Gate Exam

In how many ways can a given positive integer n 2 be expressed as the sum of 2 positive integers (which are not necessarily distinct). For example, for n = 3, the number of ways is 2, i.e., 1+2, 2+1. Give ANSWER??

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Gate Other Question

The minimum number of colours required to colour the vertices of a cycle with n nodes in
such a way that no two adjacent nodes have the same colour is
(a) 2
(b) 3
(c) 4
(d) n_2[+2 In how many ways can a given positive integer n 3 be expressed as the sum of 3 positive
integers (which are not necessarily distinct). For example, for n = 4, the number of ways is 3,i.e., 1+2+1, 2+1+1. Give only the answer without any explanation.