Question 81. After several defeats in wars, Robert Bruce went in exile and wanted to commit suicide. Just before committing suicide, he came across a spider attempting tirelessly to have its net. Time and again, the spider failed but that did not deter it to refrain from making attempts. Such attempts by the spider made Bruce curious. Thus, Bruce started observing the near-impossible goal of the spider to have the net. Ultimately, the spider succeeded in having its net despite several failures. Such act of the spider encouraged Bruce not to commit suicide. And then, Bruce went back again and won many a battle, and the rest is history. Which one of the following assertions is best supported by the above information?

Question 82. Find the sum of the expression1/(√1 + √2) + 1/(√2 + √3) + 1/(√3 + √4) + .... + 1/(√80 + √81)

Question 83. Out of all the 2-digit integers between 1 and 100, a 2-digit number has to be selected at random. What is the probability that the selected number is not divisible by 7?

Question 84. Which one of the following is the tightest upper bound that represents the number of swaps required to sort n numbers using selection sort?

Question 85. What is the maximum number of reduce moves that can be taken by a bottom-up parser for a grammar with no epsilon- and unit-production (i.e., of type A → є and A → a) to parse a string with n tokens?

Question 86. Consider the languages L1 = φ and L2 ={a}. Which one of the following represents L1L2* ᴜ L3* ?

Question 87. Match the problem domains in GROUP I with the solution technologies in GROUP II.GROUP I                                            GROUP II(P) Service oriented computing       (1) Interoperability(Q) Heterogeneous communicating      systems                                          (2) BPMN(R) Information representation        (3) Publish-find-bind(S) Process description                      (4) XML

Question 88. A scheduling algorithm assigns priority proportional to the waiting time of a process. Every process starts with priority zero (the lowest priority). The scheduler re-evaluates the process priorities every T time units and decides the next process to schedule. Which one of the following is TRUE if the processes have no I/O operations and all arrive at time zero?

Question 89. Which of the following statements is/are FALSE? 1. For every non-deterministic Turing machine, there exists an equivalent deterministic
Turing machine. 2. Turing recognizable languages are closed under union and complementation. 3. Turing decidable languages are closed under intersection and complementation. 4. Turing recognizable languages are closed under union and intersection.

Question 90. Which of the following statements are TRUE? 1. The problem of determining whether there exists a cycle in an undirected graph is in P. 2. The problem of determining whether there exists a cycle in an undirected graph is in NP. 3. If a problem A is NP-Complete, there exists a non-deterministic polynomial time algorithm to solve A.