Step 1: Identify Amniocentesis.
Amniocentesis is a technique used to test the sex of the fetus by sampling amniotic fluid. Therefore, it corresponds to (IV) Testing of sex.
Step 2: Understand Maternal Mortality Rate.
Maternal mortality rate refers to the death rate of mothers during childbirth, so it corresponds to (III) Death rate.
Step 3: Understand Vasectomy.
Vasectomy involves the ligation of the vas deferens for male sterilization, so it corresponds to (II) Ligation of vas deferens.
Step 4: Understand Tubectomy.
Tubectomy involves the ligation of the fallopian tubes in females, so it corresponds to (I) Ligation of fallopian tube.
Thus, the correct match is:
(A) - (IV), (B) - (III), (C) - (II), (D) - (I).
Final Answer:
\[
\boxed{\text{The correct match is (A) - (IV), (B) - (III), (C) - (II), (D) - (I).}}
\]