CUET · MATHS · PYQ PAPER 2023

A box contains 3 white and 2 red balls. If we draw one ball and without replacing the first ball, the probability of drawing red ball in the second draw is:

A \(\frac{8}{25}\)
B \(\frac{2}{5}\)
C \(\frac{3}{5}\)
D \(\frac{4}{5}\)

Verified Solution

Answer & Solution

Correct Answer

(B) \(\frac{2}{5}\)

Step-by-step Solution

Detailed explanation

\(P(\text{Red in 2nd draw}) = P(\text{Red in 1st})P(\text{Red in 2nd}|\text{Red in 1st}) + P(\text{White in 1st})P(\text{Red in 2nd}|\text{White in 1st})\) \(= \left(\frac{2}{5}\right)\left(\frac{1}{4}\right) + \left(\frac{3}{5}\right)\left(\frac{2}{4}\right)\)…

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

If \(x=a t^2, y=2 a t\); then \(\frac{d^2 y}{d x^2}\) is equal to

CUET 2025 Hard

Match the Integrating factor of the following Differential equations.

List - I	List - II
(A) \(\frac{d y}{d x}-y=\cos x\)	(I) \(e^x\)
(B) \(\frac{d y}{d x}=\cos x-y\)	(II) \(x^2\)
(C) \(x \frac{d y}{d x}+2 y=x^2\)	(III) \(\frac{1}{x^2}\)
(D) \(\frac{d y}{d x}=x+\frac{2}{x} y\)	(IV) \(e^{-x}\)

CUET 2023 Easy

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