Let the coefficients of x^$$-$$1 and x^$$-$$3 in the expansion of $${\left( {2{x^{{1 \over 5}}} - {1 \over {{x^{{1 \over 5}}}}}} \right)^{15}},x > 0$$, be m and n respectively. If r is a positive integer such that $$m{n^2} = {}^{15}{C_r}\,.\,{2^r}$$, then the value of r is equal to __________.

The total number of four digit numbers such that each of first three digits is divisible by the last digit, is equal to ____________.

Let $$M = \left[ {\matrix{ 0 & { - \alpha } \cr \alpha & 0 \cr } } \right]$$, where $$\alpha$$ is a non-zero real number an $$N = \sum\limits_{k = 1}^{49} {{M^{2k}}} $$. If $$(I - {M^2})N = - 2I$$, then the positive integral value of $$\alpha$$ is ____________.

Let f(x) and g(x) be two real polynomials of degree 2 and 1 respectively. If $$f(g(x)) = 8{x^2} - 2x$$ and $$g(f(x)) = 4{x^2} + 6x + 1$$, then the value of $$f(2) + g(2)$$ is _________.