The reaction sequence(s) that would lead to o-xylene as the major product is(are)

The target molecule is $$o$$-xylene, i.e. $$1,2$$-dimethylbenzene. To obtain two methyl groups ortho to each other we must make sure that the para position is blocked before the second methyl group is introduced. The only sequence that does this efficiently is given in Option A.

Step 1 (Option A)
Starting compound: toluene. Treat it with conc. $$H_2SO_4$$ (≈ 20-30 °C).
The methyl group is an ortho/para director; however, sulphonation at this temperature is para-selective because of steric hindrance in the ortho positions.
Reaction: $$\underset{\text{toluene}}{C_6H_5CH_3} \xrightarrow[20-30^{\circ}\mathrm{C}]{H_2SO_4/SO_3} C_6H_4(CH_3)(SO_3H)\ (\text{major para})$$

Thus the para position is now occupied by $$SO_3H$$, while both ortho positions remain available.

Step 2 (Option A)
Carry out a Friedel-Crafts alkylation with $$CH_3Cl/AlCl_3$$.
Because the para position is blocked by $$SO_3H$$, the incoming $$CH_3^+$$ can enter only the ortho positions relative to the original methyl group.
Reaction: $$C_6H_4(CH_3)(SO_3H) \xrightarrow[AlCl_3]{CH_3Cl} C_6H_3(CH_3)_2(SO_3H)$$(methyl enters ortho).

Step 3 (Option A)
Desulphonate the ring by heating with dilute acid/steam.
$$C_6H_3(CH_3)_2(SO_3H)\ \xrightarrow[\text{steam}]{\Delta,\, H^+} C_6H_4(CH_3)_2 \;=\; o\text{-xylene}$$

The $$SO_3H$$ group is removed cleanly, leaving two adjacent methyl groups; hence the major product is $$o$$-xylene.

Why the other options fail
• Options that attempt two successive Friedel-Crafts methylations on benzene or on toluene without a temporary blocking group give a mixture in which the para isomer predominates (steric hindrance disfavors ortho).
• Options that introduce a meta-directing group (−NO2, −COOH, etc.) before the second methyl group place the second methyl meta, not ortho, to the first one.
• Any sequence that removes the first directing methyl group (e.g., through oxidation) loses regiocontrol.

Therefore only Option A supplies a blocking group at the para position, introduces the second methyl group ortho to the first, and finally removes the blocker to give $$o$$-xylene in high yield.

Final answer: Option A which is: $$\text{toluene} \; \xrightarrow{H_2SO_4} \; p\text{-toluenesulphonic acid} \; \xrightarrow{CH_3Cl/AlCl_3} \; o\text{-methyl-}p\text{-toluenesulphonic acid} \; \xrightarrow{\text{heat, H}_2O} \; o\text{-xylene}.$$