Let $A= \{1, 2, 3, 4\}$ and $R : A \to A$ be the relation defined by $R = \{ (1, 1), (2, 3), (3, 4), ( 4, 2) \}$. The correct statement is

Let $f\left( n \right) = \left[ {\frac{1}{3} + \frac{{3n}}{{100}}} \right]n$ , where $[n]$ denotes the greatest integer less than or equal to $n$. Then $\sum\limits_{n = 1}^{56} {f\left( n \right)} $ is equal to

Show that none of the operations given above has identity.

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.

The maximum value of function $f(x) = \int\limits_0^1 {t\,\sin \,\left( {x + \pi t} \right)} dt,\,x \in \,R$ is