For $l \in R$ the equation $(2 l - 3) x^{2} + 2 l x y - y^{2} = 0$ represents a pair of distinct lines

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for all values of $l \in (- 3, 1)$

for all values of $l \in R - (0, 1)$

for all values of $l \in R - [- 3, 1]$

only when $l = 0$

answer is D.

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Detailed Solution

$\begin{array}{l} (2 l - 3) x^{2} + 2 l x y - y^{2} = 0 \\ h^{2} > a b \Rightarrow l^{2} - 2 l - 3 > 0 \end{array}$
$\begin{array}{l} \Rightarrow (l + 3) (l - 1) > 0 \\ \Rightarrow l \in R - [- 3, 1] \end{array}$

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