a strange situation! present tense? past tense?

[nixgnoy]

For days, I have been keening to write a letter to you again, but I just (have / had) no time, because I (just finished / have just finished ) my exam today. (note: this sentence is just writen by myself)

Q: As the sentence above, which one in the bracket is correct?

My comprehension is: In the first bracket, since it is now that I am writing the letter and telling the person who will receive my letter that I have no time, so the present tense should be used here. However, considering that that I am writing the letter indicates that I have time to write the letter, I just had no time in the past, therefore, the past tense should be used here. Which one is correct? Similarly, in the second bracket, which one is correct? :-?

 

[bhaisahab]

For days, I have been keening to write a letter to you again, but I just (have / had) no time, because I (just finished / have just finished ) my exam today. (note: this sentence is just writen by myself)

Q: As the sentence above, which one in the bracket is correct?

My comprehension is: In the first bracket, since it is now that I am writing the letter and telling the person who will receive my letter that I have no time, so the present tense should be used here. However, considering that that I am writing the letter indicates that I have time to write the letter, I just had no time in the past, therefore, the past tense should be used here. Which one is correct? Similarly, in the second bracket, which one is correct? :-?

For days, I have been keening to write a letter to you again, but I just (have / had) no time, because I (just finished / have just finished ) my exam today. (note: this sentence is just writen by myself)
As you have started with present perfect you should continue to use it in the second clause "haven't had any" and you should delete "just".
The last clause would be better written as "have only just finished".

"For days I have been keening to write a letter to you again, but I haven't had any time because I've only just finishedmy exams".
What is "keening" by the way?

 

[nixgnoy]

What is "keening" by the way?

Thank you very much!
In fact, I want to express the meaning that "I am keen to do sth. " or "I desire to do sth. " or "I really want to do sth. ". However, I also want to express the meaning that I have never stopped to desire to do it, so I use Present Perfect Continuous Tense. finally, it become "I have been keening to do sth." Is that right?:-?

 

[bhaisahab]

Thank you very much!
In fact, I want to express the meaning that "I am keen to do sth. " or "I desire to do sth. " or "I really want to do sth. ". However, I also want to express the meaning that I have never stopped to desire to do it, so I use Present Perfect Continuous Tense. finally, it become "I have been keening to do sth." Is that right?:-?

I'm afraid you can't use "keening", you'll have to use "keen". "Keening" means making a long, sad wailing sound.

 

[nixgnoy]

Oh! I see! Thank you very much!

I just refered to a dictionary, I found that keen is an adjective when it means "eager"; when it is a verb, it means as what you have mentioned.
so, should I change it into: I have been desiring to .... ?:-?

Why exams plus "s" by the way? the IELTS EXAM consists of 4 parts, but if I regard it as one exam, should I still plus "s" after the word "exam" ?