The number of solution$(s)$ of the equation $ln(lnx)$ = $log_xe$ is –

Let $a, b, c, d$ be real numbers between $-5$ and $5$ such that  $|a|=\sqrt{4-\sqrt{5-a}},|b|=\sqrt{4+\sqrt{5-b}},|c|=\sqrt{4-\sqrt{5+c}}$ $|d|=\sqrt{4+\sqrt{5+d}}$ Then, the product $a b c d$ is

If $\alpha, \beta $ and $\gamma$ are the roots of equation ${x^3} – 3{x^2} + x + 5 = 0$ then $y = \sum {\alpha ^2} + \alpha \beta \gamma $ satisfies the equation

The solutions of the quadratic equation ${(3|x| – 3)^2} = |x| + 7$ which belongs to the domain of definition of the function $y = \sqrt {x(x – 3)} $ are given by

If $\alpha ,\beta,\gamma$ are the roots of equation $x^3 + 2x -5 = 0$ and if equation $x^3 + bx^2 + cx + d = 0$ has roots $2 \alpha + 1, 2 \beta + 1, 2 \gamma + 1$ , then value of $|b + c + d|$ is (where $b,c,d$ are coprime)-