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 ${}^q{C_p}$.

  • [AIEEE 2012]
  • A

    Statement $1$ is true, Statement $2$ is false

  • B

    Statement $1$ is true, Statement $2$ is true,Statement $2$ is not a correct explanation of Statement $1$

  • C

    Statement $1$ is false, Statement $2$ is true

  • D

    Statement $1$ is true, Statement $2$ is true,Statement $2$ is a correct explanation of Statement $1$

Similar Questions

The domain of definition of the function $y(x)$ given by ${2^x} + {2^y} = 2$ is

  • [IIT 2000]

Product of all the solution of the equation  ${x^{1 + {{\log }_{10}}x}} = 100000x$ is

Let $S=\{1,2,3,4\}$. Then the number of elements in the set $\{f: S \times S \rightarrow S: f$ is onto and $f(a, b)=f(b, a)$ $\geq a; \forall(a, b) \in S \times S\}$ is

  • [JEE MAIN 2022]

If domain of the function $\log _e\left(\frac{6 x^2+5 x+1}{2 x-1}\right)+\cos ^{-1}\left(\frac{2 x^2-3 x+4}{3 x-5}\right)$ is $(\alpha, \beta) \cup(\gamma, \delta]$, then $18\left(\alpha^2+\beta^2+\gamma^2+\delta^2\right)$ is equal to $....$.

  • [JEE MAIN 2023]

Greatest value of the function, $f(x) =  - 1 + \frac{2}{{{2^x}^2 + 1}}$ is