When 2 mL of sodium hydroxide solution is added to few pieces of granulated zinc in a test tube and then warmed, the reaction that occurs can be written in the form of a balanced chemical equation as :

In this reaction, a base (sodium hydroxide) reacts with a metal (zinc) to produce a salt (sodium zincate) and hydrogen gas.

• Option (b) is correct because it correctly identifies the chemical formula of sodium zincate as $\mathrm{Na}_2\mathrm{ZnO}_2$ and shows the evolution of hydrogen gas ($\mathrm{H}_2$) with balanced coefficients.
• Option (a) is incorrect because the formula for sodium zincate is wrong and it incorrectly lists water as a product.
• Option (c) is incorrect because the formula for sodium zincate is written as $\mathrm{NaZnO}_2$, which is chemically inaccurate.
• Option (d) is incorrect because it suggests the formation of water ($\mathrm{H}_2\mathrm{O}$) instead of hydrogen gas.