What is Distance Learning? Distance learning is a way of learning that aims to deliver education to people remotely or who cannot be physically present in the classroom. It is an ideal solution where the teacher and students are separated by physical distance. With the advancement of...

For which $$n\in \mathbb{N}$$, does $$n+1 | \binom{2n}{n}$$ hold? For a polynomial $$p(x) = a_nx^n+\ldots + a_0$$ with integral coefficients, i.e. $$a_i\in \mathbb{Z}$$ for all $$1\leq i\leq n$$ with $$a_n\neq 0$$, if $$p(\frac{r}{s})=0$$ where $$r$$, $$s$$ are coprime integers with $$s\neq 0$$ then show that: $$r|a_0$$ ...

Given a straight line $$l$$ and points $$A$$ and $$B$$ on the same side of it find the shortest path from $$A$$ to $$B$$ which touches $$l$$. Given a function $$f:\mathbb{Q}\rightarrow\mathbb{Q}$$ such that $$f(x+y)=f(x)+f(y)$$ Show that $$f(x)=xf(1)$$ for all $$x\in\mathbb{Q}$$. Thus, infer that for such a...