GATE CSE 2021 SET-2

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?

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?

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?

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?

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.