Let $A=\{1,3,7,9,11\}$ and $B=\{2,4,5,7,8,10,12\}$. Then the total number of one-one maps $f: A \rightarrow B$,such that $f(1)+f(3)=14$,is:

If a set $A$ has $m$ elements and set $B$ has $n$ elements and the number of injections from $A$ to $B$ is $2520$. Then,$m$ is equal to

Consider the sets $A = \{(x, y) \in \mathbb{R} \times \mathbb{R} : x^2 + y^2 = 25\}$,$B = \{(x, y) \in \mathbb{R} \times \mathbb{R} : x^2 + 9y^2 = 144\}$,$C = \{(x, y) \in \mathbb{Z} \times \mathbb{Z} : x^2 + y^2 \leq 4\}$,and $D = A \cap B$. The total number of one-one functions from the set $D$ to the set $C$ is:

Function $f: R \rightarrow R$ defined by $f(x) = x^3$ is . . . . . . .

Let $A = \{1, 2, 3, 4, 5, 6\}$. The number of one-one functions $f: A \to A$ such that $f(1) \ge 3, f(3) \le 4$ and $f(2) + f(3) = 5$, is ————

The function $f(x) = \log (x + \sqrt {{x^2} + 1} )$ is: