
Let's analyze each reaction:
A. $CH_4(g) + 2O_2(g) \rightarrow CO_2(g) + 2H_2O(l)$:
This is a combustion reaction where methane reacts with oxygen to produce carbon dioxide and water.
The oxidation state of carbon changes from -4 to +4, and the oxidation state of oxygen changes from 0 to -2.
This is also a combination reaction.
So, A is matched with II.
B. $2NaH(s) \rightarrow 2Na(s) + H_2(g)$:
Sodium hydride decomposes into sodium and hydrogen.
The oxidation state of sodium changes from +1 to 0, and the oxidation state of hydrogen changes from -1 to 0.
This is a decomposition reaction.
So, B is matched with III.
C. $V_2O_5(s) + 5Ca(s) \rightarrow 2V(s) + 5CaO(s)$:
This is a displacement reaction, where calcium displaces vanadium from its oxide.
Calcium is oxidized from 0 to +2, and vanadium is reduced from +5 to 0.
So, C is matched with IV.
D. $2H_2O_2(aq) \rightarrow 2H_2O(l) + O_2(g)$:
Hydrogen peroxide decomposes into water and oxygen.
The oxidation state of oxygen in $H_2O_2$ is -1, in $H_2O$ it is -2, and in $O_2$ it is 0.
This is a disproportionation reaction, where oxygen in $H_2O_2$ is both oxidized and reduced.
So, D is matched with I.
Final Matching:
A - II
B - III
C - IV
D - I
Final Answer:
The final answer is $ A\text{-}II,\ B\text{-}III,\ C\text{-}IV,\ D\text{-}I $.
200 cc of $x \times 10^{-3}$ M potassium dichromate is required to oxidise 750 cc of 0.6 M Mohr's salt solution in acidic medium. Here x = ______ .

A substance 'X' (1.5 g) dissolved in 150 g of a solvent 'Y' (molar mass = 300 g mol$^{-1}$) led to an elevation of the boiling point by 0.5 K. The relative lowering in the vapour pressure of the solvent 'Y' is $____________ \(\times 10^{-2}\). (nearest integer)
[Given : $K_{b}$ of the solvent = 5.0 K kg mol$^{-1}$]
Assume the solution to be dilute and no association or dissociation of X takes place in solution.
Inductance of a coil with \(10^4\) turns is \(10\,\text{mH}\) and it is connected to a DC source of \(10\,\text{V}\) with internal resistance \(10\,\Omega\). The energy density in the inductor when the current reaches \( \left(\frac{1}{e}\right) \) of its maximum value is \[ \alpha \pi \times \frac{1}{e^2}\ \text{J m}^{-3}. \] The value of \( \alpha \) is _________.
\[ (\mu_0 = 4\pi \times 10^{-7}\ \text{TmA}^{-1}) \]