If every alternative letter of the English alphabet from B onwards (including B) is written in lower case (small letters) and the remaining letters are capitalized, then how is the first month of the second half of the year written?

The correct option is jUlY.

Let us break down the solution step-by-step to understand why this is correct.

Step 1: Identify the pattern for capitalization
The English alphabet consists of 26 letters from A to Z.
According to the question, starting from B (the 2nd letter), every alternative letter is written in lower case (small letters). The remaining letters are capitalized.
Let's list the positions of the letters (where A = 1, B = 2, C = 3, ..., Z = 26):
- Letters at odd positions (1st, 3rd, 5th, etc.): capitalized.
- Letters at even positions (2nd, 4th, 6th, etc.) starting with B (2nd): written in lower case.
Therefore:
- A (1) is Capitalized: A
- B (2) is lower case: b
- C (3) is Capitalized: C
- D (4) is lower case: d
And so on. In general, odd-numbered letters are UPPER CASE and even-numbered letters are lower case.

Step 2: Determine the first month of the second half of the year
A year has 12 months. The first half consists of the first 6 months (January to June).
The second half of the year begins with the 7th month, which is July.

Step 3: Apply the casing rules to the letters of "JULY"
Let us find the alphabetical position of each letter in the word "JULY" and apply the rule:
1. J: The 10th letter of the alphabet. Since 10 is an even number, it must be written in lower case: j.
2. U: The 21st letter of the alphabet. Since 21 is an odd number, it must be written in UPPER CASE: U.
3. L: The 12th letter of the alphabet. Since 12 is an even number, it must be written in lower case: l.
4. Y: The 25th letter of the alphabet. Since 25 is an odd number, it must be written in UPPER CASE: Y.

Conclusion:
Combining these letters in their correct cases, we get: jUlY.