The remainder on dividing $$5^{99}$$ by 11 is ____________.

Let 5 digit numbers be constructed using the digits $$0,2,3,4,7,9$$ with repetition allowed, and are arranged in ascending order with serial numbers. Then the serial number of the number 42923 is __________.

Let $$\alpha>0$$, be the smallest number such that the expansion of $$\left(x^{\frac{2}{3}}+\frac{2}{x^{3}}\right)^{30}$$ has a term $$\beta x^{-\alpha}, \beta \in \mathbb{N}$$. Then $$\alpha$$ is equal to ___________.

Number of 4-digit numbers that are less than or equal to 2800 and either divisible by 3 or by 11 , is equal to ____________.