It does seem to affect all the Wikiversity pages, but seems ok on local branch.
My branch is currently up-to-date with master.
I can't reproduce the bug, so the fix might be a shot in the dark.
Can there be any discrepancy between Wikiversity's version and master branch ?

I copied the quiz on Wikiversity's page to Wikibooks and it seems to work fine there.
Link - https://en.wikibooks.org/wiki/User:Harjotsinghwiki#Multiple_choice_.2F_single_response

I've also edited 1 section in Wikiversity page, Link - https://en.wikiversity.org/wiki/Help:Quiz#The_quiz_tag
Using class="wikitable" instead of class="prettytable" solves the issue.

I think this is the cause: https://gerrit.wikimedia.org/r/#/c/359656/7/templates/Quiz.mustache

Locally the result after and before the this change remains the same.
Wikibooks is not showing settings table.
Also changing class to wikitable at wikiversity resolves the issue, if that is fine.

In T169529#3401105, @Harjotsingh wrote:

Locally the result after and before the this change remains the same.
Wikibooks is not showing settings table.
Also changing class to wikitable at wikiversity resolves the issue, if that is fine.

No, that is not fine :). Some of the classes use a border around it causing it show up. We shouldn't have the settings table in the HTML.

This is the HTML:

<table class="settings">
<tr>
<td></td>
</tr>
<tr>
<td></td>
</tr>
<tr>
<td></td>
</tr>
<tr>
<td></td>
</tr>
</table>
</div>
<p><input type="hidden" name="quizId" value="1" /></p>
<div class="quizQuestions">
<div class="quizText"><i>This is where questions would appear.</i><br /></div>
</div>
<p><input type="submit" value="Submit" /></p>

We shouldn't have the settings table in there at all, let along lots of blank <td>s

Change 363634 had a related patch set uploaded (by Harjotsingh; owner: Harjotsingh):
[mediawiki/extensions/Quiz@master] Remove Settings box when Quiz is set to simple

https://gerrit.wikimedia.org/r/363634

Change 363634 abandoned by Harjotsingh:
Remove Settings box when Quiz is set to simple

https://gerrit.wikimedia.org/r/363634

Change 363635 had a related patch set uploaded (by Harjotsingh; owner: Harjotsingh):
[mediawiki/extensions/Quiz@master] Remove Settings box when Quiz is set to simple

https://gerrit.wikimedia.org/r/363635

Change 363635 merged by jenkins-bot:
[mediawiki/extensions/Quiz@master] Remove Settings box when Quiz is set to simple

https://gerrit.wikimedia.org/r/363635

Closing this as resolved as the change is reflected on Wikiversity