JEE Advance - Mathematics (1983 - No. 44)
The function $$y = 2{x^2} - In\,\left| x \right|$$ is monotonically increasing for values of $$x\left( {x \ne 0} \right)$$ satisfying the inequalities ......... and monotonically decreasing for values of $$x$$ satisfying the inequalities ............
$$x \in ( -\infty , -\frac{1}{2} ) \cup ( \frac{1}{2}, \infty )$$; $$x \in ( -\frac{1}{2}, 0 ) \cup ( 0, \frac{1}{2} )$$
$$x \in ( 0, \infty )$$; $$x \in ( -\infty, 0 )$$
$$x \in ( -\frac{1}{2}, 0 ) \cup ( \frac{1}{2}, \infty )$$; $$x \in ( -\infty, -\frac{1}{2} ) \cup ( 0, \frac{1}{2} )$$
$$x \in ( -\infty, -\frac{1}{2} )$$; $$x \in ( \frac{1}{2}, \infty )$$
$$x \in ( \frac{1}{2}, \infty )$$; $$x \in ( -\infty, -\frac{1}{2} )$$