Gate IT 2005

Question 11

How many pulses are needed to change the contents of a 8-bit up counter from 10101100 to 00100111 (rightmost bit is the LSB)?

• 134

• 133

• 124

• 123

Question 12

The numbers 1, 2, .... n are inserted in a binary search tree in some order. In the resulting tree, the right subtree of the root contains p nodes. The first number to be inserted in the tree must be

• p
• p + 1
• n - p
• n - p + 1

Question 13

A function f defined on stacks of integers satisfies the following properties. f(∅) = 0 and f (push (S, i)) = max (f(S), 0) + i for all stacks S and integers i.

If a stack S contains the integers 2, -3, 2, -1, 2 in order from bottom to top, what is f(S)?

• 6
• 4
• 3
• 2

Question 14

In a depth-first traversal of a graph G with n vertices, k edges are marked as tree edges. The number of connected components in G is

• k
• k + 1
• n - k - 1
• n - k

Question 15

In the following table, the left column contains the names of standard graph algorithms and the right column contains the time complexities of the algorithms. Match each algorithm with its time complexity.

1. Bellman-Ford algorithm 2. Kruskal’s algorithm 3. Floyd-Warshall algorithm 4. Topological sorting

A : O ( m log n) B : O (n3) C : O (nm) D : O (n + m)

• 1→ C, 2 → A, 3 → B, 4 → D
• 1→ B, 2 → D, 3 → C, 4 → A
• 1→ C, 2 → D, 3 → A, 4 → B
• 1→ B, 2 → A, 3 → C, 4 → D

Question 16

A hash table contains 10 buckets and uses linear probing to resolve collisions. The key values are integers and the hash function used is key % 10. If the values 43, 165, 62, 123, 142 are inserted in the table, in what location would the key value 142 be inserted?

• 2
• 3
• 4
• 6

Question 17

The Function Point (FP) calculated for a software project are often used to obtain an estimate of Lines of Code (LOC) required for that project. Which of the following statements is FALSE in this context.  

• The relationship between FP and LOC depends on the programming language used to implement the software.
• LOC requirement for an assembly language implementation will be more for a given FP value, than LOC for implementation in COBOL
• On an average, one LOC of C++ provides approximately 1.6 times the functionality of a single LOC of FORTRAN
• FP and LOC are not related to each other

Question 18

Consider the entities \'hotel room\', and \'person\' with a many to many relationship \'lodging\' as shown below: If we wish to store information about the rent payment to be made by person (s) occupying different hotel rooms, then this information should appear as an attribute of  

• Person
• Hotel Room
• Lodging
• None of these

Question 19

A table has fields Fl, F2, F3, F4, F5 with the following functional dependencies F1 → F3   F2→ F4   (F1 . F2) → F5 In terms of Normalization, this table is in  

• 1 NF
• 2 NF
• 3 NF
• none

Question 20

A B-Tree used as an index for a large database table has four levels including the root node. If a new key is inserted in this index, then the maximum number of nodes that could be newly created in the process are:

• 5
• 4
• 3
• 2