Question

If \( \oplus \div \odot = 2; \ \oplus \div \Delta = 3; \ \odot + \Delta = 5; \ \Delta \times \otimes = 10,\) 

Then, the value of \( (\otimes - \oplus)^2 \) is:
 

• A. 0
• B. 1
• C. 4
• D. 16

Hint:

When solving for unknowns in equations involving operations, express the variables in terms of each other and substitute to simplify the calculations.

Answer 1

The Correct Option is B

To solve the given problem, let's first decode the mathematical representation using symbols and operations:

We have the following equations based on the given information:

1. \(\oplus \div \odot = 2\)
2. \(\oplus \div \Delta = 3\)
3. \(\odot + \Delta = 5\)
4. \(\Delta \times \otimes = 10\)

We need to find the value of \((\otimes - \oplus)^2\).

Let's analyze each equation step-by-step:

• From Equation 1: \(\oplus = 2 \cdot \odot\)
• From Equation 2: \(\oplus = 3 \cdot \Delta\)

This implies \(2 \cdot \odot = 3 \cdot \Delta\). Therefore, \(\odot = \frac{3}{2} \cdot \Delta\).

Substitute \(\odot = \frac{3}{2} \cdot \Delta\) into Equation 3:

\(\frac{3}{2} \cdot \Delta + \Delta = 5\).

Simplifying this equation:

\(\frac{5}{2} \cdot \Delta = 5\).

\(\Delta = 2\).

Using \(\Delta = 2\) in Equation 4:

\(2 \times \otimes = 10\) which implies \(\otimes = 5\).

With \(\Delta = 2\), find \(\oplus\):

\(\oplus = 3 \cdot \Delta = 3 \cdot 2 = 6\).

Now calculate \((\otimes - \oplus)^2\):

\((\otimes - \oplus)^2 = (5 - 6)^2 = (-1)^2 = 1\).

Thus, the value of \((\otimes - \oplus)^2\) is 1