Which one of the following options is correct in the given expression?
`1 + [1 div {5 div 4 - 1 div (13 div 3 - 1 div 3)}]` equal to :

Options

A. `2//5`
B. `2`
C. `3//2`
D. None of these

Answer

To solve the expression \( 1 + \left[ 1 \div \left\{ 5 \div 4 - 1 \div \left( 13 \div 3 - 1 \div 3 \right) \right\} \right] \), we will follow the order of operations, commonly referred to as BODMAS/BIDMAS (Brackets, Orders, Division and Multiplication, Addition and Subtraction).

### Step-by-Step Solution:

1. **Identify the innermost brackets**:
We start with the expression inside the round brackets: \( 13 \div 3 - 1 \div 3 \).

\[ 13 \div 3 = \frac{13}{3} \]
\[ 1 \div 3 = \frac{1}{3} \]

Now, we compute \( \frac{13}{3} - \frac{1}{3} \):
\[ \frac{13}{3} - \frac{1}{3} = \frac{13 - 1}{3} = \frac{12}{3} = 4 \]

2. **Substitute back into the expression**:
Now we substitute this result back into the curly brackets:
\[ 1 + \left[ 1 \div \left\{ 5 \div 4 - 1 \div 4 \right\} \right] \]

3. **Calculate the curly brackets**:
Now we need to solve \( 5 \div 4 - 1 \div 4 \):
\[ 5 \div 4 = \frac{5}{4} \]
\[ 1 \div 4 = \frac{1}{4} \]

Now, we compute \( \frac{5}{4} - \frac{1}{4} \):
\[ \frac{5}{4} - \frac{1}{4} = \frac{5 - 1}{4} = \frac{4}{4} = 1 \]

4. **Substitute back into the expression**:
Now we substitute this result back into the square brackets:
\[ 1 + \left[ 1 \div 1 \right] \]

5. **Calculate the square brackets**:
Now we compute \( 1 \div 1 \):
\[ 1 \div 1 = 1 \]

6. **Final addition**:
Now we have:
\[ 1 + 1 = 2 \]

### Conclusion:
The final result of the expression \( 1 + \left[ 1 \div \left\{ 5 \div 4 - 1 \div (13 \div 3 - 1 \div 3) \right\} \right] \) is \( 2 \).