1
MHT CET 2021 22th September Morning Shift
+2
-0

$$y=\tan ^{-1}\left(\sqrt{\frac{1+\sin x}{1-\sin x}}\right), 0 \leq x < \frac{\pi}{2}$$, then $$\frac{d y}{d x}$$ at $$x=\frac{\pi}{6}$$ is

A
$$\frac{1}{4}$$
B
$$\frac{-1}{4}$$
C
$$\frac{-3}{2}$$
D
$$\frac{1}{2}$$
2
MHT CET 2021 21th September Evening Shift
+2
-0

If $$y=\tan ^{-1}\left[\frac{1}{1+x+x^2}\right]+\tan ^{-1}\left[\frac{1}{x^2+3 x+3}\right], x>0$$, then $$\frac{d y}{d x}=$$

A
$$\frac{1}{1+x^2}-\frac{1}{1+(x+2)^2}$$
B
$$\frac{-1}{1+x^2}+\frac{1}{1+(x+2)^2}$$
C
$$\frac{1}{1+x^2}+\frac{1}{1+(x+2)^2}$$
D
$$\frac{-1}{1+x^2}-\frac{1}{1+(x+2)^2}$$
3
MHT CET 2021 21th September Evening Shift
+2
-0

If $$\sin ^{-1}\left(\frac{3}{5}\right)+\cos ^{-1}\left(\frac{12}{13}\right)=\sin ^{-1} \alpha$$, then $$\alpha=$$

A
$$\frac{56}{65}$$
B
$$\frac{61}{65}$$
C
$$\frac{63}{65}$$
D
$$\frac{62}{65}$$
4
MHT CET 2021 21th September Morning Shift
+2
-0

$$\tan ^{-1}\left(\frac{x-1}{x-2}\right)+\tan ^{-1}\left(\frac{x+1}{x+2}\right)=\frac{\pi}{4}$$, then the values of $$x$$ are

A
$$\pm \frac{3}{\sqrt{2}}$$
B
$$\pm \frac{1}{2}$$
C
$$\pm \frac{1}{\sqrt{2}}$$
D
$$\pm \frac{\sqrt{3}}{2}$$
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