LIST-I contains metal species and LIST-II contains their properties.

List-I	List-II
(I) $\left[\mathrm{Cr}(\mathrm{CN})_{6}\right]^{4-}$	(P) $t_{2 \mathrm{g}}$ orbitals contain 4 electrons
(II) $\left[\mathrm{RuCl}_{6}\right]^{2-}$	(Q) $\mu$ (spin-only $)=4.9 \mathrm{BM}$
(III) $\left[\mathrm{Cr}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]^{2+}$	(R) low spin complex ion
(IV) $\left[\mathrm{Fe}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]^{2+}$	(S) metal ion in $4+$ oxidation state
	(T) $d^{4}$ species

[Given: Atomic number of $\mathrm{Cr}=24, \mathrm{Ru}=44, \mathrm{Fe}=26$ ]

Match each metal species in LIST-I with their properties in LIST-II, and choose the correct option

Match the compounds in LIST-I with the observations in LIST-II, and choose the correct option.

List-I	List-II
(I) Aniline	(P) Sodium fusion extract of the compound on boiling with $\mathrm{FeSO}_{4}$, followed by acidification with conc. $\mathrm{H}_{2} \mathrm{SO}_{4}$, gives Prussian blue color.
(II) $o$-Cresol	(Q) Sodium fusion extract of the compound on treatment with sodium nitroprusside gives blood red color.
(III) Cysteine	(R) Addition of the compound to a saturated solution of $\mathrm{NaHCO}_{3}$ results in effervescence.
(IV) Caprolactam	(S) The compound reacts with bromine water to give a white precipitate.
	(T) Treating the compound with neutral $\mathrm{FeCl}_{3}$ solution produces violet color.

Considering only the principal values of the inverse trigonometric functions, the value of

$$ \frac{3}{2} \cos ^{-1} \sqrt{\frac{2}{2+\pi^{2}}}+\frac{1}{4} \sin ^{-1} \frac{2 \sqrt{2} \pi}{2+\pi^{2}}+\tan ^{-1} \frac{\sqrt{2}}{\pi} $$

is

Let $$\alpha$$ be a positive real number. Let $$f: \mathbb{R} \rightarrow \mathbb{R}$$ and $$g:(\alpha, \infty) \rightarrow \mathbb{R}$$ be the functions defined by

$$ f(x)=\sin \left(\frac{\pi x}{12}\right) \quad \text { and } \quad g(x)=\frac{2 \log _{\mathrm{e}}(\sqrt{x}-\sqrt{\alpha})}{\log _{\mathrm{e}}\left(e^{\sqrt{x}}-e^{\sqrt{\alpha}}\right)} . $$

Then the value of $$\lim \limits_{x \rightarrow \alpha^{+}} f(g(x))$$ is