Let z be those complex numbers which satisfy

| z + 5 | $$ \le $$ 4 and z(1 + i) + $$\overline z $$(1 $$-$$ i) $$ \ge $$ $$-$$10, i = $$\sqrt { - 1} $$.

If the maximum value of | z + 1 |² is $$\alpha$$ + $$\beta$$$$\sqrt 2 $$, then the value of ($$\alpha$$ + $$\beta$$) is ____________.

If the arithmetic mean and geometric mean of the p^th and q^th terms of the
sequence $$-$$16, 8, $$-$$4, 2, ...... satisfy the equation
4x² $$-$$ 9x + 5 = 0, then p + q is equal to __________.

If $${I_{m,n}} = \int\limits_0^1 {{x^{m - 1}}{{(1 - x)}^{n - 1}}dx} $$, for m, $$n \ge 1$$, and
$$\int\limits_0^1 {{{{x^{m - 1}} + {x^{n - 1}}} \over {{{(1 + x)}^{m + 1}}}}} dx = \alpha {I_{m,n}}\alpha \in R$$, then $$\alpha$$ equals ___________.

Let X₁, X₂, ......., X₁₈ be eighteen observations such
that $$\sum\limits_{i = 1}^{18} {({X_i} - } \alpha ) = 36$$ and $$\sum\limits_{i = 1}^{18} {({X_i} - } \beta {)^2} = 90$$, where $$\alpha$$ and $$\beta$$ are distinct real numbers. If the standard deviation of these observations is 1, then the value of | $$\alpha$$ $$-$$ $$\beta$$ | is ____________.