
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 = ______ .

In the given figure, the blocks $A$, $B$ and $C$ weigh $4\,\text{kg}$, $6\,\text{kg}$ and $8\,\text{kg}$ respectively. The coefficient of sliding friction between any two surfaces is $0.5$. The force $\vec{F}$ required to slide the block $C$ with constant speed is ___ N.
(Given: $g = 10\,\text{m s}^{-2}$) 
Two circular discs of radius \(10\) cm each are joined at their centres by a rod, as shown in the figure. The length of the rod is \(30\) cm and its mass is \(600\) g. The mass of each disc is also \(600\) g. If the applied torque between the two discs is \(43\times10^{-7}\) dyne·cm, then the angular acceleration of the system about the given axis \(AB\) is ________ rad s\(^{-2}\).
