If $\alpha ,\beta ,\gamma $are the roots of the equation ${x^3} + x + 1 = 0$, then the value of ${\alpha ^3}{\beta ^3}{\gamma ^3}$

The number of real roots of the equation ${e^{\sin x}} - {e^{ - \sin x}} - 4$ $ = 0$ are

The sum of integral values of $a$ such that the equation $||x\ -2|\ -|3\ -x||\ =\ 2\ -a$ has a solution

The least integral value $\alpha $ of $x$ such that $\frac{{x - 5}}{{{x^2} + 5x - 14}} > 0$ , satisfies

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

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