1. Interpret the given data

   We are told that 1 g of the base furnishes $0.04$ mole of $\text{OH}^-$ in aqueous solution.

   So, the total basic equivalents produced by $1$ g of the base are: $0.04 \text{ equivalent}$ because for hydroxide ion, $1 \text{ mole of } \text{OH}^- = 1 \text{ equivalent}$

2. Condition for neutralization

   In an acid-base neutralization: $\text{acid equivalents} = \text{base equivalents}$

   Therefore, acid required $= 0.04$ equivalent.

3. Use normality relation

   The acid is a $0.1\text{ N}$ dibasic acid.

   Since normality is already given, we directly use: $\text{equivalents} = N \times V(\text{in L})$

   Hence, $0.04 = 0.1 \times V$

   $V = \frac{0.04}{0.1} = 0.4 \text{ L}$

4. Convert to mL

   $0.4 \text{ L} = 400 \text{ mL}$

5. Check options

   • A: $200$ mL
   • B: $400$ mL
   • C: $600$ mL
   • D: $800$ mL

   Therefore, the correct option is B.

Comparison with stored answer: Stored correct answer is B, which matches the derived result.