$$600 \mathrm{~mL}$$ of $$0.01~\mathrm{M} ~\mathrm{HCl}$$ is mixed with $$400 \mathrm{~mL}$$ of $$0.01~\mathrm{M} ~\mathrm{H}_{2} \mathrm{SO}_{4}$$. The $$\mathrm{pH}$$ of the mixture is ___________ $$\times 10^{-2}$$. (Nearest integer)

[Given $$\log 2=0.30$$

$$\log 3=0.48$$

$$\log 5=0.69$$

$$\log 7=0.84$$

$$\log 11=1.04]$$

When 2 litre of ideal gas expands isothermally into vacuum to a total volume of 6 litre, the change in internal energy is ____________ J. (Nearest integer)

Consider the cell

$$\mathrm{Pt}_{(\mathrm{s})}\left|\mathrm{H}_{2}(\mathrm{~g}, 1 \mathrm{~atm})\right| \mathrm{H}^{+}(\mathrm{aq}, 1 \mathrm{M})|| \mathrm{Fe}^{3+}(\mathrm{aq}), \mathrm{Fe}^{2+}(\mathrm{aq}) \mid \operatorname{Pt}(\mathrm{s})$$

When the potential of the cell is $$0.712 \mathrm{~V}$$ at $$298 \mathrm{~K}$$, the ratio $$\left[\mathrm{Fe}^{2+}\right] /\left[\mathrm{Fe}^{3+}\right]$$ is _____________. (Nearest integer)

Given : $$\mathrm{Fe}^{3+}+\mathrm{e}^{-}=\mathrm{Fe}^{2+}, \mathrm{E}^{\theta} \mathrm{Fe}^{3+}, \mathrm{Fe}^{2+} \mid \mathrm{Pt}=0.771$$

$$ \frac{2.303 \mathrm{RT}}{\mathrm{F}}=0.06 \mathrm{~V} $$

A trisubstituted compound '$$\mathrm{A}$$', $$\mathrm{C}_{10} \mathrm{H}_{12} \mathrm{O}_{2}$$ gives neutral $$\mathrm{FeCl}_{3}$$ test positive. Treatment of compound 'A' with $$\mathrm{NaOH}$$ and $$\mathrm{CH}_{3} \mathrm{Br}$$ gives $$\mathrm{C}_{11} \mathrm{H}_{14} \mathrm{O}_{2}$$, with hydroiodic acid gives methyl iodide and with hot conc. $$\mathrm{NaOH}$$ gives a compound $$\mathrm{B}, \mathrm{C}_{10} \mathrm{H}_{12} \mathrm{O}_{2}$$. Compound 'A' also decolorises alkaline $$\mathrm{KMnO}_{4}$$. The number of $$\pi$$ bond/s present in the compound '$$\mathrm{A}$$' is _____________.