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21 people (a1,a2,a3...........a21) are invited for a party. the host and the hostess shake hands with each invitee and also with each other. the invitees shakes hands with each other in a circular fashion {(a1,12)(a2,a3)(a3,a4).......... (a21,a1)} such that there are a total of 64 hand shakes . let s be the set of people such that every pair in s shake hands. The size of s is atmost
a)3 b)1 c)2 d)4

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TCS Other Question
A student has to answer 6 questions. Maximum no. of questions that can be answered from any section is 4. How many ways he can attempt the paper? A multiple choice question paper has 4 options. For a correct answer, the student is awarded 5 marks. Negative marks are awarded for wrong attempts in such a manner that if the student randomly guesses the answers, his expected score is 0. If the student has eliminated two incorrect answer options, what is his expected score if he randomly guesses from the remaining options?
a)2.50 b)1.6 c)5 d) 0