Prime Minister Narendra Modi flagged off the third Mahamana Express, which runs between which pair of Indian cities?

Introduction / Context:
This question touches on Indian Railways and current affairs. The Mahamana Express trains are premium services named in honour of Madan Mohan Malaviya, who was given the title Mahamana. When a new Mahamana Express is inaugurated, it becomes a popular news item, and exam setters often ask on which route the train runs after being flagged off by the Prime Minister.

Given Data / Assumptions:

The train is the third Mahamana Express in the series.
Prime Minister Narendra Modi flagged it off.
We are asked to identify its route from the list of city pairs.
Options include Delhi and Lucknow, Vadodara and Varanasi, Patna and Delhi, and Vadodara and Delhi.

Concept / Approach:
To answer this, we rely on factual recall from current affairs. The third Mahamana Express was announced as a link between Vadodara in Gujarat and Varanasi in Uttar Pradesh, both politically and culturally significant cities. The approach is therefore to match the route described in news reports with the options given.

Step-by-Step Solution:
Step 1: Recall that the early Mahamana Express services connected Varanasi with New Delhi and with other major centres. Step 2: For the third Mahamana Express, news reports highlighted that it would connect Vadodara and Varanasi. Step 3: Check the options and locate the pair Vadodara and Varanasi. Step 4: Recognise that the other options mention routes that belong to different trains or are not associated with the title Mahamana Express. Step 5: Select Vadodara and Varanasi as the correct route.

Verification / Alternative check:
Indian Railways press notes and current affairs magazines reported that this third Mahamana Express runs between Varanasi and Vadodara, strengthening connectivity between eastern Uttar Pradesh and Gujarat. They also mentioned that Prime Minister Modi launched the service through video conference. This independent confirmation supports the answer in the option list.

Why Other Options Are Wrong:
Delhi and Lucknow are connected by several trains including premium services like Shatabdi, but the Mahamana title is not associated with a Delhi Lucknow route at that time. Patna and Delhi have their own long distance trains but not this specific Mahamana Express. Vadodara and Delhi is another possible rail route, yet it does not match the announced pair for the third Mahamana Express flagged off in the reported event.

Common Pitfalls:
Some candidates may confuse this route with the earlier Varanasi New Delhi Mahamana Express or may guess based only on familiarity with popular corridors like Delhi Lucknow. Others may not distinguish between different categories of premium trains such as Rajdhani, Shatabdi, and Mahamana. Keeping a small list of special trains and their routes, especially when they are launched by the Prime Minister, helps prevent such confusion.

Final Answer:
The third Mahamana Express flagged off by the Prime Minister runs between Vadodara and Varanasi.