Question

List I List II
A)
${\sin }^{-1}\left(\frac{1}{2}\right)+{\cos }^{-1}(-\frac{1}{2})$ 1) $\frac{\pi }{2}$
B)
${\sin }^{-1}(-\frac{1}{2})+{\cos }^{-1}\left(\frac{1}{2}\right)$ 2) $\frac{\pi }{6}$

C)
${\sin }^{-1}\left(\frac{1}{2}\right)+{\cos }^{-1}\left(\frac{1}{2}\right)$ 3) $\frac{5\pi }{6}$
D)
${\sin }^{-1}\left(1\right)+{\cos }^{-1}(-\frac{1}{2})$ 4) $\frac{7\pi }{6}$

Correct match from List I to List II is

• A. A B C D
  3 2 1 4
• B. A B C D
  3 2 4 1
• C. A B C D
  3 4 2 1
• D. A B C D
  3 4 1 2

Answer 1

The correct option is A A B C D

3 2 1 4

A : ${\sin }^{-1}\left(\frac{1}{2}\right)+{\cos }^{-1}(-\frac{1}{2})=\frac{\pi }{6}+\pi -{\cos }^{-1}\left(\frac{1}{2}\right)=\frac{7\pi }{6}-\frac{\pi }{3}=\frac{5\pi }{6}$

B: ${\sin }^{-1}(-\frac{1}{2})+{\cos }^{-1}\left(\frac{1}{2}\right)=-{\sin }^{-1}\left(\frac{1}{2}\right)+\frac{\pi }{3}=-\frac{\pi }{6}+\frac{\pi }{3}=\frac{\pi }{6}$

C: ${\sin }^{-1}\left(\frac{1}{2}\right)+{\cos }^{-1}\left(\frac{1}{2}\right)=\frac{\pi }{6}+\frac{\pi }{3}=\frac{\pi }{2}$

D: ${\sin }^{-1}\left(1\right)+{\cos }^{-1}(-\frac{1}{2})=\frac{\pi }{2}+\pi -{\cos }^{-1}\left(\frac{1}{2}\right)=\frac{3\pi }{2}-\frac{\pi }{3}=\frac{7\pi }{6}$

$A\to 3$
$B\to 2$
$C\to 1$
$D\to 4$