Let's analyze each statement regarding Electronic Voting Machines (EVMs) in India:

1. Statement 1: The first use of EVMs in a Lok Sabha election was in the year 2004, when EVMs were deployed nationwide.
   • This statement is correct. EVMs were first used in certain areas in 1982 but were introduced nationwide for Lok Sabha elections in 2004. This marked the first instance where EVMs were deployed throughout the entire country for this election.
2. Statement 2: Votes are recorded in Control Units and VVPATs at exactly the same time.
   • This statement is incorrect. When a vote is cast, it is first recorded in the Control Unit of the EVM. The Voter Verified Paper Audit Trail (VVPAT) is a system that provides feedback to voters and it prints a paper slip that reflects the voter's choice, but it does not record the vote itself. The timing of recording in both might not be synchronized exactly.
3. Statement 3: Two PSUs, namely Bharat Electronics Ltd., and Electronics Corporation of India Ltd. have been engaged by the Election Commission of India to design and manufacture the EVMs.
   • This statement is correct. Bharat Electronics Ltd. (BEL) and Electronics Corporation of India Ltd. (ECIL), both Public Sector Undertakings (PSUs), have been tasked by the Election Commission of India with designing and manufacturing EVMs.

By analyzing the statements:

• Statement 1 is correct.
• Statement 2 is incorrect.
• Statement 3 is correct.

Therefore, the correct combination of statements is 1 and 3.