The vertices of a parallelogram in order are A(1, 2), B(4, y), C(x, 6) and D(3, 5). Then (x, y) is:

1. (6, 3)

2. (3, 6)

3. (5, 6)

4. (1, 4)

In a parallelogram, the diagonals bisect each other. Therefore, the mid-point of AC = mid-point of BD.

By mid-point formula,

(x, y) = $\Big(\dfrac{x$1 + x2}{2}, \dfrac{y1 + y2}{2}\Big)

Substituting values, we get :

For diagonal AC :

$\text{Mid-point of AC} = \Big(\dfrac{1 + x}{2}, \dfrac{2 + 6}{2}\Big) = \Big(\dfrac{1 + x}{2}, 4\Big)$

For diagonal BD:

$\text{Mid-point of BD} = \Big(\dfrac{4 + 3}{2}, \dfrac{y + 5}{2}\Big) = \Big(\dfrac{7}{2}, \dfrac{y + 5}{2}\Big)$

Since both mid-points are equal, we equate their coordinates:

$\Rightarrow \Big(\dfrac{1 + x}{2}, 4\Big) = \Big(\dfrac{7}{2}, \dfrac{y + 5}{2}\Big) \\[1em] \Rightarrow \dfrac{1 + x}{2} = \dfrac{7}{2}, 4 = \dfrac{y + 5}{2}\\[1em] \Rightarrow 1 + x = 7, y + 5 = 8 \\[1em] \Rightarrow x = 7 - 1, y = 8 - 5 \\[1em] \Rightarrow x = 6, y = 3.$

(x, y) = (6, 3).

Hence, Option 1 is the correct option.