Let $$[x]$$ be the greatest integer $$\leq x$$. Then the number of points in the interval $$(-2,1)$$, where the function $$f(x)=|[x]|+\sqrt{x-[x]}$$ is discontinuous, is ___________.

Let the positive numbers $$a_{1}, a_{2}, a_{3}, a_{4}$$ and $$a_{5}$$ be in a G.P. Let their mean and variance be $$\frac{31}{10}$$ and $$\frac{m}{n}$$ respectively, where $$m$$ and $$n$$ are co-prime. If the mean of their reciprocals is $$\frac{31}{40}$$ and $$a_{3}+a_{4}+a_{5}=14$$, then $$m+n$$ is equal to ___________.

Let $$I(x)=\int \sqrt{\frac{x+7}{x}} \mathrm{~d} x$$ and $$I(9)=12+7 \log _{e} 7$$. If $$I(1)=\alpha+7 \log _{e}(1+2 \sqrt{2})$$, then $$\alpha^{4}$$ is equal to _________.

A particle is executing simple harmonic motion (SHM). The ratio of potential energy and kinetic energy of the particle when its displacement is half of its amplitude will be