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

If $$y=\tan ^{-1}\left[\frac{\log \left(\frac{e}{x^2}\right)}{\log \left(e x^2\right)}\right]+\tan ^{-1}\left[\frac{3+2 \log x}{1-6 \log x}\right]$$, then $$\frac{d^2 y}{d x^2}=$$

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

The value of $$\sin ^{-1}\left(\frac{-1}{2}\right)+\sin ^{-1}\left(\frac{-\sqrt{3}}{2}\right)$$ is,

A
$$\frac{\pi}{3}$$
B
$$\frac{-\pi}{6}$$
C
$$\frac{-\pi}{3}$$
D
$$\frac{-\pi}{2}$$
3
MHT CET 2021 23rd September Evening Shift
MCQ (Single Correct Answer)
+2
-0

If $$\tan ^{-1}(2 x)+\tan ^{-1}(3 x)=\frac{\pi}{4}$$, where $$x>0$$, then $$x=$$

A
1
B
$$\frac{1}{6}$$
C
$$\frac{1}{3}$$
D
$$\frac{1}{2}$$
4
MHT CET 2021 23th September Morning Shift
MCQ (Single Correct Answer)
+2
-0

$$\tan \left(\cos ^{-1}\left(\frac{4}{5}\right)+\tan ^{-1}\left(\frac{2}{3}\right)\right)=$$

A
$$\frac{17}{6}$$
B
$$\frac{17}{3}$$
C
$$\frac{18}{5}$$
D
$$\frac{7}{15}$$
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