Q205 / 270 · NDA 2016 (Phase 2) · Mathematics

If the point $(a, a)$ lies between the lines $|x+y|=2$, then which one of the following is correct?

  • A
    $|a| \lt 2$
  • B
    $|a| \lt \sqrt{2}$
  • Correct answer
    C
    $|\mathrm{a}| \lt 1$
  • D
    $|a| \lt \frac{1}{\sqrt{2}}$

Solution

$\begin{aligned} & |\mathrm{x}+\mathrm{y}|=2 \Rightarrow \mathrm{x}+\mathrm{y}= \pm 2 \\ & \Rightarrow \mathrm{x}+\mathrm{y}+2=0 \text { and } \mathrm{x}+\mathrm{y}-2=0 \\ & \Rightarrow-2 \lt 2 \mathrm{a} \lt 0 \text { and }-1 \lt \mathrm{a} \lt 0 \\ & \Rightarrow|\mathrm{a}| \lt 1\end{aligned}$

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

More Straight Lines Questions