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If a, b, c are in arithmetic progression, evaluate the determinant | x+1 x+2 x+a; x+2 x+3 x+b; x+3 x+4 x+c |.

1. a + b + c
2. x + a + b + c
3. 0
4. none of these

Correct answer: 0

Solution

After row reduction the determinant equals -(a - 2b + c), which is 0 when a, b, c are in AP.

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