Let us analyze each statement in detail:
- (i) Incorrect: A thread formed on a cylindrical surface is called a straight thread, not a taper thread. Taper threads are formed on conical surfaces and gradually decrease in diameter.
- (ii) Incorrect: In a single start thread, the lead \( L \) equals the pitch (P), so \( L = P \), not \( 2P \). \( L = nP \) only when it is an n-start thread.
- (iii) Correct: In actual applications, a small clearance is necessary between internal and external threads to avoid jamming and to allow proper engagement. This is a standard manufacturing practice.
- (iv) Correct: The root of a thread is the innermost part, i.e., the portion closest to the axis. In internal threads, the root lies deep within the cut, near the centerline.
Hence, only statements (iii) and (iv) are correct.