Let $f(x) = \cos(\sqrt{P}x),$ where $P = [\lambda]$ and $[.]$ denotes the Greatest Integer Function. If the period of $f(x)$ is $\pi$,then:

Which of the following statements is true?

The function $f: N-\{1\} \rightarrow N$ defined by $f(n) = \text{the highest prime factor of } n$ is:

The function $f : N \to N$ defined by $f(x) = x - 5[\frac{x}{5}]$,where $N$ is the set of natural numbers and $[x]$ denotes the greatest integer less than or equal to $x$,is

Let $X$ be a set with exactly $5$ elements and $Y$ be a set with exactly $7$ elements. If $\alpha$ is the number of one-one functions from $X$ to $Y$ and $\beta$ is the number of onto functions from $Y$ to $X$,then the value of $\frac{1}{5!}(\beta-\alpha)$ is.

Show that an onto function $f: \{1, 2, 3\} \rightarrow \{1, 2, 3\}$ is always one-one.