1
MHT CET 2023 10th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

Considering only the principal values of an inverse function, the set

$$\mathrm{A}=\left\{x \geq 0 / \tan ^{-1} x+\tan ^{-1} 6 x=\frac{\pi}{4}\right\}$$

A
is an empty set.
B
is a singleton set.
C
contains more than two elements.
D
contains two elements.
2
MHT CET 2023 10th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

The solution of the equation $$\tan ^{-1}(1+x)+\tan ^{-1}(1-x)=\frac{\pi}{2}$$ is

A
$$x=1$$
B
$$x=0$$
C
$$x=-1$$
D
$$x=\pi$$
3
MHT CET 2023 9th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

The value of $$\tan ^{-1}\left(\frac{\sqrt{1+x^2}+\sqrt{1-x^2}}{\sqrt{1+x^2}-\sqrt{1-x^2}}\right), |x| < \frac{1}{2}, x \neq 0$$

A
$$\frac{\pi}{4}+\frac{1}{2} \cos ^{-1} x^2$$
B
$$\frac{\pi}{4}+\cos ^{-1} x^2$$
C
$$\frac{\pi}{4}-\frac{1}{2} \cos ^{-1} x^2$$
D
$$\frac{\pi}{4}-\cos ^{-1} x^2$$
4
MHT CET 2023 9th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

If $$\sin ^{-1} x+\cos ^{-1} y=\frac{3 \pi}{10}$$, then the value of $$\cos ^{-1} x+\sin ^{-1} y$$ is

A
$$\frac{\pi}{10}$$
B
$$\frac{7 \pi}{10}$$
C
$$\frac{9 \pi}{10}$$
D
$$\frac{3 \pi}{10}$$
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