D

Step 1: Understand the significance of dimensional correctness in equations.
A dimensionally correct equation signifies that the units on both sides of the equation are consistent. This does not always imply the equation is physically or mathematically correct.
Step 2: Analyze each statement:
(i) A dimensionally correct equation may be correct.
This statement is true because if an equation is dimensionally correct, it could also be a valid expression of a physical relationship.
Step 3: (ii) A dimensionally correct equation may be incorrect.
This statement is true as well. Just because an equation is dimensionally valid does not guarantee its correctness in representing a physical law.
Step 4: (iii) A dimensionally incorrect equation may be correct.
This statement is false. If an equation is dimensionally incorrect, it means the units do not match, which indicates a fundamental flaw in the equation. It cannot be seen as valid.
Step 5: (iv) A dimensionally incorrect equation may be incorrect.
This statement is true as a dimensionally incorrect equation must also be invalid.
Conclusion: Therefore, statements (i), (ii), and (iv) are correct. Hence, the correct answer is Option D: (i), (ii), and (iv) are correct.