The correct option(s) about entropy (S) is(are)
[$\mathrm{R}=$ gas constant, $\mathrm{F}=$ Faraday constant, $\mathrm{T}=$ Temperature]

The compound that does NOT liberate CO₂, on treatment with aqueous sodium bicarbonate solution, is 

Three moles of ${\mathrm{B}}_2{\mathrm{H}}_6$ are completely reacted with methanol. The number of moles of boron containing product formed is

Among PbS, CuS, HgS, MnS, $\mathrm{A}{\mathrm{g}}_2\mathrm{S}$ , NiS, CoS, $\mathrm{B}{\mathrm{i}}_2{\mathrm{S}}_3$ and $\mathrm{S}\mathrm{n}{\mathrm{S}}_2$ , the total number of black coloured sulphides is

Upon treatment with ammoniacal ${\text{H}}_2\text{S}$, the metal ion that precipitates as a sulphide is

Upon heating with $\mathrm{C}{\mathrm{u}}_2\mathrm{S}$ , the reagent(s) that give copper metal is/are

The electrochemical cell shown below is a concentration cell. \(\mathrm{M} \mid \mathrm{M}^{2+}\) (saturated solution of a sparingly soluble salt, \(\left.\mathrm{MX}_{2}\right) \| \mathrm{M}^{2 \perp}\left(0.001 \mathrm{~mol} \mathrm{dm}^{-3}\right) \mid \mathrm{M}\).
The emf of the cell depends on the difference in concentrations of \(\mathrm{M}^{2+}\) ions at the two electrodes. The emf of the cell at \(298 \mathrm{~K}\) is \(0.059 \mathrm{~V}\).
Question:
The solubility product \(\left(\mathrm{K}_{s p} ; \mathrm{mol}^{3} \mathrm{dm}^{-9}\right)\) of \(\mathrm{MX}_{2}\) at \(298 \mathrm{~K}\) based on the information available for the given concentration cell is (take \(2.303 \times \mathrm{R} \times 298 / \mathrm{F}=0.059 \mathrm{~V}\) )

Match each set of hybrid orbitals from LIST-I with complex (es) given in LIST-II.

	LIST -I		LIST -II
A)	$ds{p}^2$	P)	${\left[Fe{F}_6\right]}^{4-}$
B)	$s{p}^3$	Q)	$\left[Ti{\left(H_{2}O\right)}_{3}C{l}_3\right]$
C)	$s{p}^3{d}^2$	R)	${\left[Cr{\left(N{H}_3\right)}_6\right]}^{3+}$
D)	$d^{2}s{p}^3$	S)	${\left[FeC{l}_4\right]}^{2-}$
		T)	$Ni{\left(CO\right)}_4$
		U)	${\left[Ni{\left(CN\right)}_4\right]}^{2-}$

Statement I In water, orthoboric acid behaves as a weak monobasic acid.
Statement II In water, orthoboric acid acts as proton donor.

Let ${\tan }^{-1}\left(x\right)\in \left(-\frac{\pi }{2}, \frac{\pi }{2}\right)$, for $x\in \mathrm{ℝ}$. Then the number of real solutions of the equation $\sqrt{1+\cos \left(2x\right)}=\sqrt{2}{\tan }^{-1}\left(\tan x\right)$ in the set $\left(-\frac{3\pi }{2}, -\frac{\pi }{2}\right)\cup \left(-\frac{\pi }{2}, \frac{\pi }{2}\right)\cup \left(\frac{\pi }{2}, \frac{3\pi }{2}\right)$ is equal to

Two non-reactive monoatomic ideal gases have their atomic masses in the ratio 2 : 3. The ratio of their partial pressures, when enclosed in a vessel kept at a constant temperature, is 4 : 3. The ratio of their densities is 

Let \(\alpha\) and \(\beta\) be the distinct roots of the equation \(x^2+x-1=0\). Consider the set \(T=\{1, \alpha, \beta\}\). For a \(3 \times 3\) matrix \(M=\left(a_{i j}\right)_{3 \times 3}\), define \(R_i=a_{i 1}+a_{i 2}+a_{i 3}\) and \(C_j=a_{1 j}+a_{2 j}+a_{3 j}\) for \(i=1,2,3\) and \(j=1,2,3\).
Match each entry in List-I to the correct entry in List-II.

The correct option is

Hyperconjugation involves overlap of the following orbitals