Gate IT 2007

Question 71

Consider the following expression
ad\' + (ac)\' + bc\'d
Which of the following Karnaugh Maps correctly represents the expression?

• A
• B
• C
• D

Question 72

Consider the following expression
ad\' + (ac)\' + bc\'d
Which of the following expressions does not correspond to the Karnaugh Map obtained for the above expression??

• c\'d\'+ ad\' + abc\' + (ac)\'d
• (ac)\' + c\'d\' + ad\' + abc\'d
• (ac)\' + ad\' + abc\' + c\'d
• b\'c\'d\' + acd\' + (ac)\' + abc\'

Question 73

Let P₁, P₂,..... , P_n be n points in the xy-plane such that no three of them are collinear. For every pair of points P_i and P_j, let L_ij 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 ?

• P_a and P_b are adjacent to each other with respect to their x-coordinate
• Either P_a or P_b has the largest or the smallest y-coordinate among all the points
• The difference between x-coordinatef P_a and P_b is minimum
• None of the above

Question 74

Let P₁,P₂,…,P_n be n points in the xy-plane such that no three of them are collinear. For every pair of points P_i and P_j, let L_ij 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 P_a and P_b is

• Θ(n)
• Θ(nlogn)
• Θ(nlogsup>2n)
• Θ(n²)

Question 75

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?

• 11, 139, 170, 178, 181, 184, 201, 265
• 10, 138, 170, 178, 181, 185, 201, 265
• 10, 139, 169, 178, 181, 184, 201, 265
• 10, 138, 170, 178, 181, 185, 200, 265

Question 76

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?

• 9
• 10
• 11
• 12

Question 77

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?

• 35
• 64
• 128
• 5040

Question 78

Processes P₁ and P₂ use critical_flag in the following routine to achieve mutual exclusion. Assume that critical_flag is initialized to FALSE in the main program.
get_exclusive_access ( ) { if (critical _flag == FALSE) { critical_flag = TRUE ; critical_region () ; critical_flag = FALSE; } } Consider the following statements.
i. It is possible for both P₁ and P₂ to access critical_region concurrently.
ii. This may lead to a deadlock.
Which of the following holds?

• (i) is false and (ii) is true
• Both (i) and (ii) are false
• (i) is true and (ii) is false
• Both (i) and (ii) are true

Question 79

The minimum positive integer p such that 3^p modulo 17 = 1 is

• 5
• 8
• 12
• 16

Question 80

A firewall is to be configured to allow hosts in a private network to freely open TCP connections and send packets on open connections. However, it will only allow external hosts to send packets on existing open TCP connections or connections that are being opened (by internal hosts) but not allow them to open TCP connections to hosts in the private network. To achieve this the minimum capability of the firewall should be that of

• A combinational circuit
• A finite automaton
• A pushdown automaton with one stack
• A pushdown automaton with two stacks