Question

The shaded region is represented by the inequation :

(a) y ≥ x  

(b) y ≥ x

(c) y ≥ | x |

(d) y ≤ | x |

Answer 1

(c) y ≥ |x|

y ≥ | x |  ⇒  y x ≥ or y  ≥  - x          \(\bigg[∵|x|=\bigg\{\begin{matrix}-x,x<0\\ x,x>0 \end{matrix}\bigg\}\bigg]\)

∴  x – y ≤ 0 or y + x ≥ 0 

Plotting the points for x – y = 0, we get the 

points (0, 0) (1, 1) (2, 2) etc. 

Plotting the points for x + y = 0, we get the 

points (0, 0) (1, –1) (2, –2) etc. 

∴ (c) is the required option.