The activities of the universe are truly mysterious. In its folds lie the knowledge of the past, the present and the course of the future. Science has always endeavored to unfold the true nature of our universe, and yet after centuries of human evolution we...

The Shanti Swarup Bhatnagar Prize for Science and Technology is India's highest prize for excellence in science, mathematics and technology. The prize is given every year in seven categories to outstanding people in the fields of mathematics, physics, biology, chemistry, engineering, earth, atmospheric, ocean science,...

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,...

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...