What is the function of progestogens in contraceptive pills?

The correct answer is Option (3) → Both (1) and (2)

Oral pills contain small doses of progestogens alone or progestogen-estrogen combinations. They are taken daily for 21 days, from within the first five days of the menstrual cycle. These hormones prevent pregnancy in more than one way: they inhibit ovulation and implantation, and they also alter the quality of cervical mucus so that sperms cannot enter easily.

Option (1) Alter the quality of cervical mucus to prevent/retard entry of sperms. — Correct statement, but it is only one of the correct points, so on its own it is not the answer. The changed cervical mucus prevents or retards the entry of sperms into the uterus.

Option (2) Inhibit ovulation and implantation. — Correct statement, but it is only one of the correct points, so on its own it is not the answer. With no ovulation, there is no ovum to fertilise. The hormones also make the uterus unfit for implantation of an embryo.

NCERT Extract:
Population Stabilisation and Birth Control – “… Oral administration of small doses of either progestogens or progestogen–estrogen combinations is another contraceptive method used by the females. They are used in the form of tablets and hence are popularly called the pills. Pills have to be taken daily for a period of 21 days starting preferably within the first five days of menstrual cycle. … They inhibit ovulation and implantation as well as alter the quality of cervical mucus to prevent/retard entry of sperms.”