Consider the following recurrence relations:

For all $n>1$,

$$ \begin{aligned} & T_1(n)=4 T_1\left(\frac{n}{2}\right)+T_2(n) \\ & T_2(n)=5 T_2\left(\frac{n}{4}\right)+\theta\left(\log _2 n\right) \end{aligned} $$

Assume that for all $n \leq 1, T_1(n)=1$ and $T_2(n)=1$. 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?

What is the worst-case number of arithmetic operations performed by recursive binary search on a sorted array of size n?

A binary search tree T contains n distinct elements. What is the time complexity of picking an element in T that is smaller than the maximum element in T?