UPSC NDA Math Model Paper 1

Concept:
The Modulus Fucntion '| |' is defines as: |x|={

x,	x≥0
−x,	x<0

Calculation:
Let's make a list of the different equations for different combinations of x, y≥0 and x, y<0

Cases	Equation
x≥0 AND y≥0	x+y= 1
x≥0 AND y<0	x-y= 1
x<0 AND y≥0	-x+y= 1
x<0 AND y<0	-x-y= 1

The graph of the curve |x|+|y|=1 will look like this:
The area of the above figure wil be:4 × Area of the small triangle.
= 4×(

1

2

×1×1)
= 2 square units.