CUET Mathematics 2025 22 May Shift 1 PYQs

The random variable X can take values 0, 1, 2. If $P(X=0)=P(X=1)=\alpha$, and $E(X^2)=E(X)$, then which of the following are correct?

(A) $E(X) = 2-3\alpha$

(B) $E(X^2) = 4+7\alpha$

(C) $\alpha = \frac{1}{2}$

(D) $\alpha = \frac{1}{5}$

Choose the correct answer from the options given below:

The normal distribution curve is symmetrical about

[$\mu$ = mean, $\sigma$= standard deviation]

The random variable $x$ has a probability distribution $p(x)$ of the form

$p(x = r) = \begin{cases} r - k, & \text{if } 2 \le r \le 4, \\ 0, & \text{otherwise,} \end{cases}$

where $r \in \mathbb{N} \cup {0}$ and $k \in \mathbb{R}^+$, where $\mathbb{R}^+$ is the set of natural numbers.

Then:

(A) $k = \frac{1}{9}$

(B) $P(2 \le x \le 3) = \frac{1}{2}$

(C) $P(x = 4) = \frac{1}{3}$

(D) $P(x > 1) = \frac{7}{9}$

Choose the correct answer from the options given below.