UPSC NDA I 2016 Mathematics Solved Paper

Concept:The intersection points of two curves satisfy both equations simultaneously.Here, one curve is defined by $y = |x-1|$ and the other curve consists of two vertical lines: $x = 2$ and $x = -2$.To find intersection points, substitute each $x$ value into the first curve and compute $y$.Explanation:The curve $y = |x-1|$ can be written as:$y = \begin{cases} 1 - x, & x < 1 \\ x - 1, & x \ge 1 \end{cases}$For $x = 2$: Since $2 \ge 1$, use $y = x - 1 = 2 - 1 = 1$. So the point is $(2, 1)$.For $x = -2$: Since $-2 < 1$, use $y = 1 - x = 1 - (-2) = 3$. So the point is $(-2, 3)$.Both points satisfy both curves. Therefore, they are the points of intersection.Answer:$(-2, 3)$ and $(2, 1)$