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Please provide me question paper for Joint Entrance Screening Test examination soon ?? Here I am giving you question paper for Joint Entrance Screening Test examination in PDF file attached with it so you can get it easily.. 2. Consider the following function, defined by a recursive program: function AP(x,y: integer) returns integer; if x = 0 then return y+1 else if y = 0 then return AP(x-1,1) else return AP(x-1, AP(x,y-1)) (a) Show that on all nonnegative arguments x and y, the function AP terminates. (b) Show that for any x, AP(x, y) > y. 3. How many subsets of even cardinality does an n-element set have ? Justify answer. 4. A tournament is a directed graph in which there is exactly one directed edge between every pair of vertices. Let Tn be a tournament on n vertices. (a) Use induction to prove the following statement: Tn has a directed hamiltonian path (a directed path that visits all vertices). (b) Describe an algorithm that finds a directed hamiltonian path in a given tourna- ment. Do not write whole programs; pseudocode, or a simple description of the steps in the algorithm, will suffice. What is the worst case time complexity of your algorithm? 5. Describe two different data structures to represent a graph. For each such representa- tion, specify a simple property about the graph that can be more efficiently checked in that representation than in the other representation. Indicate the worst case time required for verifying both of your properties in either representation. 6. Two gamblers have an argument. The first one claims that if a fair coin is tossed repeatedly, getting two consecutive heads is very unlikely. The second, naturally, is denying this. They decide to settle this by an actual trial; if, within n coin tosses, no two consecutive heads turn up, the first gambler wins. (a) What value of n should the second gambler insist on to have more than a 50% chance of winning? (b) In general, let P(n) denote the probability that two consecutive heads show up within n trials. Write a recurrence relation for P(n). (c) Implicit in the second gambler’\s stand is the claim that for all sufficiently large n, there is a good chance of getting two consecutive heads in n trials; i.e. P(n) > 1/2. In the first part of this question, one such n has been demonstrated. What happens for larger values of n? Is it true that P(n) only increases with n? Justify your answer. Jest theoretical computer science paper ![]() ![]() ![]() ![]() JEST physics Question Papers Last edited by Aakashd; June 28th, 2019 at 04:37 PM. |
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please send me last 5 years jest questions for theoretical computer science @ pravasranjan90@gmail.com |