The number of modes in which a transaction may request a Lock in multiple-granularity Locking is : 

The correct answer is: option 4: Six

Concept:

In **multiple-granularity locking**, a transaction can request locks at different levels of a hierarchy (e.g., database, table, page, record), and **six types of lock modes** are defined to support both shared and exclusive access while maintaining concurrency control.

The six lock modes are:

1. IS (Intent Shared) – Indicates intention to acquire shared locks at a lower level.
2. IX (Intent Exclusive) – Indicates intention to acquire exclusive locks at a lower level.
3. S (Shared) – Allows shared access to a data item.
4. SIX (Shared Intent Exclusive) – A combination of S and IX. Shared lock on current level and intent exclusive on lower levels.
5. X (Exclusive) – Allows read and write access to a data item.
6. NULL – No lock held (may be considered in lock compatibility matrices).

Explanation of options:

• Option 1 – Two: ❌ Only covers S and X, not sufficient for multigranularity.
• Option 2 – Five: ❌ Missing one of the standard modes.
• Option 3 – Three: ❌ Too few; excludes intent modes.
• Option 4 – Six: ✅ Correct. Standard multigranularity locking defines six modes.

Hence, the correct answer is: option 4: Six