Which of the following Boolean expression is a tautology?

The number of elements in the set {x $$\in$$ R : (|x| $$-$$ 3) |x + 4| = 6} is equal to :

If the three normals drawn to the parabola, y² = 2x pass through the point (a, 0) a $$\ne$$ 0, then 'a' must be greater than :

Let a complex number z, |z| $$\ne$$ 1,

satisfy $${\log _{{1 \over {\sqrt 2 }}}}\left( {{{|z| + 11} \over {{{(|z| - 1)}^2}}}} \right) \le 2$$. Then, the largest value of |z| is equal to ____________.