Some equations are solved on the basis of certain systems. On the same basis find out the correct answer from amongst the four alternatives for the unsolved equation in the question.
a = 12 (390) 8, b = 7 (134) 5, C = 5 (?)12

Options

A. 299
B. 289
C. 279
D. 280

Explanation

To solve the equation based on the given pattern, we will analyze the equations step by step.

### Given Equations:
1. \( a = 12 (390) 8 \)
2. \( b = 7 (134) 5 \)
3. \( C = 5 (?) 12 \)

### Step 1: Analyzing the first equation \( a = 12 (390) 8 \)

- We need to find a pattern. Let's check the operation:
- We take the first number (12) and the last number (8).
- We add them: \( 12 + 8 = 20 \)
- Now, we square this result: \( 20^2 = 400 \)
- Finally, we subtract 10: \( 400 - 10 = 390 \)

This confirms that the pattern works for the first equation.

### Step 2: Analyzing the second equation \( b = 7 (134) 5 \)

- Again, we take the first number (7) and the last number (5).
- We add them: \( 7 + 5 = 12 \)
- We square this result: \( 12^2 = 144 \)
- Finally, we subtract 10: \( 144 - 10 = 134 \)

This confirms that the pattern works for the second equation as well.

### Step 3: Finding the value for \( C = 5 (?) 12 \)

- Now we apply the same pattern:
- We take the first number (5) and the last number (12).
- We add them: \( 5 + 12 = 17 \)
- We square this result: \( 17^2 = 289 \)
- Finally, we subtract 10: \( 289 - 10 = 279 \)

### Conclusion
Thus, the value for \( C \) is \( 279 \).

### Final Answer
The correct answer is \( 279 \).

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