If vmatrix x^2+x & x+1 & x-2 2x^2+3x-1 & 3x & 3x-3 x^2+2x+3 & 2x-1 & 2x-1 vmatrix = ax - 12, then a is equal to:

JEE Main 2015 Mathematics question

If , then is equal to:

(1)
(2)24Correct
(3)
(4)12

Answer: (2)

Solution

Look for a row relation. Adding rows 1 and 3 gives , which differs from row 2 only in the first entry: . Replacing by leaves the determinant unchanged, so

Δ = +x & x+1 & x-2 -4 & 0 & 0 +2x+3 &

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Question ID VK-115391