Option 1: If the Prime Minister is a member of the Rajya Sabha, they do not have to get elected to the Lok Sabha within six months. This option is incorrect.
Option 2: If the Prime Minister is a member of the Rajya Sabha, they can declare the government`s policies in both the Rajya Sabha and the Lok Sabha. This option is incorrect.
Option 3: If the Prime Minister is a member of the Rajya Sabha, they can participate in voting when a vote of no confidence is under consideration. This means that they can vote and voice their opinion in the Rajya Sabha during such a vote. This option is correct.
Option 4: If the Prime Minister is a member of the Rajya Sabha, they can take part in the budget deliberation in the Lok Sabha. This means that they can participate and discuss the budget in the Lok Sabha despite being a member of the Rajya Sabha. This option is incorrect.
Therefore, the correct answer to the question is option 3.