MHT CET 2026 20th April Morning Shift | Probability Question 5 | Mathematics

Let X be a continuous random variable with the probability density function(p.d.f.) given by
$f(x) = \begin{cases} kx, & 0 \leq x < 1 \\ k, & 1 \leq x < 2 \\ -kx + 3k, & 2 \leq x < 3 \\ 0, & \text{otherwise} \end{cases}$
$P(2 < X \leq 3) = \cdots$

$\dfrac{1}{2}$

$\dfrac{1}{3}$

$\dfrac{1}{4}$

$\dfrac{1}{5}$

MHT CET 2026 20th April Morning Shift

MCQ (Single Correct Answer)

-0

In a certain city, the ratio of men to women is $5:4$. It is found that $80\%$ of men and $90\%$ of women are literate. If a person selected at random is found to be illiterate, then the probability that the person is a man is....

$\dfrac{2}{3}$

$\dfrac{5}{7}$

$\dfrac{1}{3}$

$\dfrac{2}{7}$

MHT CET 2025 5th May Evening Shift

MCQ (Single Correct Answer)

-0

Three numbers are chosen at random from numbers 1 to 20 . The probability that they are consecutive is

$\frac{1}{190}$

$\frac{1}{120}$

$\frac{3}{190}$

$\frac{5}{190}$

MHT CET 2025 5th May Evening Shift

MCQ (Single Correct Answer)

-0

Two cards are drawn successively with replacement from fair playing 52 cards. let X denote number of kings obtained when two cards are drawn, then $\mathrm{E}\left(\mathrm{X}^2\right)=$

$\frac{24}{169}$

$\frac{26}{169}$

$\frac{27}{169}$

$\frac{28}{169}$

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