Let $A = \{a, b, c\}$. Then number of relations containing $(a,b)$ and $(b, c)$ which are reflexive and transitive but not symmetric is

A and B are two sets such that $n(A) = 5$ and $n(B) = 7$. The number of one-one functions from A to B is

For the relation R defined below, where $\mathbb{R}$ and N denotes set of real numbers and set of natural numbers respectively, Match the LIST-I with LIST-II

Choose the correct answer from the options given below:

Let $f: \mathbb{R} \to \mathbb{R}$ be defined as $f(x) = 100x + 1$, where $\mathbb{R}$ is a set of real numbers, then

For the function $f(x) = |x-1| + |x-2| + |x-3|$

Match the LIST-I with LIST-II

Choose the correct answer from the options given below:

The number of symmetric relations on set $A = \{1,2,3\}$ is

The function $f: \mathbb{R} \rightarrow [-1, 1]$ defined by $f(x) = \cos x$ is: