MHT CET 2025 19th April Evening Shift | Probability Question 28 | Mathematics

Let $A$ and $B$ are independent events with $\mathrm{P}(\mathrm{B})=\frac{2}{5}, \mathrm{P}(\mathrm{A} \cup \mathrm{B})=\frac{11}{20}$, then $\mathrm{P}\left(\mathrm{A}^{\prime} \mid \mathrm{B}\right)$ is root of the equation

$4 x^2-7 x+3=0$

$4 x^2+7 x+3=0$

$4 x^2-3 x-7=0$

$6 x^2-5 x+1=0$

MHT CET 2025 19th April Morning Shift

MCQ (Single Correct Answer)

-0

A box contains 9 tickets numbered 1 to 9 both inclusive. If 3 tickets are drawn from the box one at a time, then the probability that they are alternatively either {odd, even, odd} or {even, odd, even} is

$\frac{5}{17}$

$\frac{4}{17}$

$\frac{5}{16}$

$\frac{5}{18}$

MHT CET 2025 19th April Morning Shift

MCQ (Single Correct Answer)

-0

The probability distribution of a discrete random variable X is

$\mathrm{X}$	0	1	2	3	4
$\mathrm{P(X=}x)$	$\mathrm{2k}$	$\mathrm{k}$	$\mathrm{2k}$	$\mathrm{4k}$	$\mathrm{k}$

If $\mathrm{a}=\mathrm{P}(x<3)$ and $\mathrm{b}=\mathrm{P}(2 \leq \mathrm{X}<4)$, then

$\mathrm{a}=\mathrm{b}$

$a>b$

a $<$ b

$\mathrm{a}=\frac{1}{2} \mathrm{~b}$

MHT CET 2025 19th April Morning Shift

MCQ (Single Correct Answer)

-0

If a random variable $X$ has the p.d.f. $f(x)=\left\{\begin{array}{cc}\frac{\mathrm{k}}{x^2+1} & , \text { if } 0< x< \infty \\ 0 & , \text { otherwise }\end{array}\right.$ then c.d.f. of X is

$2 \tan ^{-1} x$

$\frac{\pi}{2} \tan ^{-1} x$

$\frac{2}{\pi} \tan ^{-1} x$

$\tan ^{-1} x$

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