The number of volleyball games that must be scheduled in a league with n teams is given by `G(n)=(n^(2)-n)/(2)` where each team plays with every other team exactly once. A league scheledules 15 games. How many teams are in the league?

Twenty-eight games were played in a football tournament with each team playing once against each other. How many teams were there?

The members of a chess club took part in a round robin competition in which each player plays with other once. All members scored the same number of points, except four juniors whose total score ere 17.5. How many members were there in the club? Assume that for each win a player scores 1 point, 1/2 for a draw, and zero for losing.

Suppose the energy of a hydrogen- like atom is given as E_(n) = (-54.4)/(n^(2))eV where ninN . Calculate the following: (a) Sketch the energy levels for this atom and compute its atomic number. (b) If the atom is in ground state, compute its first excitation potential and also its ionization potential. (c) When a photon with energy 42 eV and another photon with energy 56 eV are made to collide with this atom, does this atom absorb these photons? (d) Determine the radius of its first Bohr orbit. (e) Calculate the kinetic and potential energies in the ground state.

There are 2 women participating in a chess tournament. Every participant played 2 games with the other participants. The number of games that the men played between themselves exceeded by 66 as compared to the number of games that the men played with women. If the number of participants is n , then the value of n-6 is ______.

Two teams are to play a series of five matches between them. A match ends in a win, loss, or draw for a team. A number of people forecast the result of each match and no two people make the same forecast for the series of matches. The smallest group of people in which one person forecasts correctly for all the matches will contain n people, where n is a. 81 b. 243 c. 486 d. none of these

(i) A kabaddi coach has 14 players ready to play. How many different teams of 7 players could the coach put on the court? (ii) There are 15 persons in a party and if , each 2 of them shakes hands wit each with each other. How many handshakes happen in the party? (iii) How many chords can be drawn through 20 points on a circle? (iv) In a parking lot one hunderd, one year old cars are parked. Out of them five are to be chosen at random for to check its pollution devices. How many different set of five cars are possible? (v) How many ways can a team of 3 boys, 2 girls and 1 transgender be selected from 5 boys, 4 girls and 2 transgender?