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If the points of intersection of lines $L_{1} : y - m_{1} x - k = 0 & L_{2} : y - m_{2} x - k = 0 (m_{1} \neq m_{2})$ lies inside the triangle formed by the lines $2 x + 3 y = 1, x + 2 y = 3 & 5 x - 6 y - 1 = 0$ , then true set of values of k are

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$(\frac{1}{3}, \frac{3}{2})$

$(\frac{1}{2}, 1)$

$(0, \frac{3}{2})$

$(\frac{- 3}{2}, 0)$

answer is C.

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Detailed Solution

Clearly point of intersection of $L_{1}$ and $L_{2}$ , is (0,k) which lies on y-axis

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