1
MHT CET 2021 21th September Morning Shift
MCQ (Single Correct Answer)
+2
-0

In a meeting $$60 \%$$ of the members favour and $$40 \%$$ oppose a certain proposal. A member is selected at random and we take $$\mathrm{X}=0$$ if he opposed and $$\mathrm{X}=1$$ if he is in favour, then $$\operatorname{Var} \mathrm{X}=$$

A
0.36
B
0.24
C
0.6
D
0.06
2
MHT CET 2021 21th September Morning Shift
MCQ (Single Correct Answer)
+2
-0

The distance between parallel lines

$$\begin{aligned} & \bar{r}=(2 \hat{i}-\hat{j}+\hat{k})+\lambda(2 \hat{i}+\hat{j}-2 \hat{k}) \text { and } \\ & \bar{r}=(\hat{i}-\hat{j}+2 \hat{k})+\mu(2 \hat{i}+\hat{j}-2 \hat{k}) \text { is } \end{aligned}$$

A
$$\sqrt{2}$$
B
$$\frac{1}{3}$$ units
C
$$\frac{1}{\sqrt{3}}$$ units
D
$$\frac{\sqrt{2}}{3}$$ units
3
MHT CET 2021 21th September Morning Shift
MCQ (Single Correct Answer)
+2
-0

If $$e^{-y} \cdot y=x$$, then $$\frac{d y}{d x}$$ is

A
$$\frac{y}{1-y}$$
B
$$\frac{1}{x y(1-y)}$$
C
$$\frac{1}{x(1-y)}$$
D
$$\frac{y}{x(1-y)}$$
4
MHT CET 2021 21th September Morning Shift
MCQ (Single Correct Answer)
+2
-0

If the two lines given by $$a x^2+2 h x y+b y^2=0$$ make inclinations $$\propto$$ and $$\beta$$, then $$\tan (\alpha+\beta)=$$

A
$$\frac{h}{a+b}$$
B
$$\frac{2 h}{a+b}$$
C
$$\frac{\mathrm{h}}{\mathrm{a}-\mathrm{b}}$$
D
$$\frac{2 h}{a-b}$$
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