a) After inputting 52, which first goes to the left child of 54, it creates imbalance for the 62(as its height from left child becomes 5 and right child becomes 3 which is again the rule of AVL tree. So, we have rearrange which leads to 48 as the left child of 62 replacing 44 (44 becomes left child of this new 48 and 17 also becomes left child of this new 44) on the other side everything remains the same except 52 comes to the place of the old 48, this way the height of the 62 is still 4.