Which one of the following is not a common mechanical barrier method…

The correct answer is Option (3) → Implants

Barrier methods stop the ovum and the sperms from meeting by placing a physical barrier in their way.

Option (1) Diaphragms — A mechanical barrier.

Option (2) Vaults — A mechanical barrier.

Option (3) Implants — Not a mechanical barrier. Implants are hormonal contraceptives placed under the skin. They release progestogens or progestogen-estrogen combinations that stop ovulation and implantation; they put no barrier in the way of the sperms.

Option (4) Cervical caps — A mechanical barrier.

NCERT Extract:
Population Stabilisation and Birth Control – “… Diaphragms, cervical caps and vaults are also barriers made of rubber that are inserted into the female reproductive tract to cover the cervix during coitus. They prevent conception by blocking the entry of sperms through the cervix. They are reusable.”
Infertility – “… Various contraceptive options are available now such as natural, traditional, barrier, IUDs, pills, injectables, implants and surgical methods.”