A and B are independent events, then which of the following is/are true?
(A) \(\bar{A}\) and B are independent events
(B) \(P(A \cap B)=0\)
(C) \(\bar{A}\) and \(\bar{B}\) are independent events
(D) \(P(A \cap B)=P(A)+P(B)\)
Choose the correct answer from the options given below: