Question

how did the subsidiary alliance and doctrine of lapse weaken the indian kingdoms

Answer 1

In subsidiary alliance rulers of India were not allowed to have their own armed forces .They protected by the soldiers of East India company for which they had to pay high rents and idf the rulers were not able to pay rents their kingdom was taken away from them as penalty.
In doctrine of lapse of an Indian ruler would die without any male hire his kingdom would become company territory simply applying these policies weaken indian kingdoms.

Answer 2

Answer:

Doctrine of lapse. According to the Subsidiary alliance, the ruler (who accepted subsidiary alliance) had to accept the British army into his territory. ... It was decided that in case of any revolt/protest, the respective state would receive support of British army.