If $A = \{x, y\}$ then the power set of $A$ is

$S=\{(x, y, z): x, y, z \in Z, x+2 y+3 z=42$ $\mathrm{x}, \mathrm{y}, \mathrm{z} \geq 0\}$ ...........

Let $A=\left\{n \in N \mid n^{2} \leq n+10,000\right\}, B=\{3 k+1 \mid k \in N\}$ and $C=\{2 k \mid k \in N\}$, then the sum of all the elements of the set $A \cap(B-C)$ is equal to $.....$

Let $A =\{ x \in R :| x +1|<2\}$ and $B=\{x \in R:|x-1| \geq 2\}$. Then which one of the following statements is NOT true ?

Let $S = \{ x \in R:x \ge 0$ and $2\left| {\sqrt x - 3} \right| + \sqrt x \left( {\sqrt x - 6} \right) + 6 = 0\} $ then $S:$ . . .

If $\mathrm{A}=\{\mathrm{x} \in {R}:|\mathrm{x}-2|>1\}, \mathrm{B}=\left\{\mathrm{x} \in {R}: \sqrt{\mathrm{x}^{2}-3}>1\right\}$, $\mathrm{C}=\{\mathrm{x} \in {R}:|\mathrm{x}-4| \geq 2\}$ and ${Z}$ is the set of all integers, then the number of subsets of the set $(A \cap B \cap C)^{c} \cap {Z}$ is .... .