Let $A = \{1, 2, 3\}$. The total number of distinct relations that can be defined over $A$ is

Let $A$ and $B$ be two non-empty subsets of a set $X$ such that $A$ is not a subset of $B$, then

$A$ set contains $2n + 1$ elements. The number of subsets of this set containing more than $n$ elements is equal to

In an examination,$40 \%$ students failed in Hindi,$50 \%$ students failed in English. If $21 \%$ students failed in both the subjects,find the percentage of those who passed in Hindi.

If $S$ and $T$ are two sets such that $S$ has $21$ elements,$T$ has $32$ elements,and $S \cap T$ has $11$ elements,how many elements does $S \cup T$ have?

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