-:15 questions on Real Analysis for NET and GATE aspirants:- The answers: 1. D , 2. A , 3. C , 4. B , 5. B , 6. C , 7. C , 8. D , 9. B , 10. C , 11. , 12. A ,...

## 27 AugFive great ‘Unsolved’ problems in Theoretical Physics

Theoretical Physics, considered one of the most thrilling, exciting and pain staking branches in all of sciences, deals with explaining the mysteries of the universe in the beautiful complexities of mathematics as it has been the language of physicists from time immemorial. The brilliant minds...

## 23 AugThe Flower Puzzle Generalized

This article is a crazy generalization of the Flower puzzle by Ankush Goswami published in Gonit Sora on 12th July 2012. We now suppose that instead of three there are $$m$$ temples $$A_{1}, A_{2},dots ,A_{m }$$ and instead of doubling, the flowers increase $$n$$ times...

## 02 AugIMO 2012

The 53rd International Mathematical Olympiad (IMO) was held this year at Mar del Plata, Argentina. The question papers can be downloaded here. The 52nd IMO was held last year at the Netherlands. The IMO problem short-list with the solutions of that IMO can be downloaded here. The...

## 25 JulNavier-Stokes equation

This is an equation which describes the motion of an incompressible fluid and is given by ∂∂t ui + j=13uj∂ui∂xj = ν Δ ui - ∂p∂xi + fi (x,t) x  R3, t ≥ 0, 1 ≤ i ≤ 3 div u = j=13∂uj∂xj = 0...

## 23 JulBirch Swinnerton-Dyer conjecture

This is a conjecture regarding the number of rational points in elliptic curves i.e. curves in two-dimensional plane with the equation y2 = x3 + a x + b  for some whole numbers a,b. In the early 1960’s, the British mathematicians Brian Birch and Peter Swinnerton-Dyer started...

## 12 JulThe Flower Puzzle

Consider the following puzzle: There are three temples say A, B and C. A priest takes with him some flowers and visits A. The flowers instantly double itself, and the priest keeps some of those flowers in A and proceeds towards B. At B also the...

## 22 Jun50 questions on linear algebra for NET and GATE aspirants

Find the correct options:   1)  $$M=\left(\begin{array}{ccc}1 & 2 & 2 \\0 & 2 & 2 \\0 & 1 & 1 \end{array}\right)$$ and $$V={ Mx^{T} : x\in R^{3}}.$$ Then $$dim V$$ is (a)   0   (b)   1   (c)   2   (d)   3   2)  $$A^{2}-A=0,$$ where $$A$$ is a $$9\times 9$$ matrix....