iCON Education - Inverse Trigonometric Functions BITSAT Test

Question 1: Palette 1/4

BITSAT 2024 MCQ

If $ y=\tan ^{-1}\left(\frac{\sqrt{x}-x}{1+x^{\frac{3}{2}}}\right) $, then $ y^{\prime}(1) $ is equal to

A

0

B

$ \frac{1}{2} $

C

-1

D

$ -\frac{1}{4} $

Question 2: Palette 2/4

BITSAT 2023 MCQ

If $\cot ^{-1} \sqrt{\cos \alpha}-\tan ^{-1} \sqrt{\cos \alpha}=x$, then $\sin x$ is equal to

A

$\cot ^2\left(\frac{\alpha}{2}\right)$

B

$\tan ^2\left(\frac{\alpha}{2}\right)$

C

$\cot \left(\frac{\alpha}{2}\right)$

D

$\tan \alpha$

Question 3: Palette 3/4

BITSAT 2022 MCQ

If $x \in \left( {0,{\pi \over 2}} \right)$, then the value of ${\cos ^{ - 1}}\left( {{7 \over 2}(1 + \cos 2x) + \sqrt {({{\sin }^2}x - 48{{\cos }^2}x)\sin x} } \right)$ is equal to

A

$x - {\cos ^{ - 1}}(7\cos x)$

B

$x + {\sin ^{ - 1}}(7\cos x)$

C

$x + {\cos ^{ - 1}}(6\cos x)$

D

$x + {\cos ^{ - 1}}(7\cos x)$

Question 4: Palette 4/4

BITSAT 2021 MCQ

The minimum value of ${({\sin ^{ - 1}}x)^3} + {({\cos ^{ - 1}}x)^3}$ is equal to

A

${{{\pi ^3}} \over {32}}$

B

${{5{\pi ^3}} \over {32}}$

C

${{9{\pi ^3}} \over {32}}$

D

${{11{\pi ^3}} \over {32}}$