Q205 / 270 · NDA 2022 (Phase 1) · Mathematics

Consider the inequations $5 x-4 y+12 \lt 0, x+y \lt 2, x \lt 0$ and $y \gt 0$. Which one of the following points lies in the common region?

  • A
    $(0,0)$
  • B
    $(-2,4)$
  • C
    $(-1,4)$
  • Correct answer
    D
    $(-1,2)$

Solution

(a) $\because x \gt 0$ and $y \gt 0$ So $(0,0)$ not lies in region (b) $-2+4=2$ is not less than 2 So, $(-2,4)$ not lies in region (c) $-1+4=3 \gt 2$ So, $(-1,4)$ not lies in region (d) $-1+2=1 \lt 2$ and $5(-1)-4(2)+12=-5-8+12=-1 \lt 0$ Since, satisfy all inequation So, $(-1,2)$ lies in region

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

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