1
MHT CET 2021 23th September Morning Shift
MCQ (Single Correct Answer)
+2
-0

The equation of line, where length of the perpendicular segment from origin to the line is 4 and the inclination of this perpendicular segment with the positive direction of X-axis is 30$$^\circ$$, is

A
$$ x+\sqrt{3} y=8 $$
B
$$ x-\sqrt{3} y=8 $$
C
$$ \sqrt{3x} -y=8 $$
D
$$ \sqrt{3x} +y=8 $$
2
MHT CET 2021 23th September Morning Shift
MCQ (Single Correct Answer)
+2
-0

If $$\int \frac{\sin x}{\sin (x-\alpha)} d x=A x+B \log \sin (x-\alpha)+c$$, then the value of A and B are respectively (where $$\mathrm{c}$$ is a constant of integration)

A
$$\cos \alpha, \sin \alpha$$
B
$$\sin \alpha, \cos \alpha$$
C
$$-\cos \alpha, \sin \alpha$$
D
$$-\sin \alpha, \cos \alpha$$
3
MHT CET 2021 23th September Morning Shift
MCQ (Single Correct Answer)
+2
-0

The probability distribution of the number of doublets in four throws of a pair of dice is given by

A
$$\mathrm{X}$$ 0 1 2 3 4
$$\mathrm{P(X) :}$$ $$\frac{1}{5}$$ $$\frac{1}{5}$$ $$\frac{1}{5}$$ $$\frac{1}{5}$$ $$\frac{1}{5}$$
B
$$\mathrm{X}$$ 0 1 2 3
$$\mathrm{P(X) :}$$ $$\frac{1}{4}$$ $$\frac{1}{4}$$ $$\frac{1}{4}$$ $$\frac{1}{4}$$
C
$$\mathrm{X}$$ 1 2 3 4
$$\mathrm{P(X) :}$$ $$\frac{1}{4}$$ $$\frac{1}{4}$$ $$\frac{1}{4}$$ $$\frac{1}{4}$$
D
$$\mathrm{X}$$ 0 1 2 3 4
$$\mathrm{P(X) :}$$ $$\frac{625}{1296}$$ $$\frac{125}{324}$$ $$\frac{25}{216}$$ $$\frac{5}{324}$$ $$\frac{1}{1296}$$
4
MHT CET 2021 23th September Morning Shift
MCQ (Single Correct Answer)
+2
-0

Let $$\vec{v}=2 \hat{i}+2 \hat{j}-\hat{k}$$ and $$\bar{w}=\hat{i}+3 \hat{k}$$. If $$\bar{u}$$ is a unit vector, then the maximum value of the scalar triple product $$[\bar{u} \bar{v} \bar{w}]$$ is

A
$$\sqrt{6}$$
B
$$\sqrt{10}$$
C
$$\sqrt{13}$$
D
$$\sqrt{89}$$
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