If $(x + 1)$ is a factor of ${x^4} - (p - 3){x^3} - (3p - 5){x^2}$ $ + (2p - 7)x + 6$, then $p = $

Consider the following two statements

$I$. Any pair of consistent liner equations in two variables must have a unique solution.

$II$. There do not exist two consecutive integers, the sum of whose squares is $365$.Then,

The equation $\sqrt {3 {x^2} + x + 5} = x - 3$ , where $x$ is real, has

The equation $x^2-4 x+[x]+3=x[x]$, where $[x]$ denotes the greatest integer function, has:

The number of solutions of $\frac{{\log 5 + \log ({x^2} + 1)}}{{\log (x - 2)}} = 2$ is

If $x$ is real, then the value of $\frac{{{x^2} + 34x - 71}}{{{x^2} + 2x - 7}}$ does not lie between