Assume that R is a relation on the set Z of integers and it is given by $(x, y) \in R \Leftrightarrow |x - y| \leq 1$. Then, R is

Let R be the relation over the set A of all straight lines in a plane such that $l_{1} \mathrm{R} l_{2} \Leftrightarrow l_{1}$ is parallel to $l_{2}$. Then R is :

If a function $f: R \to T$, defined by $f(x) = \sqrt{3}\sin x + \cos x$ is an onto function, then the interval of $T$ is

Let $f : [2, \infty) \to \mathbf{R}$ be a function defined by $f(x) = x^2 - 4x + 5$. The range of $f$ is :

If $n(A) = 3$, $n(B) = 2$, then number of all possible surjective function from set A to set B are :

Let f: $\mathbb{R} \rightarrow \mathbb{R}$ be defined as $f(x) = 10x$. Then (Where $\mathbb{R}$ is the set of real numbers)

Consider the function $f: \mathbb{R} \rightarrow \mathbb{R}$ defined by $f(x) = \frac{x}{x^2+1}$ then