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 domain of definition of the function $y(x)$ given by ${2^x} + {2^y} = 2$ is
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
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 $....$.
Greatest value of the function, $f(x) = - 1 + \frac{2}{{{2^x}^2 + 1}}$ is