1
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
$$\frac{1}{2}$$
2
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
$$\frac{7}{15}$$
3
MHT CET 2021 23th September Morning Shift
MCQ (Single Correct Answer)
+2
-0

If $$\tan ^{-1}\left[\frac{\sqrt{1+x^2}-\sqrt{1-x^2}}{\sqrt{1+x^2}+\sqrt{1-x^2}}\right]=\alpha$$, then the value of $$\sin 2 \alpha$$ is

A
$$x^3$$
B
$$\sqrt{x}$$
C
$$x$$
D
$$\mathrm{x}^2$$
4
MHT CET 2021 22th September Evening Shift
MCQ (Single Correct Answer)
+2
-0

If $$2 \tan ^{-1}(\cos x)=\tan ^{-1}(2 \operatorname{cosec} x)$$, then the value of $$x$$ is

A
$$\frac{\pi^{\mathrm{c}}}{6}$$
B
$$\frac{\pi^{\mathrm{c}}}{4}$$
C
$$\frac{\pi^{\mathrm{c}}}{3}$$
D
$$\frac{\pi^{\mathrm{c}}}{12}$$
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