CUET · MATHS · PYQ PAPER 2023

Let \(A\) and \(B\) be two events in a random experiment with sample space such that \(P(B) \neq 0\) and \(P(A \mid B)=1\).
Which of the following is true?

A \(A \subset B\)
B \(B \subset A\)
C \(A=\varnothing\)
D \(B=\varnothing\)

Verified Solution

Answer & Solution

Correct Answer

(B) \(B \subset A\)

Step-by-step Solution

Detailed explanation

\(P(A \mid B) = \frac{P(A \cap B)}{P(B)}\) \(1 = \frac{P(A \cap B)}{P(B)}\) \(P(A \cap B) = P(B)\) \(B \subset A\)

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
(A) If A and B are mutually exclusive events, then \(P ( A \cup B )=\)	(I) \(\frac{ P ( A \cap B )}{ P ( B )}, P ( B ) \neq 0\)
(B) If A and B are independent events, then \(P ( A \cap B )=\)	(II) \(\frac{ P ( A \cap B )}{ P ( A )}, P ( A ) \neq 0\)
(C) If A and B are two events of a sample space of an experiment, then \(P ( A / B )=\)	(III) \(P ( A ) \cdot P ( B )\)
(D) If A and B are two events of a sample space of an experiment, then \(P ( B / A )=\)	(IV) \(P ( A )+ P ( B )\)

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The feasible region corresponding to the linear constraints of a Linear Programming Problem (LPP) is represented by the shaded region in the given figure. Which of the following is not a constraint to the given LPP?

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Match List-I with List-II

List-I (Differential Equation)	List-II (Order and Degree)
(A) \(\left(\frac{d^2 y}{d x^2}\right)^2-e^x\left(\frac{d y}{d x}\right)^4+1=0\)	(I) order \(=1\) and degree \(=2\)
(B) \(\left(\frac{d y}{d x}\right)^2+x y=0\)	(II) order \(=2\) and degree \(=1\)
(C) \(\left(1+\frac{d y}{d x}\right)^{3 / 2}=4\left(\frac{d^2 y}{d x^2}\right)^2\)	(III) order \(=2\) and degree \(=2\)
(D) \(\sqrt{\frac{d^2 y}{d x^2}}+1=\frac{d y}{d x}\)	(IV) order \(=2\) and degree \(=4\)

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LIST I	LIST II
A. Spermatozoa	I. Embedding of sperms
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Let \(A\) and \(B\) be two events in a random experiment with sample space such that \(P(B) \neq 0\) and \(P(A \mid B)=1\). Which of the following is true?

Step-by-step Solution

Let \(A\) and \(B\) be two events in a random experiment with sample space such that \(P(B) \neq 0\) and \(P(A \mid B)=1\).
Which of the following is true?