TCS Company

The thankgiving banquet at No.2, Ritcher Street, had 49 guests which consisted of 6 statesmen, 26 relatives and
their families. At the end of a banquet 19 people shake hands with other , some of which were between the
statesmen alone, some between relatives alone and some between the statesmen and relatives. How many
handshakes will there be in total?
(a)342 (b) 171 (c) 180 (d) 162

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TCS Other Question

5 men and 5 women meet and men dance with women. Which of the following are always true? A. there are 2
men who have danced with same number of women. B. There are 2 women who have danced with same number
of men.
(a) Both A and B (b) A only
(c) B only (d) Neither A nor B
Given a collection of points P in the plane , a 1-set is a point in P that can be separated from the rest by a line, .i.e
the point lies on one side of the line while the others lie on the other side. The number of 1-sets of P is denoted
by n1(P). The minimum value of n1(P) over all configurations P of 5 points in the plane in general position (.i.e
no three points in P lie on a line) is
(a) 3 (b) 5 (c) 2 (d)7