Test Page

Question 1
Let G be a connected undirected weighted graph. Consider the following two statements.

S1: There exists a minimum weight edge in G which is present in every minimum spanning tree of G.
S2: If every edge in G has distinct weight, then G has a unique minimum spanning tree.

Which one of the following options is correct?
A
Both S1 and S2 are true
B
S1 is true and S2 is false
C
S1 is false and S2 is true
D
Both S1 and S2 are false
Algorithm   Minimum Spanning Tree
Question 2
Let H be a binary min-heap consisting of n elements implemented as an array. What is the worst case time complexity of an optimal algorithm to find the maximum element in H?
A
\Theta (1)
B
\Theta (\log n)
C
\Theta ( n)
D
\Theta (n \log n)
Data Structure   Heap Tree
Question 3
Consider the following ANSI C program:
int main () {
    Integer x;
    return 0;
} 
Which one of the following phases in a seven-phase C compiler will throw an error?
A
Lexical analyzer
B
Syntax analyzer
C
Semantic analyzer
D
Machine dependent optimizer
Compiler Design   Syntax-directed Translation
Question 4
The format of the single-precision floating point representation of a real number as per the IEEE 754 standard is as follows:

\begin{array}{|c|c|c|} \hline \text{sign} & \text{exponent} & \text{mantissa} \\ \hline \end{array}

Which one of the following choices is correct with respect to the smallest normalized positive number represented using the standard?
A
exponent = 00000000 and mantissa = 0000000000000000000000000
B
exponent = 00000000 and mantissa = 0000000000000000000000001
C
exponent = 00000001 and mantissa = 0000000000000000000000000
D
exponent = 00000001 and mantissa = 0000000000000000000000001
Digital Logic   Number System
Question 5
Which one of the following circuits implements the Boolean function given below?

f(x,y,z) = m_0+m_1+m_3+m_4+m_5+m_6

where m_i is the i^{th} minterm.

A
A
B
B
C
C
D
D
Digital Logic   Combinational Circuit
Question 6
Consider the following statements S1 and S2 about the relational data model:

S1: A relation scheme can have at most one foreign key.
S2: A foreign key in a relation scheme R cannot be used to refer to tuples of R.

Which one of the following choices is correct?
A
Both S1 and S2 are true
B
S1 is true and S2 is false
C
S1 is false and S2 is true
D
Both S1 and S2 are false
Database Management System   Relational Schema
Question 7
Consider the three-way handshake mechanism followed during TCP connection establishment between hosts P and Q. Let X and Y be two random 32-bit starting sequence numbers chosen by P and Q respectively. Suppose P sends a TCP connection request message to Q with a TCP segment having SYN bit =1, SEQ number =X, and ACK bit =0. Suppose Q accepts the connection request. Which one of the following choices represents the information present in the TCP segment header that is sent by Q to P?
A
SYN bit =1, SEQ number =X+1, ACK bit =0, ACK number =Y, FIN bit =0
B
SYN bit =0, SEQ number =X+1, ACK bit =0, ACK number =Y, FIN bit =1
C
SYN bit =1, SEQ number =Y, ACK bit =1, ACK number =X+1, FIN bit =0
D
SYN bit =1, SEQ number =Y, ACK bit =1, ACK number =X, FIN bit =0
Computer Network   Transport Layer Protocol
Question 8
What is the worst-case number of arithmetic operations performed by recursive binary search on a sorted array of size n?
A
\Theta (\sqrt{n})
B
\Theta ( \log _2 (n))
C
\Theta ( n^2)
D
\Theta ( n)
Data Structure   Array
Question 9
Let L \subseteq \{0,1\}^* be an arbitrary regular language accepted by a minimal DFA with k states. Which one of the following languages must necessarily be accepted by a minimal DFA with k states?
A
L - \{01\}
B
L \cup \{01\}
C
\{0,1\}^* -L
D
L \cdot L
Theory of Computation   Regular Language
Question 10
Consider the following ANSI C program.
 #include < stdio.h >
int main( ) 
{
    int arr[4][5];
    int  i, j;
    for (i=0; i < 4; i++) 
  {
        for (j=0; j < 5; j++) 
        {
            arr[i][j] = 10 * i + j;
        }
    }
    printf("%d", *(arr[1]+9));
    return 0;
}
What is the output of the above program?
A
14
B
20
C
24
D
30
C Programming   Array and Pointer
There are 10 questions to complete.
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