Consider the following statements:

1. The Speaker of the Legislative Assembly shall vacate his/her office if he/she ceases to be a member of the Assembly.

2. Whenever the Legislative Assembly is dissolved, the Speaker shall vacate his/her office immediately.

Which of the statements given above is/are correct?

The correct option is 1 only.

Let us analyze both statements in detail based on the constitutional provisions regarding the Speaker of a State Legislative Assembly in India (Article 179 of the Constitution of India):

Analysis of Statement 1:
According to Article 179(a) of the Indian Constitution, a member holding office as Speaker or Deputy Speaker of an Assembly shall vacate his/her office if he/she ceases to be a member of the Assembly. Therefore, Statement 1 is correct.

Analysis of Statement 2:
According to the proviso to Article 179 of the Indian Constitution, whenever the Legislative Assembly is dissolved, the Speaker does not vacate his/her office immediately. Instead, the Speaker continues in office until immediately before the first meeting of the new Assembly after the dissolution. Therefore, Statement 2 is incorrect.

Hence, only Statement 1 is correct.