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

If $y = f(x) = \frac{{ax + b}}{{cx – a}}$, then $x$ is equal to

If $x \in [0, 1]$, then the number of solution $(s)$ of the equation $2[cos^{-1}x] + 6[sgn(sinx)] = 3$ is (where $[.]$ denotes greatest integer function and sgn $(x)$ denotes signum function of $x$)-

Range of the function $f(x) = \frac{{{x^2}}}{{{x^2} + 1}}$ is

Domain of the function $f(x)\,=\,\frac{1}{{\sqrt {(x + 1)({e^x} – 1)(x – 4)(x + 5)(x – 6)} }}$