Ramanujan trophy is associated with the game

In almost every exam questions from sports cups and trophies are asked. You should know that there are some tournaments and trophies which are very popular. Questions from them are often asked in the examination. A few of these international cups and trophies are as follows. In all popular government job exams, you can expect one or two questions from this section. Ranji Trophy — Ranji Trophy is the most important domestic cricket tournament in India. The tournament is played between multiple teams representing regional and state cricket associations.

Currently, 38 teams take part in the competition. It is played between teams from different regions and states of India. Ranji Trophy is named after the Indian Cricketer, Ranjitsingh ji who has played international cricket. There are a total of 38 teams that play the Ranji Cricket Tournament. The first match was played between Madras and Mysore on 4th November This trophy was first presented in the jumping Competition in Ireland.

Switzerland won Aga Khan Trophy thrice in the years , , and Beighton Cup is one of the oldest cups in the History of Hockey. In the beginning, it was organized by the Indian Football later the Calcutta Hockey League took over it in Davis cup is named after American collegian Dwight Filley Davis. The first match of the Davis Cup was played in Introduced in , the Rangaswami Cup, was originally known as Inter-Provincial Tournament meant to pick up players for the national team for the Olympics.

Bhopal won the tournament twice in and and finished runners-up thrice. Bhopal hosted the reputed tournament thrice in , and Hide Explanation. Wellington Trophy is associated with Rowing. These extra dimensions are rolled up tightly in tiny little spaces too small for us to perceive.

These tiny spaces have a particular geometric structure. Calabi—Yau manifold is a class of geometric objects that have similar structure and one of the simplest classes of Calabi-Yau manifolds comes from K3 surfaces.

In mathematics, theta functions are special functions of several complex variables. German Mathematician Carl Gustav Jacob Jacobi came up with several closely related theta function s known as Jacobi theta functions.

Theta functions were studied extensively by Ramanujan. He came up with the Ramanujan theta function , which generalizes the form of Jacobi theta functions while also capturing their general properties. In particular, the Jacobi triple product takes on an elegant form when written in terms of the Ramanujan theta function. Ramanujan theta function has several important applications. It is used to determine the critical dimensions in Bosonic string theory, superstring theory and M-theory.

In a letter to Hardy, Ramanujan described several new functions that behaved differently from known theta functions , or modular forms , and yet closely mimicked them. These were the first ever examples of mock modular forms. More than 80 years later, in , a description for these functions was provided by Sander Zwegers. Further, Ramanujan predicted that his mock modular forms corresponded to ordinary modular forms producing similar outputs for roots of 1.

Ken Ono ultimately showed that a mock modular form could be computed just as Ramanujan predicted.