What approximate value will come in place of the question mark (?) in the following questions ? (You are not expected to calculate the exact value.)
`((7.82)^2-(2.07)^2)/((4.96))=?xx3.17`

Options

A. 14
B. 11
C. 9
D. 4

Answer

To solve the equation \(\frac{(7.82)^2 - (2.07)^2}{4.96} = ? \times 3.17\), we will approximate the numbers involved for easier calculation.

### Step-by-Step Solution:

1. **Approximate the Values**:
- Approximate \(7.82\) to \(8\).
- Approximate \(2.07\) to \(2\).
- Approximate \(4.96\) to \(5\).

So, we rewrite the expression as:
\[ \frac{(8)^2 - (2)^2}{5} \]

2. **Calculate the Squares**:
- Calculate \(8^2 = 64\).
- Calculate \(2^2 = 4\).

Now, substitute these values into the expression:
\[ \frac{64 - 4}{5} \]

3. **Perform the Subtraction**:
- Subtract \(4\) from \(64\):
\[ 64 - 4 = 60 \]

4. **Divide by 5**:
- Now divide \(60\) by \(5\):
\[ \frac{60}{5} = 12 \]

5. **Set Up the Equation**:
- We have:
\[ 12 = ? \times 3.17 \]

6. **Solve for ?**:
- To find \(?\), divide \(12\) by \(3.17\):
\[ ? = \frac{12}{3.17} \]

7. **Approximate the Division**:
- Since \(3.17\) is approximately \(3\), we can simplify:
\[ ? \approx \frac{12}{3} = 4 \]

### Final Answer:
The approximate value that will come in place of the question mark (?) is **4**.

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