Select the most appropriate option to fill in the blanks. They travelled by…

• English uses no article with the phrase "by + means of transport" (by bus, by train, by car, by plane): this is a fixed idiomatic pattern that treats the mode of travel in a generic sense rather than as one specific object.

• English requires the definite article "the" before a noun phrase that has exactly one possible referent in its context, such as "the sun" or "the capital of India", because the phrase itself identifies a single, unique entity rather than one among several.

1. In "They travelled by ______ train...", the word "train" follows "by" and names the means of transport, so the idiomatic zero-article pattern applies, giving the first blank as "no article required".

2. In "...to ______ capital of India", the phrase "capital of India" can refer to only one city, so the definite article is required, giving the second blank as "the".

• Swapping in "the" before "train" ("by the train") would imply one specific, previously mentioned train, which nothing earlier in the sentence supports, confirming the zero-article pattern fits the first blank.

• Swapping in "a" before "capital" ("a capital of India") would imply India could have more than one capital, which is not true, confirming that the definite article is required for the second blank.

Putting the two blanks together, the sentence reads "They travelled by train to the capital of India.", so the correct fill is "no article required; the".