Identify compound A formed in the reaction

The reaction implied here is the formation of a sodium acetylide from a terminal alkyne. A terminal alkyne such as propyne, $\mathrm{CH_3-C\equiv CH}$ on treatment with a strong base like sodium amide gives $\mathrm{CH_3-C\equiv C^-\ Na^+}$

So the intermediate compound $A$ should be the sodium salt of a terminal alkyne.

Nature of reaction with B

Sodium acetylides are strong nucleophiles and react with primary alkyl halides via $S_N2$ reaction to form a higher alkyne.

General reaction: $\mathrm{R-C\equiv C^-\ Na^+ + R'-Br \rightarrow R-C\equiv C-R' + NaBr}$

Check the options

Option A

$A=\mathrm{CH_3-C\equiv C^-\ Na^+},\quad B=\mathrm{CH_3-CH_2-CH_2-Br}$ Reaction: $\mathrm{CH_3-C\equiv C^-\ Na^+ + CH_3CH_2CH_2Br \rightarrow CH_3-C\equiv C-CH_2CH_2CH_3}$ This gives an internal alkyne, which is a standard alkylation of sodium acetylide with a primary alkyl bromide.

So this is correct.

Option B

$A=\mathrm{CH_3-CH=CH_2},\quad B=\mathrm{CH_3-CH_2-CH_2-Br}$ Propene does not behave like an acetylide ion and will not undergo the required nucleophilic substitution to form the expected alkyne product.

So this is incorrect.

Option C

$A=\mathrm{CH_3-C\equiv C^-\ Na^+},\quad B=\mathrm{CH_3-CH_2-CH_3}$ Propane is an alkane, not a good electrophile, and cannot react with sodium acetylide in this way.

So this is incorrect.

Option D

$A=\mathrm{CH_3-CH_2-CH_3},\quad B=\mathrm{CH_3-C\equiv CH}$ Propane is not the reactive intermediate formed, and terminal alkyne alone is not the electrophile for this coupling.

So this is incorrect.

Conclusion

The only feasible pair is: $A=\mathrm{CH_3-C\equiv C^-\ Na^+},\quad B=\mathrm{CH_3-CH_2-CH_2-Br}$

Hence, the correct option is A.