1. The phrase “by above sequence of reactions” in this haloalkanes context typically refers to the Wurtz reaction:

$2RBr + 2Na \xrightarrow[\text{dry ether}]{} R-R + 2NaBr$

So we need to find how many different structural isomers of alkyl bromides, $RBr$, can give 2-methylbutane on coupling.

2. Target hydrocarbon:

$\text{2-methylbutane} = CH_3-CH(CH_3)-CH_2-CH_3$

In Wurtz reaction using only one kind of alkyl bromide $RBr$, the product is:

$R-R$

Hence the target alkane must be splittable into two identical alkyl fragments.

3. Let us check whether 2-methylbutane can be written as $R-R$ for some alkyl group $R$.

2-methylbutane has 5 carbons. If it were formed as $R-R$, total carbons would be:

$2 \times (\text{number of carbons in } R) = 5$

This is impossible, since 5 is odd.

So one single alkyl bromide cannot give 2-methylbutane by self-coupling.

4. Therefore, the only way to get 2-methylbutane in Wurtz reaction is by cross coupling of two different alkyl bromides:

$RBr + R'Br + 2Na \to R-R' + 2NaBr$

Now split 2-methylbutane across each C–C bond and see which pair of alkyl bromides can form it.

Structure with labels:

$CH_3-CH(CH_3)-CH_2-CH_3$

There are 4 C–C bonds to consider effectively as distinct cuts:

Cut 1: between terminal $CH_3$ and $CH$

Fragments:

• $CH_3\cdot$ = methyl
• $\cdot CH(CH_3)-CH_2-CH_3$ = sec-butyl

This gives bromides:

• $CH_3Br$ (bromomethane)
• $CH_3CH(Br)CH_2CH_3$ (2-bromobutane)

Cut 2: between $CH$ and $CH_2$

Fragments:

• $(CH_3)_2CH\cdot$ = isopropyl
• $\cdot CH_2CH_3$ = ethyl

This gives bromides:

• $(CH_3)_2CHBr$ (2-bromopropane)
• $CH_3CH_2Br$ (bromoethane)

Cut 3: between branched $CH_3$ and central $CH$

This is equivalent to Cut 1, again giving:

• methyl + sec-butyl

So no new bromides.

5. Collect all distinct structural isomers of $RBr$ involved:

6. $CH_3Br$

7. $CH_3CH(Br)CH_2CH_3$ (2-bromobutane)

8. $CH_3CH_2Br$ (bromoethane)

9. $(CH_3)_2CHBr$ (2-bromopropane)

Thus, the maximum number of distinct structural isomeric alkyl bromides that can produce 2-methylbutane is:

$4$

6. Therefore the correct option is:

$\boxed{4}$

which corresponds to Option C.