If the sum of the co-efficient of all the positive even powers of x in the binomial expansion of $${\left( {2{x^3} + {3 \over x}} \right)^{10}}$$ is $${5^{10}} - \beta \,.\,{3^9}$$, then $$\beta$$ is equal to ____________.

If the mean deviation about the mean of the numbers 1, 2, 3, .........., n, where n is odd, is $${{5(n + 1)} \over n}$$, then n is equal to ______________.

Let $$\overrightarrow b = \widehat i + \widehat j + \lambda \widehat k$$, $$\lambda$$ $$\in$$ R. If $$\overrightarrow a $$ is a vector such that $$\overrightarrow a \times \overrightarrow b = 13\widehat i - \widehat j - 4\widehat k$$ and $$\overrightarrow a \,.\,\overrightarrow b + 21 = 0$$, then $$\left( {\overrightarrow b - \overrightarrow a } \right).\,\left( {\widehat k - \widehat j} \right) + \left( {\overrightarrow b + \overrightarrow a } \right).\,\left( {\widehat i - \widehat k} \right)$$ is equal to _____________.

The total number of three-digit numbers, with one digit repeated exactly two times, is ______________.