CUET · CHEMISTRY · PYQ PAPER 2025

If the rate constant for the first order reaction is \(2 \times 10^{-5} s^{-1}\), then the half-life will be

A 577.5 min
B 677.5 min
C 277.5 min
D 177.5 min

Verified Solution

Answer & Solution

Correct Answer

(A) 577.5 min

Step-by-step Solution

Detailed explanation

\(t_{1/2} = \frac{ln(2)}{k}\) \(t_{1/2} = \frac{0.693}{2 \times 10^{-5} s^{-1}}\) \(t_{1/2} = 34650 s = 34650 \times \frac{1}{60} min\) \(t_{1/2} = 577.5 min\)

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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Let \(X\) denotes the number of hours you study during a randomly selected school day. The random variable \(X\) has the following probability distribution.

X	0	1	2	3	4
P(X)	K	2K	2K	2K	K

Match List - I with List - II.

LIST - I	LIST - II
(A) Value of K	(I) \(\frac{1}{4}\)
(B) Probability you study at least two hours	(II) \(\frac{1}{8}\)
(C) Probability you study exactly two hours	(III) \(\frac{3}{8}\)
(D) Probability you study at most one hour	(IV) \(\frac{5}{8}\)

Choose the correct answer from the options given below:

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