1
MHT CET 2023 9th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

Two tangents to the circle $$x^2+y^2=4$$ at the points $$\mathrm{A}$$ and $$\mathrm{B}$$ meet at the point $$\mathrm{P}(-4,0)$$. Then the area of the quadrilateral $$\mathrm{PAOB}, \mathrm{O}$$ being the origin, is

A
$$2 \sqrt{3}$$ sq. units
B
$$8 \sqrt{3}$$ sq. units
C
$$4 \sqrt{3}$$ sq. units
D
$$6 \sqrt{3}$$ sq. units
2
MHT CET 2023 9th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

$$\mathrm{f}: \mathbb{R}-\left(-\frac{3}{5}\right) \rightarrow \mathbb{R}$$ is defined by $$f(x)=\frac{3 x-2}{5 x+3}$$, then $$f \circ f(1)$$ is

A
1
B
$$\frac{-13}{29}$$
C
$$\frac{13}{29}$$
D
$$-1$$
3
MHT CET 2023 9th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

The value of $$\cot \left(\sum_\limits{n=1}^{23} \cot ^{-1}\left(1+\sum_\limits{k=1}^n 2 k\right)\right)$$ is

A
$$\frac{23}{25}$$
B
$$\frac{25}{23}$$
C
$$\frac{23}{24}$$
D
$$\frac{24}{23}$$
4
MHT CET 2023 9th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

An object is moving in the clockwise direction around the unit circle $$x^2+y^2=1$$. As it passes through the point $$\left(\frac{1}{2}, \frac{\sqrt{3}}{2}\right)$$, its $$y$$-co-ordinate is decreasing at the rate of 3 units per sec. The rate at which the $$x$$-co-ordinate changes at this point is

A
2 units/sec
B
$$3 \sqrt{3}$$ units/sec
C
$$\sqrt{3}$$ units /sec
D
$$2 \sqrt{3}$$ units /sec
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