GATE-CS-2015 (Set 1)

Question 31

A file is organized so that the ordering of data records is the same as or close to the ordering of data entries in some index. Then that index is called

• Dense
• Sparse
• Clustered
• Unclustered

Question 32

The height of a tree is the length of the longest root-to-leaf path in it. The maximum and minimum number of nodes in a binary tree of height 5 are

• 63 and 6, respectively
• 64 and 5, respectively
• 32 and 6, respectively
• 31 and 5, respectively

Question 33

• 0.99
• 1
• 99
• 0.9

Question 34

Consider the following relations:

SELECT S. Student_Name, sum(P.Marks)
     FROM Student S, Performance P
     WHERE S.Roll_No = P.Roll_No
     GROUP BY S.Student_Name 

The number of rows that will be returned by the SQL query is _________

• 0
• 1
• 2
• 3

Question 35

The binary operator ≠ is defined by the following truth table Which one of the following is true about the binary operator ≠?

• Both commutative and associative
• Commutative but not associative
• Not commutative but associative
• Neither commutative nor associative

Question 36

Consider a LAN with four nodes S1, S2, S3 and S4. Time is divided into fixed-size slots, and a node can begin its transmission only at the beginning of a slot. A collision is said to have occurred if more than one node transmit in the same slot. The probabilities of generation of a frame in a time slot by S1, S2, S3 and S4 are 0.1, 0.2, 0.3 and 0.4, respectively. The probability of sending a frame in the first slot without any collision by any of these four stations is _________.

• 0.462
• 0.711
• 0.5
• 0.652

Question 37

Suppose the following disk request sequence (track numbers) for a disk with 100 tracks is given: 45, 20, 90, 10, 50, 60, 80, 25, 70. Assume that the initial position of the R/W head is on track 50. The additional distance that will be traversed by the R/W head when the Shortest Seek Time First (SSTF) algorithm is used compared to the SCAN (Elevator) algorithm (assuming that SCAN algorithm moves towards 100 when it starts execution) is _________ tracks

• 8
• 9
• 10
• 11

Question 38

Consider the following C function.

C

int fun1 (int n)
{
   int i, j, k, p, q = 0;
   for (i = 1; i < n; ++i)
   {
      p = 0;
      for (j = n; j > 1; j = j/2)
         ++p;
      for (k = 1; k < p; k = k*2)
         ++q;
   }
   return q;
}

Which one of the following is the time complexity for function fun1?

• n³
  

• n (logn)²
  

• nlogn 
  

• nlog(logn)
  

Question 39

Consider a max heap, represented by the array: 40, 30, 20, 10, 15, 16, 17, 8, 4. Now consider that a value 35 is inserted into this heap. After insertion, the new heap is

• 40, 30, 20, 10, 15, 16, 17, 8, 4, 35
• 40, 35, 20, 10, 30, 16, 17, 8, 4, 15
• 40, 30, 20, 10, 35, 16, 17, 8, 4, 15
• 40, 35, 20, 10, 15, 16, 17, 8, 4, 30

Question 40

Suppose L = {p, q, r, s, t} is a lattice represented by the following Hasse diagram: For any x, y ∈ L, not necessarily distinct, x ∨ y and x ∧ y are join and meet of x, y respectively. Let L³ = {(x,y,z): x, y, z ∈ L} be the set of all ordered triplets of the elements of L. Let pr be the probability that an element (x,y,z) ∈ L³ chosen equiprobably satisfies x ∨ (y ∧ z) = (x ∨ y) ∧ (x ∨ z). Then

• Pr = 0
• Pr = 1
• 0 < Pr ≤ 1/5
• 1/5 < Pr < 1