Statement $1$ : If $A$ and $B$ be two sets having $p$ and $q$ elements respectively, where $q > p$. Then the total number of functions from set $A$ to set $B$ is $q^P$.
Statement $2$ : The total number of selections of $p$ different objects out of $q$ objects is ${}^q{C_p}$.
Statement $1$ is true, Statement $2$ is false
Statement $1$ is true, Statement $2$ is true,Statement $2$ is not a correct explanation of Statement $1$
Statement $1$ is false, Statement $2$ is true
Statement $1$ is true, Statement $2$ is true,Statement $2$ is a correct explanation of Statement $1$
The function $f\left( x \right) = \left| {\sin \,4x} \right| + \left| {\cos \,2x} \right|$, is a periodic function with period
Let $f(x) = {(x + 1)^2} - 1,\;\;(x \ge - 1)$. Then the set $S = \{ x:f(x) = {f^{ - 1}}(x)\} $ is
Period of $f(x) = nx + n - [nx + n]$, $n \in N$
where [ ] denotes the greatest integer function is :
The range of the function $f(x) = \frac{{\sqrt {1 - {x^2}} }}{{1 + \left| x \right|}}$ is
The period of the function $f(x) = e^{x -[x]+|cos\, \pi x|+|cos\, 2\pi x|+....+|cos\, n\pi x|}$ (where $[.]$ denotes greatest integer function); is:-