If $X = \{ {4^n} - 3n - 1:n \in N\} $ and $Y = \{ 9(n - 1):n \in N\} ,$ then $X \cup Y$ is equal to

If $\mathrm{S}=\{\mathrm{a} \in \mathrm{R}:|2 \mathrm{a}-1|=3[\mathrm{a}]+2\{\mathrm{a}\}\}$, where $[\mathrm{t}]$ denotes the greatest integer less than or equal to $t$ and $\{t\}$ represents the fractional part of $t$, then $72 \sum_{\mathrm{a} \in \mathrm{S}} \mathrm{a}$ is equal to....................

If $X = \{ {8^n} - 7n - 1:n \in N\} $ and $Y = \{ 49(n - 1):n \in N\} ,$ then

Let $S=\{1,2,3, \ldots \ldots, n\}$ and $A=\{(a, b) \mid 1 \leq$ $a, b \leq n\}=S \times S$. A subset $B$ of $A$ is said to be a good subset if $(x, x) \in B$ for every $x \in S$. Then, the number of good subsets of $A$ is

Let $A = \{x:x \in R,\,|x|\, < 1\}\,;$ $B = \{x:x \in R,\,|x - 1| \ge 1\}$ and $A \cup B = R - D,$then the set $D$ is