1
MHT CET 2025 26th April Evening Shift
MCQ (Single Correct Answer)
+2
-0

A fair coin is tossed a fixed number of times. If the probability of getting 5 tails is same as the probability of getting 7 tails, then the probability of getting 3 tails is

A

$\frac{44}{2^{13}}$

B

$\frac{55}{2^{10}}$

C

$\frac{55}{2^{13}}$

D

$\frac{44}{2^{10}}$

2
MHT CET 2025 26th April Morning Shift
MCQ (Single Correct Answer)
+2
-0

The probability that a person is not a sportsperson is $\frac{1}{6}$. Then the probability that out of the 6 members of the family, 5 are sportspersons is

A
$\left(\frac{5}{6}\right)^5$
B
$6\left(\frac{5}{6}\right)^5$
C
$5\left(\frac{5}{6}\right)^6$
D
$\left(\frac{5}{6}\right)^6$
3
MHT CET 2025 26th April Morning Shift
MCQ (Single Correct Answer)
+2
-0

The cumulative distribution function of a discrete random variable X is

$$ \begin{array}{|c|c|c|c|c|c|c|c|c|} \hline \mathrm{X}=x & -4 & -2 & 0 & 2 & 4 & 6 & 8 & 10 \\ \hline \mathrm{~F}(\mathrm{X}=x) & 0.1 & 0.3 & 0.5 & 0.65 & 0.75 & 0.85 & 0.90 & 1 \\ \hline \end{array} $$

then $\frac{P(X \leqslant 0)}{P(X>0)}=$

A

$\frac{1}{2}$

B

1

C

$\frac{1}{3}$

D

$\frac{1}{5}$

4
MHT CET 2025 26th April Morning Shift
MCQ (Single Correct Answer)
+2
-0

The following is p.d.f. of continuous random variable X

$$ \mathrm{f}(x)= \begin{cases}\frac{x}{8} & , \text { if } 0 < x < 4 \\ 0 & , \text { otherwise }\end{cases} $$

Then $F(0.5), F(1.7)$ and $F(5)$ is respectively

A
$\frac{1}{64}, 1,0.18$
B
$0.0156,0.18,1$
C
$0.18,0.0156,1$
D
$1,0.0156,0.18$
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