Answer: D
Let $T(k)$ be the running time to merge $k$ arrays, where each of them has $n$ elements. We have the following recursion:
$$T(k)=2 T(k / 2)+O(k n)$$
Again, we can use the recursion tree method to solve this recursion. Also, you can observe that $n$ is independent of $k$, therefore, this is exactly similar to the recursion we saw for the running time of Merge sort, with an extra $n$ at each level. So, we have:
$$T(k)=O(n k \log k).$$
This question is inspired from one of the popular GATE PYQ: https://gateoverflow.in/1762/Gate-cse-2012-question-39
For this GATE PYQ if we put $k=n$ in the above time complexity AFTER solving reccurance then we get $$T(k)=2 T(k / 2)+O(k\times n) =O(nk \log k) = O(n^2 \log n) $$
The amazing and important point is: We can not put $k=n$ before solving recurrence, putting $k=n$ before solving recurrence will get you the wrong answer. (You should know why it is the case if you can not understand then spend a few hours in understanding and then tag Sachin Mittal 1 under PYQ comment section.)
Putting $k=n$ before solving recuurance:
$$T(k)=2 T(k / 2)+O(k\times n) \\\implies T(n)=2 T(n/ 2)+O(n^2) = O(n^2) \color{red}{\text{ WRONG}} $$
Hence Option A is wrong here. In fact we can not write recurrence relation directly.
