Consider the B⁺ tree in the adjoining figure, where each node has at most two keys and three links.

Keys K 15 and then K 25 are inserted into this tree in that order. Exactly how many of the following nodes (disregarding the links) will be present in the tree after the two insertions?

Consider the B⁺ tree in the adjoining figure, where each node has at most two keys and three links.

Now the key K 50 is deleted from the B⁺ tree resulting after the two insertions made earlier. Consider the following statements about the B⁺ tree resulting after this deletion.

i) The height of the tree remains the same.

ii) The node (disregarding the links) is present in the tree.

iii) The root node remains unchanged (disregarding the links).

Which one of the following options is true ?

The order of an internal node in a B⁺ tree index is the maximum number of children it can have. Suppose that a child pointer takes 6 bytes, the search field value takes 14 bytes, and the block size is 512 bytes. What is the order of the internal node?

Consider a table T in a relational database with a key field K. A B-tree of order p is used as an access structure on K, where p denotes the maximum number of tree pointers in a B-tree index node. Assume that K is 10 bytes long; disk block size is 512 bytes; each data pointer P_D is 8 bytes long and each block pointer P_B is 5 bytes long. In order for each B-tree node to fit in a single disk block, the maximum value of p is