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

In the following,state whether $A = B$ or not:
$A = \{2, 4, 6, 8, 10\}$; $B = \{x : x \text{ is a positive even integer and } x \le 10\}$

Which of the following is the empty set?

Let $A = \{1, 2, \{3, 4\}, 5\}$. Which of the following statements are incorrect and why?
$1 \in A$

Which of the following is an example of the null set?
Set of odd natural numbers divisible by $2$.

The set $\{n(n+1)(2n+1) : n \in \mathbb{Z}\}$ is a subset of: