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JEE Main · 2024 · 08 Apr 2024 · Shift 2 · Determinants

If

α \neq = a, β \neq = b, γ \neq = c

and

α a a b β b c c γ = 0

, then

\frac{a}{α - a} + \frac{b}{β - b} + \frac{γ}{γ - c}

is equal to :

(A)2
(B)3
(C)0✓ Correct
(D)1

Answer: (C)

Solution

Row-reduce the determinant:

R_{1} \to R_{1} - R_{2}

,

R_{2} \to R_{2} - R_{3}

:

α - a 0 a b - β β - b b 0 c - γ γ = 0

Expanding and dividing through by

(α - a) (β - b) (γ - c)

leads directly to

\frac{a}{α - a} + \frac{b}{β - b} + \frac{γ}{γ - c} = 0

JEE Main · 2024 · 08 Apr 2024 · Shift 2 · Single correct option

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