Explanation:

To determine whether an array represents a binary max-heap, we need to check if the heap property is satisfied for all elements in the array. The heap property states that for any given index i, the value at index i should be greater than or equal to the values at its children.

In the given options, we need to check which array satisfies the heap property.

Option a: 25,12,16,13,10,8,14
- At index 1 (root): 25
- Left child (index 2): 12
- Right child (index 3): 16
- Here, the root value (25) is greater than both its children, satisfying the heap property.
- Next, we need to check the children of index 2.
- Left child (index 4): 13
- Right child (index 5): 10
- Here, the heap property is violated as the root value (12) is less than its left child (13).
- Hence, option a does not represent a binary max-heap.

Option b: 25,14,12,13,10,8,16
- At index 1 (root): 25
- Left child (index 2): 14
- Right child (index 3): 12
- Here, the root value (25) is greater than both its children, satisfying the heap property.
- Next, we need to check the children of index 2.
- Left child (index 4): 13
- Right child (index 5): 10
- Here, the heap property is violated as the root value (14) is less than its left child (13).
- Hence, option b does not represent a binary max-heap.

Option c: 25,14,16,13,10,8,12
- At index 1 (root): 25
- Left child (index 2): 14
- Right child (index 3): 16
- Here, the root value (25) is greater than both its children, satisfying the heap property.
- Next, we need to check the children of index 2.
- Left child (index 4): 13
- Right child (index 5): 10
- Here, the heap property is satisfied as the root value (14) is greater than both its children.
- Similarly, the heap property is satisfied for the remaining elements in the array.
- Hence, option c represents a binary max-heap.

Therefore, the correct answer is option c) 25,14,16,13,10,8,12.