UPSC NDA Math Model Paper 4

For x < 0, y = -x - 1 and y = x + 1 y = -x - 1, when x = 0, y = -1 ⇒ (0, -1) and when y = 0, x = -1 ⇒ (-1, 0) And y = x + 1, when x = 0, y = 1 ⇒ (0, 1) and y = 0, x = -1 ⇒ (-1, 0) For x > 0, y = x - 1 and y = -x + 1 y = x - 1, when x = 0, y = -1, (0, -1) and when y = 0, x = 1 ⇒ (1, 0) And, y = -x + 1, when x = 0, y = 1, (0, 1) and when y = 0, x = 1 ⇒ (1, 0) We get square, now length of side = distance between any two points Consider points (1, 0) and (0, 1) Distance $=\sqrt{(1-0)^2+(0-1)^2}=\sqrt{2}$ Area of square $=(\sqrt{2})^{2}$ = 2 sq units Hence, option (3) is correct.