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$If t h e s y s t e m o f l i n e a r e q u a t i o n s x + k y + 3 z = 0, 3 x + k y - 2 z = 0, 2 x + 4 y - 3 z = 0 h a s a n o n - z e r o s o l u t i o n (x, y, z) t h e n \frac{x z}{y^{2}} i s e q u a l t o$

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-10

answer is A.

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Detailed Solution

For non-zero solution, $Δ = 0$

We get k = 11

On $(2) - (1) : 2 x = 5 z \Rightarrow x = \frac{5 z}{2}$

$from (1) : z = - 2 y \Rightarrow y = \frac{- z}{2}$

$∴ \frac{x z}{y^{2}} = 10$

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