1
MHT CET 2024 4th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

A man and his wife appear for an interview for two posts. The probability of the husband's selection is $\frac{1}{7}$ and that of the wife's selection is $\frac{1}{5}$. If they appear for the interview independently, then the probability that only one of them is selected, is

A
$\frac{1}{7}$
B
$\frac{2}{7}$
C
$\frac{6}{7}$
D
$\frac{4}{7}$
2
MHT CET 2024 4th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

The expected value of the sum of the two numbers obtained on the uppermost faces, when two fair dice are rolled, is

A
7
B
12
C
6
D
5
3
MHT CET 2024 4th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

For an entry to a certain course, a candidate is given twenty problems to solve. If the probability that the candidate can solve any problem is $\frac{3}{7}$, then the probability that he is unable to solve at most two problem is

A
$\frac{256}{49}\left(\frac{4}{7}\right)^{18}$
B
$\frac{1966}{49}\left(\frac{4}{7}\right)^{18}$
C
$\frac{1710}{49}\left(\frac{4}{7}\right)^{18}$
D
$\frac{1726}{49}\left(\frac{4}{7}\right)^{18}$
4
MHT CET 2024 4th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

A random variable has the following probability distribution

$\mathrm{X:}$ 0 1 2 3 4 5 6 7
$\mathrm{P}(x):$ 0 $\mathrm{2p}$ $\mathrm{2p}$ $\mathrm{3p}$ $\mathrm{p^2}$ $\mathrm{2p^2}$ $\mathrm{7p^2}$ $\mathrm{2p}$

Then the value of p is

A
$\frac{1}{10}$
B
$\frac{1}{30}$
C
$\frac{1}{100}$
D
$\frac{3}{20}$
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