Q. The set of values of $x$ for which the inequalities $x^{2} - 3x - 10 < 0,\ 10x - x^{2} - 16 > 0$ hold simultaneously, is
A) (-2, 5)
B) (2, 8)
C) (-2, 8)
D) (2, 5)
Explanation
(d)
Given inequalities are
$x^{2} - 3x - 10 < 0$ and $10x - x^{2} - 16 > 0$
$\Rightarrow \ \ \ (x + 2)(x - 5) < 0$ and $(x - 2)(x - 8) < 0$
$\Rightarrow \ \ x \in ( - 2,\ 5)$ and $x \in (2,\ 8)$
$\Rightarrow \ \ x \in (2,\ 5)$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.