Let ℝ denote the set of all real numbers. Let $z_1 = 1 + 2i$ and $z_2 = 3i$ be two complex numbers, where $i = \sqrt{-1}$. Let

$$S = \{(x, y) \in \mathbb{R} \times \mathbb{R} : |x + iy - z_1| = 2|x + iy - z_2| \}.$$

Then which of the following statements is (are) TRUE?

Let the set of all relations $R$ on the set $\{a, b, c, d, e, f\}$, such that $R$ is reflexive and symmetric, and $R$ contains exactly $10$ elements, be denoted by $\mathcal{S}$.

Then the number of elements in $\mathcal{S}$ is ________________.

For any two points $M$ and $N$ in the $XY$-plane, let $\overrightarrow{MN}$ denote the vector from $M$ to $N$, and $\vec{0}$ denote the zero vector. Let $P, Q$ and $R$ be three distinct points in the $XY$-plane. Let $S$ be a point inside the triangle $\triangle PQR$ such that

$$\overrightarrow{SP} + 5\; \overrightarrow{SQ} + 6\; \overrightarrow{SR} = \vec{0}.$$

Let $E$ and $F$ be the mid-points of the sides $PR$ and $QR$, respectively. Then the value of

$\frac{\text { length of the line segment } E F}{\text { length of the line segment } E S}$

is ________________.

Let $S$ be the set of all seven-digit numbers that can be formed using the digits $0, 1$ and $2$. For example, $2210222$ is in $S$, but $0210222$ is NOT in $S$.

Then the number of elements $x$ in $S$ such that at least one of the digits $0$ and $1$ appears exactly twice in $x$, is equal to ____________.