Case analysis Previous Year Questions (PYQs) for CMI BS Hons: 3+ Solved Questions with Step-by-Step Solutions

In a football league, a collection of teams play against each other a number of times. A team gets 3 points for each match that it wins, 1 point for each match that it draws and 0 points for each match that it loses.

A new game show on TV has 100 boxes numbered $1,2,\dots ,100$, each containing a mystery prize. The prizes are of different types, $a,b,c,\dots$, in decreasing order of value, and are distributed randomly among the boxes. The most expensive item is of type $a$, a diamond ring, and there is exactly 1 of these. You are told that the number of items at least doubles as you move to the next category — there are at least twice as many items of type $b$ as of type $a$, at least twice as many items of type $c$ as of type $b$ and so on.

26 children participated in a chess tournament. A child got two points for winning, zero for losing and one point for a draw. Each child played against every other child. After the tournament was over no child had an odd score. There were no draws in the entire tournament and no two players had the same score. For convenience assume that the children are named $A,B,C,\dots ,Z$, by the 26 letters of the English alphabet in increasing order of scores, so $A$ has lowest score, $Z$ has highest score. Thus we have $A<B<C<\cdots <X<Y<Z$. Pick all statements which are true.