Correct option is b. phenolphthaline
Reaction of an acid with a base generates heat. If you try to titrate a solution of ammonia with sulfuric acid, it is possible that the reaction mixture will become hot, and some of the ammonia in the solution will volatilize (escape) from it. This could lead to under-estimating the amount of ammonia present in solution.
In order to avoid this possibility, it is better to carry out a back-titration, wherein the ammonium hydroxide is carefully reacted with an EXCESS of standard (e.g. 0.1N) sulfuric acid. The resulting solution will contain ammonium sulfate [{NH4)2SO4} and unreacted sulfuric acid.
If you then take this reaction mixture, and titrate it against standard (e.g. 0.1N) sodium hydroxide using phenolphthaline indicator, you can precisely determine the amount of unreacted sulfuric acid that is present in the reaction mixture. By subtracting the amount of acid that remained unreacted from the total amount of standard sulfuric acid originally added to the reaction, you can determine the amount of sulfuric acid that would have reacted with the ammonia present in the aqueous NH4OH solution. This is also the same amount (normality) of ammonia that was originally present in the ammonia solution.
NH3 + H2O <==> NH4OH
NH4OH + 1/2 H2SO4 → {NH4)2SO4 + H2)
NaOH + 1/2 H2SO4 → Na2SO4 + H2O