CUET · MATHS · PYQ PAPER 2025

The probability distribution of a random variable X is
X 0 1 2 3 4
P(X) 0.2 k k 2k k

Match List-I with List-II
List-I List-II
(A) value of \(k\) (I) \(\frac{16}{25}\)
(B) \(P(x \geq 2)\) (II) \(\frac{9}{25}\)
(C) \(P(X=3)\) (III) \(\frac{4}{25}\)
(D) \(P(X<2)\) (IV) \(\frac{8}{25}\)
Choose the Correct answer from the options given below :

A (A) - (III), (B) - (II), (C) - (I), (D) - (IV)
B (A) - (III), (B) - (I), (C) - (II), (D) - (IV)
C (A) - (II), (B) - (III), (C) - (I), (D) - (IV)
D (A) - (III), (B) - (I), (C) - (IV), (D) - (II)

Verified Solution

Answer & Solution

Correct Answer

(D) (A) - (III), (B) - (I), (C) - (IV), (D) - (II)

Step-by-step Solution

Detailed explanation

(A) \(\sum P(X) = 1 \) \(0.2 + k + k + 2k + k = 1 \) \(0.2 + 5k = 1 \) \(5k = 0.8 \) \(k = 0.16 = \frac{16}{100} = \frac{4}{25} \) (A) - (III) (B) \(P(X \geq 2) = P(X=2) + P(X=3) + P(X=4) \) \(P(X \geq 2) = k + 2k + k = 4k \)…

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

Solution of \(\frac{d y}{d x}+y=2\) is:

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Consider the equation of the line \(\vec{r}=-\hat{i}+2 \hat{k}+\mu(4 \hat{i}-\hat{j}+2 \hat{k})\).
Match List-I with List-II

List-I	List-II
(A) It passes through the point	(I) \(4,-1,2\)
(B) Its direction ratios are	(II) \(\frac{4}{\sqrt{21}}, \frac{-1}{\sqrt{21}}, \frac{2}{\sqrt{21}}\)
(C) Its Cartesian form is	(III) \((-1,0,2)\)
(D) Its direction cosines are	(IV) \(\frac{x+1}{4}=\frac{y}{-1}=\frac{z-2}{2}\)

Choose the correct answer from the options given below :

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It is given that mean and variance of a binomial variate X are 2 and 1 respectively. Find the probability that X takes value greater than or equal to 1.

CUET 2023 Hard

Match List - I with List - II.

LIST-I ((Function)y)	LIST-II (\((\) Derivative \() \frac{d y}{d x}\))
(A) \(y=\cos \sqrt{x}\)	(I) \(\frac{\sec (\tan \sqrt{x}) \tan (\tan \sqrt{x}) \sec ^2 \sqrt{x}}{2 \sqrt{x}}\)
(B) \(y=\sqrt{\sin x}\)	(II) \(-3 x^2 \cos \left(x^3\right) \sin \left(\sin \left(x^3\right)\right)\)
(C) \(y=\sec (\tan \sqrt{x})\)	(III) \(\frac{\cos x}{2 \sqrt{\sin x}}\)
(D) \(y=\cos \left(\sin \left(x^3\right)\right)\)	(IV) \(-\frac{1}{2 \sqrt{x}} \sin \sqrt{x}\)

Choose the correct answer from the options given below:

CUET 2023 Medium

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List-I	List-II
(A) value of \(k\)	(I) \(\frac{16}{25}\)
(B) \(P(x \geq 2)\)	(II) \(\frac{9}{25}\)
(C) \(P(X=3)\)	(III) \(\frac{4}{25}\)
(D) \(P(X<2)\)	(IV) \(\frac{8}{25}\)