NIMCET 2013 — Mathematics PYQ

Solution

Equations of the Boundary:

The curve $|x|+|y|=1$ consists of four straight lines depending on the quadrants:

1. Quadrant I ($x\ge 0,y\ge 0$): $x+y=1$

2. Quadrant II (x < 0, y \ge 0): $-x+y=1$

3. Quadrant III (x < 0, y < 0): $-x-y=1$

4. Quadrant IV (x \ge 0, y < 0): $x-y=1$

Shape Identification:

These four lines form a square with vertices at:

Area Calculation:

The region is composed of $4$ identical right-angled triangles (one in each quadrant).

Alternative Method (Diagonal of Square):

The length of the diagonal $d$ (from $(-1,0)$ to $(1,0)$) is $2$.