Step 1: Understanding the Question:
We need the one correct statement. We will look at numbers and dates first, because these are easy to check.
Step 2: Test the number of seats.
A majority in the Lok Sabha needs 272 seats. The BJP got 282, which is above the line but below 300. This kills option 1.
Step 3: Test the date of the candidate announcement.
Narendra Modi was announced as the BJP's candidate for Prime Minister in 2013, a few months before the polls, not in 2012. This kills option 4.
Step 4: Test the coalition claim.
Even with 282 seats, the BJP kept its pre poll partners and ran the government as the NDA. The claim of no coalition partner is wrong, so option 3 is out.
Step 5: Test the history claim.
Going back in time, Rajiv Gandhi's Congress won a single party majority in 1984. Thirty years later, in 2014, the BJP repeated this feat. The claim is right.
Step 6: Conclude.
Option 2 is the only statement that survives all four checks.
Final Answer:
A single party won a Lok Sabha majority in 1984 and again in 2014, so option 2 is correct.
\[ \boxed{\text{Option 2}} \]