Concept:
This is an Assertion-Reason type question. In such questions, we must check two things:
\[
\text{First, whether Assertion (A) is correct or not}
\]
\[
\text{Second, whether Reason (R) is correct or not}
\]
After that, we check whether Reason correctly explains the Assertion.
Step 1: Check Assertion (A).
Assertion says that bottle gourd is one of the most important cucurbitaceous vegetable crops grown throughout tropical and sub-tropical regions of the country.
Bottle gourd belongs to the family Cucurbitaceae. It is widely grown in tropical and sub-tropical regions because it performs well under warm climatic conditions.
Therefore,
\[
A \text{ is correct}
\]
Step 2: Check Reason (R).
Reason says that Arka Keshav is a long fruited variety of bottle gourd.
Arka Keshav is indeed a variety of bottle gourd and it is known for long fruits.
Therefore,
\[
R \text{ is also correct}
\]
Step 3: Check whether R explains A.
Although Reason is correct, it only gives the name of one variety of bottle gourd.
It does not explain why bottle gourd is an important cucurbitaceous vegetable crop or why it is grown in tropical and sub-tropical regions.
So,
\[
R \text{ is not the correct explanation of } A
\]
Step 4: Final conclusion.
Both Assertion and Reason are correct, but Reason does not correctly explain Assertion.
\[
\therefore \text{Correct Answer is (B)}
\]