The longest distance of the point (a, 0) from the curve 2x² + y² = 2x is

• 1 + a

• $\left|1 - \mathrm{a}\right|$

• $\sqrt{1 - 2\mathrm{a} +2{\mathrm{a}}^2}$

• $\sqrt{1 - 2\mathrm{a} + 3{\mathrm{a}}^2}$

If f : R $\to$ R is defined by f(x) = $\left[\frac{\mathrm{x}}{5}\right]$ for x ∈ R, where [y] denotes the greatest integer not exceeding y, then $\left\{\mathrm{f}\left(\mathrm{x}\right) : \left|\mathrm{x}\right| < 71\right\}$ is equal to

• $\left\{- 14, - 13, . . . 0, . . . 13, 14\right\}$

• $\left\{- 14, - 13, . . . 0, . . . 14, 15\right\}$

• $\left\{- 15, - 14, . . . 0, . . . 14, 15\right\}$

• $\left\{- 15, - 14, . . . 0, . . . 13, 14\right\}$