A: 50 ml, decinormal HCl when mixed with 50 ml, decinormal `H_(2) SO_(4)`, then normality of `H^(+)` ion in resultant solution is 0.1 N.
R: Here, `MV = M_(1)V_(1) - M_(2)V_(2)`

Options

A. If both Assertion & Reason are true and the reason is the correct explanation of the assertion
B. If both Assertion & Reason are true but the reason is not the correct explanation of the assertion
C. If Assertion is true statement but Reason is false
D. If both Assertion and Reason are false statements

Answer

To solve the problem, we need to determine the normality of \( H^+ \) ions in the resultant solution when 50 mL of decinormal \( HCl \) is mixed with 50 mL of decinormal \( H_2SO_4 \).

### Step 1: Understand the given concentrations
- \( HCl \) is decinormal, which means its normality \( N_1 = 0.1 \, N \).
- \( H_2SO_4 \) is also decinormal, so its normality \( N_2 = 0.1 \, N \).

### Step 2: Determine the volumes of the solutions
- Volume of \( HCl \) solution, \( V_1 = 50 \, mL \).
- Volume of \( H_2SO_4 \) solution, \( V_2 = 50 \, mL \).

### Step 3: Calculate the total volume of the mixed solution
- Total volume \( V_f = V_1 + V_2 = 50 \, mL + 50 \, mL = 100 \, mL \).

### Step 4: Calculate the total equivalents of \( H^+ \) ions from both acids
- For \( HCl \), it releases 1 equivalent of \( H^+ \) per mole, so:
\[ \text{Equivalents from } HCl = N_1 \times V_1 = 0.1 \, N \times 50 \, mL = 5 \, equivalents \]

- For \( H_2SO_4 \), it releases 2 equivalents of \( H^+ \) per mole, so:
\[ \text{Equivalents from } H_2SO_4 = N_2 \times V_2 \times 2 = 0.1 \, N \times 50 \, mL \times 2 = 10 \, equivalents \]

### Step 5: Calculate the total equivalents of \( H^+ \) ions in the resultant solution
- Total equivalents of \( H^+ \) ions:
\[ \text{Total } H^+ = 5 + 10 = 15 \, equivalents \]

### Step 6: Calculate the normality of \( H^+ \) ions in the resultant solution
- Normality of \( H^+ \) ions in the final solution:
\[ N_f = \frac{\text{Total equivalents of } H^+}{\text{Total volume in L}} = \frac{15 \, equivalents}{0.1 \, L} = 0.15 \, N \]

### Step 7: Conclusion
The assertion states that the normality of \( H^+ \) ions in the resultant solution is \( 0.1 \, N \), which is incorrect based on our calculations. Therefore, the assertion is false.