Let $G$ be any undirected graph with positive edge weights, and $T$ be a minimum spanning tree of $G$. For any two vertices, $u$ and $v$, let $d_1(u, v)$ and $d_2(u, v)$ be the shortest distances between $u$ and $v$ in $G$ and $T$, respectively. Which ONE of the options is CORRECT for all possible $G, T, u$ and $v$ ?

Consider the following recurrence relation :

$$T(n)=2 T(n-1)+n 2^n \text { for } n>0, T(0)=1$$

Which ONE of the following options is CORRECT?

$$\text { The pseudocode of a function fun( ) is given below : }$$

 fun(int A[0, .., n-1]) {
    for i = 0 to n-2
        for j=0 to n-i-2
            if (A[]]>A[j + 1])
                then swap A[j] and A[j+1]
}

Let $A[0, \ldots, 29]$ be an array storing 30 distinct integers in descending order. The number of swap operations that will be performed, if the function fun( ) is called with $A[0, \ldots, 29]$ as argument, is _________. (Answer in integer)

The maximum value of $x$ such that the edge between the nodes $B$ and $C$ is included in every minimum spanning tree of the given graph is _______. (Answer in integer)