The distance between the points (4, p) and (1, 0) is 5 units, then the value of p is

1. 4 only

2. -4 only

3. ±4

4. 0

By distance formula,

d = $\sqrt{(x$2 - x1)^2 + (y2 - y1)^2}

Given,

Distance between (4, p) and (1, 0) is 5 units.

$\therefore 5 = \sqrt{(1 - 4)^2 + (0 - p)^2} \\[1em] \Rightarrow 5 = \sqrt{(-3)^2 + (-p)^2} \\[1em] \Rightarrow 5 = \sqrt{9 + p^2} \\[1em] \Rightarrow p^2 + 9 = 5^2 \text{ [On squaring both sides]} \\[1em] \Rightarrow p^2 + 9 = 25 \\[1em] \Rightarrow p^2 = 16 \\[1em] \Rightarrow p = \sqrt{16} \\[1em] \Rightarrow p = \pm 4.$

Hence, Option 3 is the correct option.