The value of `9xx[(9-4)div{(8div" of "4)+(4div4 " of "2)}]` is :

Options

A. a)20
B. b)60
C. c)`(45)/(4)`
D. d)`(45)/(2)`

Answer

To solve the expression \( 9 \times \left[ (9 - 4) \div \left\{ \left( 8 \div 4 \right) + \left( 4 \div 4 \times 2 \right) \right\} \right] \), we will follow the order of operations (BODMAS/BIDMAS).

### Step-by-step Solution:

1. **Calculate the innermost brackets**:
- Start with \( 8 \div 4 \):
\[ 8 \div 4 = 2 \]

2. **Calculate the next part**:
- Now calculate \( 4 \div 4 \):
\[ 4 \div 4 = 1 \]
- Then multiply this result by 2:
\[ 1 \times 2 = 2 \]

3. **Combine the results in the curly brackets**:
- Now add the results from steps 1 and 2:
\[ 2 + 2 = 4 \]

4. **Substitute back into the expression**:
- The expression now looks like:
\[ 9 \times \left[ (9 - 4) \div 4 \right] \]

5. **Calculate \( 9 - 4 \)**:
\[ 9 - 4 = 5 \]

6. **Now divide by 4**:
\[ 5 \div 4 = \frac{5}{4} \]

7. **Finally, multiply by 9**:
\[ 9 \times \frac{5}{4} = \frac{45}{4} \]

Thus, the final value of the expression is:
\[ \frac{45}{4} \]