
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 $.
What will be the equilibrium constant of the given reaction carried out in a \(5 \,L\) vessel and having equilibrium amounts of \(A_2\) and \(A\) as \(0.5\) mole and \(2 \times 10^{-6}\) mole respectively?
The reaction : \(A_2 \rightleftharpoons 2A\)

Cobalt chloride when dissolved in water forms pink colored complex $X$ which has octahedral geometry. This solution on treating with cone $HCl$ forms deep blue complex, $\underline{Y}$ which has a $\underline{Z}$ geometry $X, Y$ and $Z$, respectively, are
What will be the equilibrium constant of the given reaction carried out in a \(5 \,L\) vessel and having equilibrium amounts of \(A_2\) and \(A\) as \(0.5\) mole and \(2 \times 10^{-6}\) mole respectively?
The reaction : \(A_2 \rightleftharpoons 2A\)
A black body is at a temperature of 2880 K. The energy of radiation emitted by this body with wavelength between 499 nm and 500 nm is U1, between 999 nm and 1000 nm is U2 and between 1499 nm and 1500 nm is U3. The Wien's constant, b = 2.88×106 nm-K. Then,