Explanation:

Statement 1: State government pursuing anti-secular politics is liable to action under Article 356.
- Article 356 of the Indian Constitution deals with the imposition of President's Rule in a state. It empowers the President to suspend the state government and impose direct Central rule.
- However, the Constitution does not explicitly mention anti-secular politics as a ground for imposing President's Rule.
- Article 356 provides for the imposition of President's Rule in a state in case of a breakdown of constitutional machinery. It can be invoked if there is a failure of the state government to comply with constitutional provisions or if there is a situation where the governance of the state cannot be carried out in accordance with the Constitution.
- Therefore, while a state government pursuing anti-secular politics may be considered undemocratic or against the principles of secularism, it may not necessarily be a ground for imposing President's Rule under Article 356. Hence, statement 1 is incorrect.

Statement 2: Indian concept of secularism connotes a complete separation between religion and the state.
- The Indian concept of secularism is different from the Western concept of secularism which emphasizes a complete separation between religion and the state.
- In India, secularism is enshrined in the Preamble of the Constitution which declares India to be a secular country.
- The Indian concept of secularism does not mean the absence of religion from public life but rather the equal treatment and protection of all religions by the state.
- The Indian Constitution guarantees freedom of religion to all individuals and prohibits discrimination on the grounds of religion.
- The state is expected to treat all religions impartially and not favor or discriminate against any particular religion.
- The state can intervene in religious matters for social welfare, reform, or to prevent discrimination or oppression.
- Therefore, the Indian concept of secularism does not imply a complete separation between religion and the state. Hence, statement 2 is correct.

Conclusion:
- In conclusion, statement 1 is incorrect as the imposition of President's Rule under Article 356 does not directly apply to state governments pursuing anti-secular politics. However, statement 2 is correct as the Indian concept of secularism does not connote a complete separation between religion and the state. Therefore, the correct answer is option 'A' - 1 only.