Which one is correct? having many but easy works "are" big problem in life. having a few but tough works "is" a big problem in life.

The problem is with the way they are written Mehboob, I have taken the liberty to write them the way that I would,but in your examples the second one would be the closest to being correct. Usually you would use "are" as the plural and "is" as the singular, however in your examples the emphasis is on "the problem" (singular) and not "works" (plural) therefore we would use "is" as per your second sentence.

Rewritten: "Having many easy works is a big problem in life".

                 "Having a few tough works is a big problem in life".

Both now demonstrate using "is" (singular) for the problem and ignoring the plural, works. Sorry it's a long drawn out explanation, hope it makes sense.

"Having a few but tough works is the problem..." is the right answer. grammatically, the problem is the subject of this sentence

Grammar is not easy but to my understanding in the present form both of these sentences are free of any critical grammar mistake. However, the results can be different if the sentences are in complete form.

not100% sure but I, think it may be "having a few but tough works 'is a big problem in life" is gramatically right answer. 

Peter's answer is apt.My problem is,do we have the word 'works' in English?Is it ever put in plural?

Thank you for inviting me to answer and I'm sorry about being late in my reply due to health issues.I think the second is grammatically correct.

The second one is gramatically correct, having a few but tough works is a big problem in life.

Both questions can be grammatically right but i would prefer second one '' Having a few but tough works 'is a big problem in life''

The one with "is" is right but the one with "are" is wrong.

Remember that you started the sentence with: "Having".

If the sentence began with a plural noun (like "jobs"), then "are" must be used.