1
MHT CET 2025 19th April Evening Shift
MCQ (Single Correct Answer)
+2
-0

Let X be a discrete random variable. The probability distribution of X is given below

$$ \begin{array}{|c|c|c|c|} \hline \mathrm{X} & 30 & 10 & -10 \\ \hline \mathrm{P}(\mathrm{X}) & \frac{1}{5} & \mathrm{~A} & \mathrm{~B} \\ \hline \end{array} $$

and $\mathrm{E}(\mathrm{X})=4$, then the value of AB is equal to

A
$\frac{3}{10}$
B
$\frac{2}{15}$
C
$\frac{1}{15}$
D
$\frac{3}{20}$
2
MHT CET 2025 19th April Evening Shift
MCQ (Single Correct Answer)
+2
-0

The projection of the line segment joining the points $(2,1,-3)$ and $(-1,0,2)$ on the line whose direction ratios are $3,2,6$ is

A
$\frac{19}{7}$ units
B
$\frac{17}{7}$ units
C
$\frac{11}{7}$ units
D
$\frac{15}{7}$ units
3
MHT CET 2025 19th April Evening Shift
MCQ (Single Correct Answer)
+2
-0

If $x^{\frac{2}{5}}+y^{\frac{2}{5}}=\mathrm{a}^{\frac{2}{5}}$ then $\frac{\mathrm{d} y}{\mathrm{~d} x}=$

A
$\sqrt[5]{\left(\frac{y}{x}\right)^3}$
B
$\quad-\sqrt[5]{\left(\frac{x}{y}\right)^3}$
C
$\sqrt[5]{\left(\frac{x}{y}\right)^3}$
D
$\quad-\sqrt[5]{\left(\frac{y}{x}\right)^3}$
4
MHT CET 2025 19th April Evening Shift
MCQ (Single Correct Answer)
+2
-0
The perpendicular distance between the lines given by $(x-2 y+1)^2+\mathrm{k}(x-2 y+1)=0$ is $\sqrt{5}$, then $\mathrm{k}=$
A
5
B
2
C
4
D
6

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