The system of equations kx + y + z = 1, x + ky + z = k and x + y + zk = k² has no solution if k is equal to :

In a school, there are three types of games to be played. Some of the students play two types of games, but none play all the three games. Which Venn diagrams can justify the above statement?

If cot^$$-$$1($$\alpha$$) = cot^$$-$$1 2 + cot^$$-$$1 8 + cot^$$-$$1 18 + cot^$$-$$1 32 + ...... upto 100 terms, then $$\alpha$$ is :

Team 'A' consists of 7 boys and n girls and Team 'B' has 4 boys and 6 girls. If a total of 52 single matches can be arranged between these two teams when a boy plays against a boy and a girl plays against a girl, then n is equal to :