Let $$a_{1}=8, a_{2}, a_{3}, \ldots, a_{n}$$ be an A.P. If the sum of its first four terms is 50 and the sum of its last four terms is 170 , then the product of its middle two terms is ___________.

Let $$f: \mathbb{R} \rightarrow \mathbb{R}$$ be a differentiable function such that $$f^{\prime}(x)+f(x)=\int_\limits{0}^{2} f(t) d t$$. If $$f(0)=e^{-2}$$, then $$2 f(0)-f(2)$$ is equal to ____________.

The remainder, when $$19^{200}+23^{200}$$ is divided by 49 , is ___________.

The number of 3-digit numbers, that are divisible by either 2 or 3 but not divisible by 7, is ____________.