Q53 / 160 · AP EAMCET 2018 (23 Apr Shift 2) · Mathematics

If $[x]$ denotes the greatest integer not exceeding $x$, then the values of $x$ satisfying $[x]^2-7[x]+12 \leq 0$ are

  • A
    $1 \leq x < 4$
  • Correct answer
    B
    $3 \leq x < 5$
  • C
    $-5 < x \leq-3$
  • D
    $2 \leq x \leq 4$

Solution

$\begin{aligned} & \text { Given equation, } \\ & \qquad[x]^2-7[x]+12 \leq 0 \\ & \Rightarrow \quad[x]^2-4[x]-3[x]+12 \leq 0 \\ & \Rightarrow \quad([x]-4)([x]-3) \leq 0 \quad \Rightarrow \quad[x] \in[3,4] \\ & \Rightarrow \quad x \in[3,5) .\end{aligned}$

Hence, the correct answer is option: 'B'.

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