The number of solutions of the equation $$\sin x = {\cos ^2}x$$ in the interval (0, 10) is _________.

For real numbers a, b (a > b > 0), let

Area $$\left\{ {(x,y):{x^2} + {y^2} \le {a^2}\,and\,{{{x^2}} \over {{a^2}}} + {{{y^2}} \over {{b^2}}} \ge 1} \right\} = 30\pi $$

and

Area $$\left\{ {(x,y):{x^2} + {y^2} \le {b^2}\,and\,{{{x^2}} \over {{a^2}}} + {{{y^2}} \over {{b^2}}} \le 1} \right\} = 18\pi $$

Then, the value of (a $$-$$ b)² is equal to ___________.

Let f and g be twice differentiable even functions on ($$-$$2, 2) such that $$f\left( {{1 \over 4}} \right) = 0$$, $$f\left( {{1 \over 2}} \right) = 0$$, $$f(1) = 1$$ and $$g\left( {{3 \over 4}} \right) = 0$$, $$g(1) = 2$$. Then, the minimum number of solutions of $$f(x)g''(x) + f'(x)g'(x) = 0$$ in $$( - 2,2)$$ is equal to ________.

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 __________.