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: $$r|a_0$$ ...

In this article  we shall show that the characteristic polynomial of both $$AB$$ and $$BA$$ are the same, where $$A$$ and $$B$$ are $$n\times n$$ matrices over $$R$$, a ring with unity. Let $$\Phi_T\in R[\lambda]$$ denote the characteristic polynomial of $$T$$. Thus, we intend to show,...

The Assam Higher Secondary Education Council(AHSEC) is responsible for conducting the 12th standard examinations for the students studying in the state board schools in Assam. Some of the AHSEC 2016 question papers are available for download below. Alternative English, Physics, Mathematics, Computer Science (Featured Image Source :...

[caption id="attachment_7804" align="alignright" width="320"] Image Source : Shutterstock[/caption] This is my interview experience at CMI for MSc in Applications of Mathematics. The syllabus for MSc in Applications of Mathematics includes single variable calculus, linear algebra, theory of equations, combinatorics and some other topics from class 12th...

The Assam Higher Secondary Education Council(AHSEC) is responsible for conducting the 12th standard examinations for the students studying in the state board schools in Assam. Some of the AHSEC 2015 question papers are available for download below. English, Alternative English, Physics, Chemistry, Mathematics, Biology (Featured Image Source...