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1.

The minimum positive integer p such that 3p modulo 17 = 1 is(A) 5(B) 8(C) 12(D) 16

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2.

Consider a weighted undirected graph with positive edge weights and let uv be an edge in the graph. It is known that the shortest path from the source vertex s to u has weight 53 and the shortest path from s to v has weight 65. Which one of the following statements is always true?(A) weight (u, v) < 12(B) weight (u, v) ≤ 12(C) weight (u, v) > 12(D) weight (u, v) ≥ 12

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3.

What is the largest integer m such that every simple connected graph with n vertices and n edges contains at least m different spanning trees?(A) 1(B) 2(C) 3(D) n

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4.

Let A be the . What is the maximum value of xTAx where the maximum is taken over all x that are the unit eigenvectors of A?(A) 5(B) (5 + √5)/2(C) 3(D) (5 – √5)/2

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5.

The head of a hard disk serves requests following the shortest seek time first (SSTF) policy. The head is initially positioned at track number 180.What is the maximum cardinality of the request set, so that the head changes its direction after servicing every request if the total number of tracks are 2048 and the head can start from any track?(A) 9(B) 10(C) 11(D) 12

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6.

The head of a hard disk serves requests following the shortest seek time first (SSTF) policy. The head is initially positioned at truck number 180.Which of the request sets will cause the head to change its direction after servicing every request assuming that the head does not change direction if there is a tie in SSTF and all the requests arrive before the servicing starts?(A) 11, 139, 170, 178, 181, 184, 201, 265(B) 10, 138, 170, 178, 181, 185, 201, 265(C) 10, 139, 169, 178, 181, 184, 201, 265(D) 10, 138, 170, 178, 181, 185, 200, 265

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7.

Let P1,P2,…,Pn be n points in the xy-plane such that no three of them are collinear. For every pair of points Pi and Pj, let Lij be the line passing through them. Let Lab be the line with the steepest gradient among all n(n−1)/2 lines.The time complexity of the best algorithm for finding Pa and Pb is(A) Θ(n)(B) Θ(nlogn)(C) Θ(nlogsup>2n)(D) Θ(n2)

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8.

Let P1, P2,….. , Pn be n points in the xy-plane such that no three of them are collinear. For every pair of points Pi and Pj, let Lij be the line passing through them. Let Lab be the line with the steepest gradient amongst all n(n -1)/2 lines.Which one of the following properties should necessarily be satisfied ?(A) Pa and Pb are adjacent to each other with respect to their x-coordinate(B) Either Pa or Pb has the largest or the smallest y-coordinate among all the points(C) The difference between x-coordinatef Pa and Pb is minimum(D) None of the above

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9.

Consider the following expressionad’ + (ac)’ + bc’dWhich of the following Karnaugh Maps correctly represents the expression?(A) A(B) B(C) C(D) D

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10.

Consider the following expressionad’ + (ac)’ + bc’dWhich of the following expressions does not correspond to the Karnaugh Map obtained for the above expression??(A) c’d’+ ad’ + abc’ + (ac)’d(B) (ac)’ + c’d’ + ad’ + abc’d(C) (ac)’ + ad’ + abc’ + c’d(D) b’c’d’ + acd’ + (ac)’ + abc’

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11.

When searching for the key value 60 in a binary search tree, nodes containing the key values 10, 20, 40, 50, 70 80, 90 are traversed, not necessarily in the order given. How many different orders are possible in which these key values can occur on the search path from the root to the node containing the value 60?(A) 35(B) 64(C) 128(D) 5040

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12.

The function f is defined as follows:int f (int n) {if (n <= 1) return 1;else if (n % 2 == 0) return f(n/2);else return f(3n - 1);}Assuming that arbitrarily large integers can be passed as a parameter to the function, consider the following statements.1. The function f terminates for finitely many different values of n ≥ 1.ii. The function f terminates for infinitely many different values of n ≥ 1.iii. The function f does not terminate for finitely many different values of n ≥ 1.iv. The function f does not terminate for infinitely many different values of n ≥ 1.Which one of the following options is true of the above?(A) (i) and (iii)(B) (i) and (iv)(C) (ii) and (iii)(D) (ii) and (iv)

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