Set $A$ has $3$ elements and set $B$ has $4$ elements. The number of injection that can be defined from $A$ to $B$ is
$144$
$12$
$24$
$64$
Let $A$ be the set of all $50$ students of Class $X$ in a school. Let $f: A \rightarrow N$ be function defined by $f(x)=$ roll number of the student $x$. Show that $f$ is one-one but not onto.
Show that none of the operations given above has identity.
If $f(x) = \log \frac{{1 + x}}{{1 - x}}$, then $f(x)$ is
Let ${a_2},{a_3} \in R$ such that $\left| {{a_2} - {a_3}} \right| = 6$ and $f\left( x \right) = \left| {\begin{array}{*{20}{c}}
1&{{a_3}}&{{a_2}}\\
1&{{a_3}}&{2{a_2} - x}\\
1&{2{a_3} - x}&{{a_2}}
\end{array}} \right|,x \in R.$ Then the greatest value of $f(x)$ is