The shortest path from the root to a leaf in a binary heap of $31$ nodes is

Answer:

The correct answer is: $5\mathrm{.}00$

Question $14$

Correct

Mark $1\mathrm{.}00$ out of $1\mathrm{.}00$

The maximum number of nodes along any path from root to a leaf in a binary heap of $540$ nodes is

Answer:

The correct answer is: $10$

Question $15$

Incorrect

Mark $0\mathrm{.}00$ out of $1\mathrm{.}00$

After $33$ nodes have been inserted into an initially empty binary heap, the number of nodes in its left subtree will be:

Answer:

The correct answer is: $17$

Please show the formulas and working out required to obtain these answers