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Solution

Insert elements one by one in AVL tree.

Insert $35$:

Tree is balanced. No rotation.

Insert $50$:

$50$ becomes right child of $35$.

Tree is balanced. No rotation.

Insert $40$:

$40$ goes to left of $50$.

This creates Right-Left imbalance at $35$.

For Right-Left case, we do:

Right rotation at $50$

Left rotation at $35$

So far:

Left rotations $=1$

Right rotations $=1$

Insert $25$:

$25$ goes to left side.

Tree remains balanced. No rotation.

Insert $30$:

$30$ goes to right of $25$.

This creates Left-Right imbalance at $35$.

For Left-Right case, we do:

Left rotation at $25$

Right rotation at $35$

Now total:

Left rotations $=2$

Right rotations $=2$

Insert $60$:

$60$ goes to right side.

Tree remains balanced. No rotation.

Insert $78$:

$78$ goes to right of $60$.

This creates Right-Right imbalance at $50$.

For Right-Right case, we do:

Left rotation at $50$

Now total:

Left rotations $=3$

Right rotations $=2$

Insert $20$:

$20$ goes to left side.

Tree remains balanced. No rotation.

Insert $28$:

$28$ goes to right of $25$.

Tree still remains balanced. No rotation.

Therefore, total rotations are:

$3$ left rotations and $2$ right rotations.