If $f: N \rightarrow R$ is defined by $f(1)=-1$ and $f(n+1)=3f(n)+2$ for $n \geq 1$, then $f$ is

If $P(S)$ denotes the set of all subsets of a given set $S$,then the number of one-to-one functions from the set $S = \{ 1, 2, 3 \}$ to the set $P(S)$ is

If the function $f: R \rightarrow R$ is defined by $f(x) = |x|(x - \sin x)$,then which of the following statements is $TRUE$?

The number of functions $f: \{1, 2, \ldots, 100\} \rightarrow \{0, 1\}$ that assign $1$ to exactly one of the positive integers less than or equal to $98$ is equal to $\qquad$.

Let $f : X \rightarrow Y$ be a function such that $f(x) = \sqrt{x - 2} + \sqrt{4 - x} .$ Then the set of $X$ and $Y$ for which $f(x)$ is both injective as well as surjective,is-

Given that for any $n \in N$, there exist an odd integer $q$ and a non-negative integer $r$ such that $n$ can be written uniquely as $n = q \times 2^r$. Let $f: N \rightarrow N \times N$ be a function defined by $f(n) = \left(r+1, \frac{q+1}{2}\right)$. Then,