Why is there no 的 in the question 你是第一次去北京吗 (is this your first time going to Beijing)?
The structures are different

[1. 你] [2. 是第一次去北京] [3. 吗]?
[1. you (subject)] [2. are going to Beijing for the first time (verb clause)] [3. final particle indicates question form]

The verb clause &quot;是第一次去北京&quot; describes what you 'do'- you go to Beijing for the first time
~

[1.你] [2. 是第一次去北京的] [3.吗]?
[1.You (subject)] [2. 是第一次去北京的 (adjectival clause)] [3. final particle indicates question form]

The adjectival clause '是第一次去北京的' describes what 'you' are - 'you are the person who goes to Beijing for the first time'
Other example:
我不会屈服 I will not yield (describe what I do)
我是不会屈服的 I am a person who will not yield (describe who I am)