Smoking is a known cause of certain serious health problems, including

This is a classical “cause and effect” question.
The form is:
Both A and B exist
Conclusion: A causes B happen.
Assumption: B does not cause A (the reverse relationship is not correct)

ANALYZE THE STIMULUS:

Fact: smokers have more anxious and nervous than nonsmokers
Conclusion: smoking leads to more anxious and nervous (note: the conclusion is inferred)
Assumption: Anxiety and nervousness do not lead to smoking

ANALYZE EACH ANSWER:

Which of the following is an assumption on which the argument rests?

a) Anxiety and nervousness can lead to serious health problems.
Wrong.
The flow is:
X - smoking ==> Z -serious health problems.
--AND—
Y - anxiety and nervousness ==> Z- serious health problems.
Clearly, it does not mean X must lead to Y just because both X and Y lead to Z. It’s totally wrong logic.

b) Anxiety and nervousness do not make individuals more likely to start smoking.
Correct. This is cause & effect question. Smoking leads to anxiety and nervousness only if Anxiety and nervousness do not make people smoke.

c) Equivalent numbers of smokers and nonsmokers were surveyed for the study.
Wrong. C is TEMPTING but wrong. Assume you have a whole population 1 million people. You're supposed to take survey, you need 1000 non-smokers and 1000 smokers in order to have a good sample.
==> Clearly, your sample is perfect to have a reliable conclusion if you have exactly 1000 non-smokers and 1000 smokers.

What if you take 1100 non-smokers and 1000 smokers (in-equivalent numbers), your conclusion will not be reliable? Nope, because 1000 is a base in order to get conclusion reliable. If you add 2 or 3 people in the sample, your conclusion is still reliable.
Thus, C is not an assumption. (because if you negate the assumption, the conclusion MUST be incorrect).
Note: the stimulus talk about "the survey" which implies "sampling technique".

d) Smokers are aware of the various health problems attributed to smoking, including lung cancer and emphysema.
Wrong. The fact people are aware of health problems attributed to smoking does not mean smoking leading to anxiety and nervousness.

e) Smokers who had smoked a cigarette immediately before responding to the survey were more anxious and nervous than smokers who had not smoked for several hours.
Wrong. Clearly out of scope. We talk about smokers in general, NOT only smokers who had smoked a cigarette immediately before responding to the survey.

Hope it helps.