GATE CSE 2021 SET-2


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




There are 5 questions to complete.

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