1
JEE Main 2022 (Online) 28th July Morning Shift
+4
-1

Considering only the principal values of the inverse trigonometric functions, the domain of the function $$f(x)=\cos ^{-1}\left(\frac{x^{2}-4 x+2}{x^{2}+3}\right)$$ is :

A
$$\left(-\infty, \frac{1}{4}\right]$$
B
$$\left[-\frac{1}{4}, \infty\right)$$
C
$$(-1 / 3, \infty)$$
D
$$\left(-\infty, \frac{1}{3}\right]$$
2
JEE Main 2022 (Online) 28th July Morning Shift
+4
-1

Considering the principal values of the inverse trigonometric functions, the sum of all the solutions of the equation $$\cos ^{-1}(x)-2 \sin ^{-1}(x)=\cos ^{-1}(2 x)$$ is equal to :

A
0
B
1
C
$$\frac{1}{2}$$
D
$$-\frac{1}{2}$$
3
JEE Main 2022 (Online) 27th July Evening Shift
+4
-1

The domain of the function $$f(x)=\sin ^{-1}\left[2 x^{2}-3\right]+\log _{2}\left(\log _{\frac{1}{2}}\left(x^{2}-5 x+5\right)\right)$$, where [t] is the greatest integer function, is :

A
$$\left(-\sqrt{\frac{5}{2}}, \frac{5-\sqrt{5}}{2}\right)$$
B
$$\left(\frac{5-\sqrt{5}}{2}, \frac{5+\sqrt{5}}{2}\right)$$
C
$$\left(1, \frac{5-\sqrt{5}}{2}\right)$$
D
$$\left[1, \frac{5+\sqrt{5}}{2}\right)$$
4
JEE Main 2022 (Online) 26th July Evening Shift
+4
-1

If $$0 < x < {1 \over {\sqrt 2 }}$$ and $${{{{\sin }^{ - 1}}x} \over \alpha } = {{{{\cos }^{ - 1}}x} \over \beta }$$, then the value of $$\sin \left( {{{2\pi \alpha } \over {\alpha + \beta }}} \right)$$ is :

A
$$4 \sqrt{\left(1-x^{2}\right)}\left(1-2 x^{2}\right)$$
B
$$4 x \sqrt{\left(1-x^{2}\right)}\left(1-2 x^{2}\right)$$
C
$$2 x \sqrt{\left(1-x^{2}\right)}\left(1-4 x^{2}\right)$$
D
$$4 \sqrt{\left(1-x^{2}\right)}\left(1-4 x^{2}\right)$$
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