1
MHT CET 2023 11th May Morning Shift
+2
-0

Three of six vertices of a regular hexagon are chosen at random. The probability that the triangle with these three vertices is equilateral, equals ___________.

A
$$\frac{1}{2}$$
B
$$\frac{1}{5}$$
C
$$\frac{1}{10}$$
D
$$\frac{1}{20}$$
2
MHT CET 2023 11th May Morning Shift
+2
-0

A binomial random variable $$\mathrm{X}$$ satisfies $$9. p(X=4)=p(X=2)$$ when $$n=6$$. Then $$p$$ is equal to

A
$$\frac{1}{4}$$
B
$$\frac{1}{2}$$
C
$$\frac{1}{8}$$
D
$$\frac{1}{5}$$
3
MHT CET 2023 10th May Evening Shift
+2
-0

The three ships namely A, B and C sail from India to Africa. If the odds in favour of the ships reaching safely are $$2: 5,3: 7$$ and $$6: 11$$ respectively, then probability of all of them arriving safely is

A
$$\frac{18}{595}$$
B
$$\frac{11}{34}$$
C
$$\frac{196}{217}$$
D
$$\frac{1}{595}$$
4
MHT CET 2023 10th May Evening Shift
+2
-0

If the sum of mean and variance of a Binomial Distribution is $$\frac{15}{2}$$ for 10 trials, then the variance is

A
1.5
B
2.5
C
4.5
D
3.5
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