1
MHT CET 2024 15th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

The value of the integral $\int_0^{\frac{\pi}{2}} \frac{\sqrt{\cot x}}{\sqrt{\cot x}+\sqrt{\tan x}} \mathrm{dx}$ is

A
$\frac{\pi}{4}$
B
$\frac{\pi}{2}$
C
$\frac{\pi}{8}$
D
$2 \pi$
2
MHT CET 2024 15th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

Variance of first n natural numbers is ________.

A
$\mathrm{n}^2-\frac{1}{12}$
B
$\frac{(\mathrm{n}-1)^2}{12}$
C
$\frac{\mathrm{n}^2}{12}-1$
D
$\frac{\mathrm{n}^2-1}{12}$
3
MHT CET 2024 15th May Evening Shift
MCQ (Single Correct Answer)
+2
-0
 

Suppose three coins are tossed simultaneously. If $X$ denotes the number of heads, then probability distribution of x is

A
$X=x$ 0 1 2 3
$P(X=x)$ $\frac{2}{8}$ $\frac{2}{8}$ $\frac{3}{8}$ $\frac{1}{8}$
B
$X=x$ 0 1 2 3
$P(X=x)$ $\frac{1}{8}$ $\frac{3}{8}$ $\frac{3}{8}$ $\frac{1}{8}$
C
$X=x$ 0 1 2
$P(X=x)$ $\frac{3}{8}$ $\frac{3}{8}$ $\frac{2}{8}$
D
$X=x$ 0 1 2 3
$P(X=x)$ $\frac{1}{8}$ $\frac{1}{8}$ $\frac{3}{8}$ $\frac{3}{8}$
4
MHT CET 2024 15th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

Four fair dice are thrown independently 27 times. Then the expected number of times, at least two dice show up a three or a five is

A
11
B
12
C
9
D
10
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