GATE CS 2021 | Set 2

Question 11

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?

• Θ(1)

• Θ(logn)

• Θ(n)

• Θ(nlogn)

Question 12

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?

• Lexical analyzer
  

• Syntax analyzer
  

• Semantic analyzer
  

• Machine dependent optimizer
  

Question 13

The format of the single-precision floating point representation of a real number as per the IEEE 754 standard is as follows: Which one of the following choices is correct with respect to the smallest normalized positive number represented using the standard?

• exponent =00000000 and mantissa =0000000000000000000000000
• exponent =00000000 and mantissa =0000000000000000000000001
• exponent =00000001 and mantissa =0000000000000000000000000
• exponent =00000001 and mantissa =0000000000000000000000001

Question 14

Which one of the following circuits implements the Boolean function given below?

f(x,y,z) = m0 + m1 + m3 + m4 + m5 + m6 

where mi is the ith minterm.

• A
• B
• C
• D

Question 15

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?

• Both S1 and S2 are true
• S1 is true and S2 is false
• S1 is false and S2 is true
• Both S1 and S2 are false

Question 16

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?

• SYN bit =1, SEQ number =X+1, ACK bit =0, ACK number =Y, FIN bit =0
• SYN bit =0, SEQ number =X+1, ACK bit =0, ACK number =Y, FIN bit =1
• SYN bit =1, SEQ number =Y, ACK bit =1, ACK number =X+1, FIN bit =0
• SYN bit =1, SEQ number =Y, ACK bit =1, ACK number =X, FIN bit =0

Question 17

Let L⊆{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?

• L−{01}
• L∪{01}
• {0,1}*–L
• L⋅L

Question 18

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?

• 14
• 20
• 24
• 30

Question 19

Consider the following sets, where n≥2:

• S1: Set of all n×n matrices with entries from the set {a,b,c}
• S2: Set of all functions from the set {0,1,2 ... ,n²−1} to the set {0,1,2}

Which of the following choice(s) is/are correct?

• There does not exist a bijection from S1 to S2
• There exists a surjection from S1 to S2
• There exists a bijection from S1 to S2
• There does not exist an injection from S1 to S2

Question 20

Let L₁ be a regular language and L₂ be a context-free language. Which of the following languages is/are context-free?

• L₁∩L₂\'
• (L₁\'∪L₂\')\'
• L₁∪(L₂∪L₂\')
• (L₁∩L₂)∪(L₁∩L₂)