The number of elements in the set $\{ (a,\,b):2{a^2} + 3{b^2} = 35,\;a,\,b \in Z\} $, where $Z$ is the set of all integers, is

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

$\{ 3,4\}  \in A$

Which of the following are examples of the null set

$\{ x:x$ is a natural numbers, $x\, < \,5$ and $x\, > \,7\} $

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

$\varnothing \subset A$

Set $A$ has $m$ elements and Set $B$ has $n$ elements. If the total number of subsets of $A$ is $112$ more than the total number of subsets of $B$, then the value of $m \times n$ is