CUET Mathematics 2025 15 May Shift 1 PYQs

Match List-I with List-II

Let $A$ and $B$ be two events such that $P(A) = 0.2$, $P(B) = 0.4$, $P(B|A) = 0.5$

List-I	List-II
(A) $P(A \cap B)$	(I) $0.5$
(B) $P(A|B)$	(II) $0.8$
(C) $P(A \cup B)$	(III) $0.25$
(D) $P(A')$	(IV) $0.1$

Choose the correct answer from the options given below:

Let X denote the number of hours a student studies on a selected day. The probability distribution of X is given by (where k is some unknown constant)

$P(X = x_i) = \begin{cases} 0.5, & \text{if } x_i = 0, \\ kx_i, & \text{if } x_i = 1, \\ k(4 - x_i), & \text{if } x_i = 2 \text{ or } 3, \\ 0, & \text{otherwise}. \end{cases}$

Then the value of k is

A random variable X has the following probability distribution

X	0	1	2	3	4	5	6	7	8
P(X)	a	3a	5a	7a	9a	11a	13a	15a	17a

Then the values of 'a' and P(0 < X < 5) respectively are