MCQ
Match List $I$ with List $II$ and select the correct answer using the code given below the lists :
| List $I$ | List $II$ |
| $P$ $\quad\left(\frac{1}{y^2}\left(\frac{\cos \left(\tan ^{-1} y\right)+y \sin \left(\tan ^{-1} y\right)}{\cot \left(\sin ^{-1} y\right)+\tan \left(\sin ^{-1} y\right)}\right)^2+y^4\right)^{1 / 2}$ takes value | $1.\quad$ $\frac{1}{2} \sqrt{\frac{5}{3}}$ |
| $Q.\quad$ If $\cos x+\cos y+\cos z=0=\sin x+\sin y+\sin z$ then possible value of $\cos \frac{x-y}{2}$ is | $2.\quad$ $\sqrt{2}$ |
| $R.\quad$ If $\cos \left(\frac{\pi}{4}-x\right) \cos 2 x+\sin x \sin 2 x \sec x=\cos x \sin 2 x \sec x+$ $\cos \left(\frac{\pi}{4}+x\right) \cos 2 x$ then possible value of $\sec x$ is | $3.\quad$ $\frac{1}{2}$ |
| $S.\quad$ If $\cot \left(\sin ^{-1} \sqrt{1-x^2}\right)=\sin \left(\tan ^{-1}(x \sqrt{6})\right), x \neq 0$, then possible value of $x$ is | $4.\quad$ $1$ |
Codes: $ \quad P \quad Q \quad R \quad S $
- A$\quad 4 \quad 3 \quad 1 \quad 2 $
- ✓$\quad 4 \quad 3 \quad 2 \quad 1 $
- C$\quad 3 \quad 4 \quad 2 \quad 1 $
- D$\quad 3 \quad 4 \quad 1 \quad 2 $
