Consider a max heap, represented by the array: 40, 30, 20, 10, 15, 16, 17, 8, 4. Now consider that a value 35 is inserted into this heap. After insertion, the new heap is

To insert an element into a binary max-heap stored in a 1-indexed array:

1. Initial Array: [40, 30, 20, 10, 15, 16, 17, 8, 4] with size $n = 9$.

2. Append the new element: Insert $35$ at index $10$:

   $$\text{Array}[10] = 35$$

3. Up-heapify (Bubble-up):

   • Compare with its parent at index $\lfloor 10/2 \rfloor = 5$ (which has value $15$): Since $35 > 15$, swap $\text{Array}[10]$ and $\text{Array}[5]$. Now $\text{Array}[5] = 35$ and $\text{Array}[10] = 15$.

   • Compare with its new parent at index $\lfloor 5/2 \rfloor = 2$ (which has value $30$): Since $35 > 30$, swap $\text{Array}[5]$ and $\text{Array}[2]$. Now $\text{Array}[2] = 35$ and $\text{Array}[5] = 30$.

   • Compare with its new parent at index $\lfloor 2/2 \rfloor = 1$ (which has value $40$): Since $35 \le 40$, the max-heap property is satisfied, and the process terminates.

4. Final Array Representation: 40, 35, 20, 10, 30, 16, 17, 8, 4, 15

Therefore, option (B) is correct.