CUET Mathematics 2026 30th May Shift 1 PYQs

If X is a random variable which can take values 0,1,2,3 such that $E(X^2) = 2E(X)$.

If $P(X=0) = P(X=1) = m\ \&\ P(X=2) = 2m$, then which of the following are TRUE?

A. $P(X=1) = \dfrac{1}{13}$

B. $P(X=3) = \dfrac{1}{13}$

C. $E(X) = \dfrac{18}{13}$

D. $P(X=2) = \dfrac{6}{13}$

Choose the correct answer from the options given below:

A discrete random variable X takes the values 0, 1, 2, 3, 4 and its mean is 1.6. If $P(X=1) = 0.4$, $P(X=4) = P(X=2)$ and $P(X=3) = 2P(X=2)$, then $P(X=0)$ is :

A car hire firm has two cars, which is hire out day by day. The number of demands for cars on each day is distributed as a Poisson distribution with mean 1.5. Then which of the following is/are TRUE? (use $e^{-1.5} = 0.2231$)

A. The probability of days when no car is required is 0.2231

B. The probability of days when some demand is refused is 0.1913

C. The probability of days when no car is required is 0.1913

D. The probability of days when some demand is refused is 0.2231

Choose the correct answer from the options given below: