Explanation:

• When the House is in session, it is the Speaker who can call for a floor test. But when the Assembly is not in session, the Governor’s residuary powers under Article 163 allow him to call for a floor test. In 2020, the Supreme Court in Shivraj Singh Chouhan & Ors versus Speaker case upheld the powers of the Speaker to call for a floor test if there is a prima facie view that the government has lost its majority. 
• Governor would not need the advice of council of ministers if the Constitution requires him to carry out any function at her/his discretion.

Hence only statement 2nd is correct.