Hint: When a strong base is added to a solution of a strong acid neutralisation reaction takes place. Equal moles or equal volumes of the sodium hydroxide will react with hydrochloric acid to give sodium chloride and water and will liberate heat. If one compound is exhausted then extra moles of another will be left as it is in the solution and base the solution acidic or basic depending upon which of them is leftover in the solution.
As the volume of sodium hydroxide \[NaOH\] added to the solution of hydrochloric acid \[HCl\] is two times more than the volume of acid where both are of same concentration, here hydrochloric acid is the limiting reagent. The resulting solution will have more portions or more moles of base \[NaOH\] than acid \[HCl\] and hence it will be basic in nature. A basic solution turns the red litmus solution blue. The indicator phenolphthalein turns to pink colour when added to an alkaline solution. Methyl orange indicator gives a yellow colour with alkaline.
Hence, The correct answer is option (B).
Note: The limiting reagent in a chemical reaction is defined as a reactant that is totally consumed when the chemical reaction is completed and there’s no more of this reactant left to react. The amount of product formed is limited by this reagent as the reaction cannot continue without it even if a large amount of the reactants are left.