The remainder obtained when the polynomial $1 + x + x^3 + x^9 + x^{27} + x^{81} + x^{243}$ is divided by $x - 1$ is

Consider the sets $\phi, A = \{1, 3\}, B = \{1, 5, 9\}, C = \{1, 3, 5, 7, 9\}$. Insert the symbol $\subset$ or $\not\subset$ between the pair of sets: $B \dots C$.

If $aN = \{ax : x \in N\}$ and $bN \cap cN = dN$,where $b, c \in N$ are coprime numbers,then:

Let $A$ and $B$ be two sets. Then

The set $A = \{ x : x \in \mathbb{R}, x^2 = 16 \text{ and } 2x = 6 \}$ is equal to

Let $S = \{0, 1, 5, 4, 7\}$. Then the number of all subsets of $S$ is: