If $[x]$ denotes the greatest integer function, then the solution set of the inequation $\frac{[x] - 1}{2 - [x]} > 0,$ is

R - {2}

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(1, 2)

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ϕ

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R - {1, 2}

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Solution

The correct option is C $ϕ$
$\frac{[x] - 1}{2 - [x]} > 0 \Rightarrow \frac{[x] - 1}{[x] - 2} < 0$
By wavy curve method,
$[x] \in (1, 2)$
Since, $[x]$ is always an integer,
$x \in ϕ$

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