The most relevant political cause of the Indian Rebellion of 1857 from the options provided is:
B. The British East India Company gained greater control through its doctrine of lapse.
The doctrine of lapse was a policy that allowed the British East India Company to annex states where the ruler was died without a direct heir. This policy created resentment among Indian princes and contributed to the discontent that fueled the rebellion. While option C also references a key trigger for the revolt (the rumor about animal fat), option B directly addresses a political cause related to the governance and control exerted by the British East India Company in India.