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Design & Analysis of AlgorithmsWrite short notes on: Cook's Theorem20247mFormal Language & Automata TheoryWrite a short note on: Rice's theorem20257mDesign and Analysis of Algorithms What is the Master's Theorem? State the general form and the three cases of the theorem. Use it to solve the following recurrence relations: (i) T(n) = 2T(n/2) + n (ii) T(n) = 3T(n/2) + n^2 (iii) T(n) = 2T(n/2) + n/\log n Explain which case applies in each situation.20247mDesign and Analysis of Algorithms Write short notes on any two of the following: (i) Asymptotic Notations (ii) Clique decision problem (iii) Max-flow-min-cut theorem (iv) Union-Find Algorithm202214m