1
MHT CET 2021 24th September Morning Shift
MCQ (Single Correct Answer)
+2
-0

If the lines respresented by $$a x^2-b x y-y^2=0$$ make angle $$\alpha$$ and $$\beta$$ with the positive direction of $$\mathrm{X}$$-axis, then $$\tan (\alpha+\beta)=$$

A
$$\frac{a}{a+b}$$
B
$$\frac{b}{1+b}$$
C
$$\frac{b}{1+a}$$
D
$$\frac{-b}{1+a}$$
2
MHT CET 2021 24th September Morning Shift
MCQ (Single Correct Answer)
+2
-0

If the probability distribution function of a random variable X is given as

$$\mathrm{X=x_i}$$ $$-2$$ $$-1$$ 0 1 2
$$\mathrm{P(X=x_i)}$$ 0.2 0.3 0.15 0.25 0.1

Then F(0) is equal to

A
$$\mathrm{P}(\mathrm{X}>0)$$
B
$$\mathrm{1-P(X>0)}$$
C
$$1-\mathrm{P}(\mathrm{X}<0)$$
D
$$\mathrm{P}(\mathrm{X}<0)$$
3
MHT CET 2021 24th September Morning Shift
MCQ (Single Correct Answer)
+2
-0

The particular solution of the differential equation $$ \frac{d y}{d x}=\frac{x+y+1}{x+y-1} $$ when $$ \mathrm{x}=\frac{2}{3} $$ and $$ y=\frac{1}{3} $$ is

A
$$ 2 x+2 y-2=\log |x+y| $$
B
$$ y-x+\frac{1}{3}=\log |x+y| $$
C
$$ x+y-1=\log |x+y| $$
D
$$ 4 x-5 y-1=\log |x+y| $$
4
MHT CET 2021 24th September Morning Shift
MCQ (Single Correct Answer)
+2
-0

If $$a \sin \theta=b \cos \theta$$, where $$a, b \neq 0$$, then $$a\cos 2 \theta+b \sin 2 \theta=$$

A
$$\mathrm{ab}$$
B
a
C
b
D
$$\frac{a}{b}$$
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