Gate Exam

What is the value of
LIM (1-1/N)^2N ?
N-INFINITY

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Gate Other Question

Consider the set S = {1, w, w2}, where w and w2 are cube roots of unity. If *
denotes the multiplication operation, the structure (S, *) forms Consider a company that assembles computers. The probability of a faulty
assembly of any computer is p. The company therefore subjects each
computer to a testing process. This testing process gives the correct result for
any computer with a probability of q. What is the probability of a computer
being declared faulty?