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Question 1

The increasing order of following functions in terms of asymptotic complexity is: [Tex]\\\\ f_{1}(n) = n^{0.999999}log (n)\\\\ f_{2}(n) = 10000000n\\\\ f_{3}(n) = 1.000001^{n} f_{4}(n) = n^{2} [/Tex]

f1(n); f4(n); f2(n); f3(n)
f1(n); f2(n); f3(n); f4(n);
f2(n); f1(n); f4(n); f3(n)
f1(n); f2(n); f4(n); f3(n)

Question 2

Which of the following changes to typical QuickSortimproves its performance on average and are generally done in practice.

1) Randomly picking up to make worst case less 
 likely to occur.
2) Calling insertion sort for small sized arrays 
 to reduce recursive calls.
3) QuickSort istail recursive, so tail call 
 optimizations can be done.
4) A linear time median searching algorithm is used 
 to pick the median, so that the worst case time 
 reduces to O(nLogn)

1 and 2
2, 3, and 4
1, 2 and 3
2, 3 and 4

Question 3

The output of following C program is

GATE CS 2015 Mock Test
tseT kcoM 5102 SC ETAG
Nothing is printed on screen
Segmentation Fault

Question 4

Consider the situation in which the disk read/write head is currently located at track 45 (of tracks 0-255) and moving in the positive direction. Assume that the following track requests have been made in this order: 40, 67, 11, 240, 87. What is the order in which optimised C-SCAN would service these requests and what is the total seek distance?

Question 5

Let swap() be a function that swaps two elements using their addresses. Consider the following C function. If an array {10, 20, 30, 40, 50, 60, 70, 80} is passed to the function, the array is changed to

{20, 10, 40, 30, 60, 50, 80, 70}
{10, 30, 20, 40, 60, 50, 80, 70}
{10, 20, 30, 40, 50, 60, 70, 80}
{80, 70, 60, 50, 40, 30, 20, 10}

Question 6

Given an array that represents elements of arithmetic progression in order. It is also given that one element is missing in the progression, the worst case time complexity to find the missing element efficiently is:

Θ(n)
Θ(nLogn)
Θ(Logn)
Θ(1)

Question 7

Consider the following two problems of graph. 1) Given a graph, find if the graph has a cycle that visits every vertex exactly once except the first visited vertex which must be visited again to complete the cycle. 2) Given a graph, find if the graph has a cycle that visits every edge exactly once. Which of the following is true about above two problems.

Problem 1 belongs NP Complete set and 2 belongs to P
Problem 1 belongs to P set and 2 belongs to NP Complete set
Both problems belong to P set
Both problems belong to NP complete set

Question 8

Select the correct asymptotic complexity of an algorithm with runtime T(n, n) where

T(x, c) = Θ(x) for c <= 2,
T(c, y) = Θ(y) for c <= 2, and
T(x, y) = Θ(x+y) + T(x/2, y/2)

Θ(nLogn)
Θ(n²)
Θ(n)
Θ(n²Logn)

Question 9

Consider the following three table to store student enrollements in different courses.

Student(, Name)
Course(, Name)
EnrollMents()

What does the following query do?

SELECT S.Name
FROM Student S, Course C, Enrollments E
WHERE S.EnrollNo = E.EnrollNo AND 
 C.Name = "DBMS" AND
 E.CourseID = C.CourseID AND
 S.EnrollNo IN 
 (SELECT S2.EnrollNo
 FROM Student S2, Course C2, Enrollments E2
 WHERE S2.EnrollNo = E2.EnrollNo AND
 E2.CourseID = C2.CourseID
 C2.Name = "OS")

Name of all students who are either enrolled in "DBMS" or "OS" courses
Name of all students who are enrolled in "DBMS" and "OS"
Name of all students who are either enrolled in "DBMS" or "OS" or both.
None of the above

Question 10

Consider the following Employee table

ID salary DeptName
1 10000 EC
2 40000 EC
3 30000 CS
4 40000 ME
5 50000 ME
6 60000 ME 
7 70000 CS

How many rows are there in the result of following query?

SELECT E.ID
FROM Employee E
WHERE EXISTS (SELECT E2.salary
 FROM Employee E2
 WHERE E2.DeptName = 'CS'
 AND E.salary > E2.salary)

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