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1
MHT CET 2025 22nd April Morning Shift
MCQ (Single Correct Answer)
+2
-0

The probability that a certain kind of component will survive a given test is $\frac{2}{3}$. The probability that at most 2 components out of 4 tested, will survive is

A
$\frac{31}{3^4}$
B
$\frac{32}{3^4}$
C
$\frac{33}{3^4}$
D
$\frac{35}{3^4}$
2
MHT CET 2025 22nd April Morning Shift
MCQ (Single Correct Answer)
+2
-0

A coin is tossed until one head appears or a tail appears 4 times in succession. The probability distribution of the number of tosses is

A

$$ \begin{array}{|l|c|c|c|c|} \hline \mathrm{X} & 1 & 2 & 3 & 4 \\ \hline \mathrm{P}(\mathrm{X}=x) & \frac{1}{8} & \frac{1}{8} & \frac{1}{2} & \frac{1}{4} \\ \hline \end{array} $$

B

$$ \begin{array}{|l|c|c|c|c|} \hline \mathrm{X} & 1 & 2 & 3 & 4 \\ \hline \mathrm{P}(\mathrm{X}=x) & \frac{1}{4} & \frac{1}{2} & \frac{1}{8} & \frac{1}{8} \\ \hline \end{array} $$

C

$$ \begin{array}{|l|c|c|c|c|} \hline \mathrm{X} & 1 & 2 & 3 & 4 \\ \hline \mathrm{P}(\mathrm{X}=x) & \frac{1}{8} & \frac{1}{4} & \frac{1}{8} & \frac{1}{2} \\ \hline \end{array} $$

D

$$ \begin{array}{|l|c|c|c|c|} \hline \mathrm{X} & 1 & 2 & 3 & 4 \\ \hline \mathrm{P}(\mathrm{X}=x) & \frac{1}{2} & \frac{1}{4} & \frac{1}{8} & \frac{1}{8} \\ \hline \end{array} $$

3
MHT CET 2025 22nd April Morning Shift
MCQ (Single Correct Answer)
+2
-0

The p.d.f. of a continuous random variable X is $f(x)=\left\{\begin{array}{cl}\frac{x^2}{18} & , \text { if }-3 < x < 3 \\ 0 & \text { otherwise }\end{array}\right.$

Then $\mathrm{P}[|\mathrm{X}|<2]=$

A
$\frac{1}{27}$
B
$\frac{2}{13}$
C
$\frac{8}{27}$
D
$\frac{4}{27}$
4
MHT CET 2025 22nd April Morning Shift
MCQ (Single Correct Answer)
+2
-0

In a single toss of a fair die, the odds against the event that number 4 or 5 turns up is

A
$2: 1$
B
$1: 3$
C
$2: 3$
D
$1: 1$
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