Let the abscissae of the two points P and Q be the roots of $$2{x^2} - rx + p = 0$$ and the ordinates of P and Q be the roots of $${x^2} - sx - q = 0$$. If the equation of the circle described on PQ as diameter is $$2({x^2} + {y^2}) - 11x - 14y - 22 = 0$$, then $$2r + s - 2q + p$$ is equal to __________.

The number of values of x in the interval $$\left( {{\pi \over 4},{{7\pi } \over 4}} \right)$$ for which

$$14\cos e{c^2}x - 2{\sin ^2}x = 21 - 4{\cos ^2}x$$ holds, is ____________.

For a natural number n, let $${\alpha _n} = {19^n} - {12^n}$$. Then, the value of $${{31{\alpha _9} - {\alpha _{10}}} \over {57{\alpha _8}}}$$ is ___________.

Let $$f:R \to R$$ be a function defined by

$$f(x) = {\left( {2\left( {1 - {{{x^{25}}} \over 2}} \right)(2 + {x^{25}})} \right)^{{1 \over {50}}}}$$. If the function $$g(x) = f(f(f(x))) + f(f(x))$$, then the greatest integer less than or equal to g(1) is ____________.