Ampere's Circuital law is

The correct answer is Option (1) → Not independent of Biot savart law, its relationship to the biot savart law is similar as what gauss law is to coulomb's law

Ampere's circuital law can be derived from the Biot-Savart law, so it is not an independent law. In the same way, Gauss's law of electrostatics follows from Coulomb's law: the integral law in each pair expresses the same physics as the inverse-square law it comes from.

NCERT (2026-27):
Points to Ponder – “… Ampere’s Circuital law is not independent of the Biot-Savart law. It can be derived from the Biot-Savart law. Its relationship to the Biot-Savart law is similar to the relationship between Gauss’s law and Coulomb’s law.”