GATE CSE 2019 Paper 1 — page 20

Questions 58–60 of 65. Imported answers require review unless explicitly marked reviewed.

Let Σ be the set of all bijections from {1, ..., 5} to {1, ..., 5}, where id denotes the identity function, i.e. id(i) = i, ∀i. Let ∘ denote composition on functions. For a string x = x₁ x₂ ··· xₙ ∈ Σⁿ, n ≥ 0, let π(x) = x₁ ∘ x₂ ∘ ··· ∘ xₙ. Consider the language L = {x ∈ Σ* | π(x) = id}. The minimum number of states in any DFA accepting L is ________.

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Consider that 15 machines need to be connected in a LAN using 8-port Ethernet switches. Assume that these switches do not have any separate uplink ports. The minimum number of switches needed is ________.

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What is the minimum number of 2-input NOR gates required to implement a 4-variable function expressed in sum-of-minterms form as f = Σ (0, 2, 5, 7, 8, 10, 13, 15)? Assume that all the inputs and their complements are available. Answer: ________.

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2019 · Paper 1

Question 48

Question 49

Question 50