## 10 MayFew Problems - 3

Let $$ABC$$ be an acute angled triangle such that $$\angle BAC = 45 ^o$$. Let $$D$$ be a point on $$AB$$ such that $$CD \perp AB$$. Let $$P$$ be an internal point of the segment $$CD$$. Prove that $$AP\perp BC$$ if and only if...

## 19 Jan50 Multiple Choice Questions on Mechanical Engineering

Q1. Which one of the following is correct? (IES, 2008) In normal shock wave in one dimensional flow A) the entropy remains constant B) the entropy increases across the shock C) the entropy decreases across the shock D) the velocity, pressure, and density increase across the shock   Q2....

## 17 DecFew Problems - 2

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: $$r|a_0$$ ...

## 31 AugA Problem in Linear Algebra

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,...

## 30 AugFew Problems - 1

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...

## 20 AugShortlisted Problems of the 56th International Mathematical Olympiad

The International Mathematical Olympiad (IMO) is an yearly competition for pre-college students, held every year in a different country. The shortlisted problems of the previous year's IMO is released with the IMO problems of the current year. The 56th IMO was held in Thailand last...

## 20 Jul"Mathematics Lab"

Sounds strange, right? Well, "Mathematics Lab" is something we are not well-acquainted with. We all had "Physics lab", "Chemistry Lab", "Biology Lab" in our schools/colleges but not "Mathematics Lab". Last month, I and my friend Ajoy Dutta got an opportunity to design a "Mathematics Lab",...

## 12 JulInternational Mathematical Olympiad (IMO) 2016 Questions

The 57th International Mathematical Olympiad was recently held in Hong Kong. The IMO is a prestigous competition for school students and consists of six problems to be solved over two days. The questions of the IMO can be found below. [pdf-embedder url="http://gonitsora.com/wp-content/uploads/2016/07/2016_eng.pdf"] If the questions are not...

## 29 JunAHSEC 2016 Question Papers

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 :...