CUET · MATHS · PYQ PAPER 2025

Which of the following statements are correct?
(A) The mean and variance of the Poisson distribution are equal.
(B) The mean and variance of a Binomial distribution are equal.
(C) An unbiased die is thrown again and again until two sixes are obtained, then the probability of obtaining the second six in the 3rd throw is \(\frac{5}{108}\).
(D) If the variance of a Poisson distribution is 2 , then \(P(X=2)=2 e^{-2}\).
Choose the correct answer from the options given below :

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

Verified Solution

Answer & Solution

Correct Answer

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

Step-by-step Solution

Detailed explanation

Statement (A): Correct. Statement (B): Incorrect. Statement (C): Correct. \(P(\text{1 six in first 2 throws}) = \binom{2}{1} \left(\frac{1}{6}\right)^1 \left(\frac{5}{6}\right)^1 = \frac{5}{18}\)…

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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List - I	List - II
(A) \(Ni ^{2+}\)	(I) Pink
(B) \(Cu ^{2+}\)	(II) Purple
(C) \(Mn ^{2+}\)	(III) Green
(D) \(Ti ^{3+}\)	(IV) Blue

List-l (Metal)	List-II (Properties)
(A) \(Sc ^{3+}\)	(I) \(3 d^3\)
(B) \(Cr ^{3+}\)	(II) Colorless
(C) \(Cu ^{2+}\)	(III) \(3 d^8\)
(D) \(Ni ^{2+}\)	(IV) \(3 d^9\)