Choice "B" is correct. Actual authority arises from the communications between the principal and the agent. Whether the agent discloses the principal to the third party with whom the agent contracts has no effect on the communications between the principal and the agent.
Choice "c" is incorrect. Apparent authority arises from the communications between the principal and the third party with whom the agent deals. If the principal is undisclosed, as under the facts here, the third party has no idea that there is a principal, and so there are no communications between the third party and the principal from which apparent authority can arise.
Choice "a" is incorrect. A principal generally is not liable for an agent's torts, but can be liable when the torts are authorized. The fact that the principal is undisclosed has no effect on this rule.
Choice "d" is incorrect. When a principal is undisclosed, the third party with whom the agent deals may hold either the agent or the principal liable on contracts that the agent enters into on the principal's behalf.