1
MHT CET 2025 20th April Morning Shift
MCQ (Single Correct Answer)
+2
-0

If X is a binomial variable with range $\{0,1,2,3,4\}$ and $\mathrm{P}(\mathrm{X}=3)=3 \mathrm{P}(\mathrm{X}=4)$ then the parameter ' $p$ ' of the binomial distribution is

A
$\frac{1}{4}$
B
$\frac{3}{4}$
C
$\frac{1}{3}$
D
$\frac{2}{5}$
2
MHT CET 2025 20th April Morning Shift
MCQ (Single Correct Answer)
+2
-0

Two cards are drawn simultaneously from a well shuffled pack of 52 cards. If X is the random variable of getting queens, then the value of $2 E(X)+3 E\left(X^2\right)$ for the number of queens is

A
$\frac{132}{221}$
B
$\frac{108}{221}$
C
$\frac{176}{221}$
D
$\frac{68}{221}$
3
MHT CET 2025 20th April Morning Shift
MCQ (Single Correct Answer)
+2
-0

A random variable $X$ has the following probability distribution

$$ \begin{array}{|l|c|c|c|c|c|} \hline \mathrm{X}: & 0 & 1 & 2 & 3 & 4 \\ \hline \mathrm{P}(\mathrm{X}): & \mathrm{k} & 2 \mathrm{k} & 4 \mathrm{k} & 2 \mathrm{k} & \mathrm{k} \\ \hline \end{array} $$

then the value of $\mathrm{P}(1 \leqslant \mathrm{X}<4 \mid \mathrm{X} \leqslant 2)=$

A
$\frac{5}{6}$
B
$\frac{6}{7}$
C
$\frac{7}{8}$
D
$\frac{8}{9}$
4
MHT CET 2025 20th April Morning Shift
MCQ (Single Correct Answer)
+2
-0

If two numbers $p$ and $q$ are chosen randomly from the set $\{1,2,3,4\}$, one by one, with replacement, then the probability of getting $\mathrm{p}^2 \geq 4 \mathrm{q}$ is

A
$\frac{1}{4}$
B
$\frac{7}{16}$
C
$\frac{1}{2}$
D
$\frac{9}{16}$
MHT CET Subjects
EXAM MAP