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

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 ____________.

Let $$A = \left[ {\matrix{ i & { - i} \cr { - i} & i \cr } } \right],i = \sqrt { - 1} $$. Then, the system of linear equations $${A^8}\left[ {\matrix{ x \cr y \cr } } \right] = \left[ {\matrix{ 8 \cr {64} \cr } } \right]$$ has :

If n is the number of irrational terms in the
expansion of $${\left( {{3^{1/4}} + {5^{1/8}}} \right)^{60}}$$, then (n $$-$$ 1) is divisible by :