jee-main 2024 Q61

jee-main · India · session1_31jan_shift1 Inequalities Quadratic Inequality Holding for All x (or a Restricted Domain)

Let $S$ be the set of positive integral values of $a$ for which $\frac { a x ^ { 2 } + 2 a + 1 x + 9 a + 4 } { x ^ { 2 } - 8 x + 32 } < 0 , \quad \forall x \in \mathbb { R }$. Then, the number of elements in $S$ is:
(1) 1
(2) 0
(3) $\infty$
(4) 3

Let $S$ be the set of positive integral values of $a$ for which $\frac { a x ^ { 2 } + 2 a + 1 x + 9 a + 4 } { x ^ { 2 } - 8 x + 32 } < 0 , \quad \forall x \in \mathbb { R }$. Then, the number of elements in $S$ is:\\
(1) 1\\
(2) 0\\
(3) $\infty$\\
(4) 3

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