The number of elements in the set $\left\{ n \in N : 10 \leq n \leq 100\right.$ and $3^{ n }-3$ is a multiple of $7\}$ is $........$.

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 $S:$ . . .

Let $a>0, a \neq 1$. Then, the set $S$ of all positive real numbers $b$ satisfying $\left(1+a^2\right)\left(1+b^2\right)=4 a b$ is

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

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 $S=\{4,6,9\}$ and $T=\{9,10,11, \ldots, 1000\}$. If

$A=\left\{a_{1}+a_{2}+\ldots+a_{k}: k \in N, a_{1}, a_{2}, a_{3}, \ldots, a_{k} \in S\right\}$ then the sum of all the elements in the set $T - A$ is equal to $......$