Step 1: About the scheme's implementation date.
The Mukhyamantri Gram Sadak Evam Vikas Yojana was launched on 23 April 2011 in the state, so statement (I) is correct.
Step 2: Funding of the scheme.
This scheme is not 100% state-funded; it often includes central government funds and other sources, so statement (II) is incorrect.
Step 3: Employment provision under the scheme.
The scheme provides employment opportunities to rural unemployed persons, typically ensuring about 100 days of work, so statement (III) is correct.
Step 4: Management method.
The scheme's management is generally done through government agencies, and while public participation may be encouraged, it is not the primary basis, so statement (IV) is incorrect.
Conclusion:
Only statements (I) and (III) are correct.