The constitution of India lays down that the Vice-President should not be a member of either the House of Parliament or a House of the state legislature. If any such person is elected Vice-President, he is deemed to have vacated his seat in that House on the date on which he enters upon his office as Vice-President.

But he acts as the ex-officio Chairman of Rajya Sabha. 

Further Reading:

• Rajya Sabha
• Vice President of India