What will come in place of the question mark(?) in the following questions ? (a,b,c are integers)
`? xx(absaxxabsb)=-ab`

Options

A. -1
B. 1
C. 0
D. c

Answer

To solve the equation given in the question, we need to find the value of the question mark (?) in the expression:

\[ ? \cdot |a| \cdot |b| = -ab \]

### Step-by-Step Solution:

1. **Start with the given equation:**
\[ ? \cdot |a| \cdot |b| = -ab \]

2. **Isolate the question mark (?):**
To isolate the question mark, we can divide both sides of the equation by \(|a| \cdot |b|\):
\[ ? = \frac{-ab}{|a| \cdot |b|} \]

3. **Simplify the right-hand side:**
We know that \(|a|\) is the absolute value of \(a\) and \(|b|\) is the absolute value of \(b\). The expression can be simplified as follows:
\[ ? = -\frac{ab}{|a| \cdot |b|} \]

4. **Evaluate the fraction:**
The fraction \(\frac{ab}{|a| \cdot |b|}\) can be evaluated based on the signs of \(a\) and \(b\):
- If \(a\) and \(b\) are both positive, \(|a| = a\) and \(|b| = b\), thus \(\frac{ab}{|a| \cdot |b|} = 1\).
- If \(a\) is positive and \(b\) is negative, \(|b| = -b\), thus \(\frac{ab}{|a| \cdot |b|} = -1\).
- If \(a\) is negative and \(b\) is positive, \(|a| = -a\), thus \(\frac{ab}{|a| \cdot |b|} = -1\).
- If both \(a\) and \(b\) are negative, \(|a| = -a\) and \(|b| = -b\), thus \(\frac{ab}{|a| \cdot |b|} = 1\).

In all cases, we can conclude that:
\[ ? = -1 \]

5. **Final Answer:**
Therefore, the value that comes in place of the question mark (?) is:
\[ ? = -1 \]