#1 It is great that you read all you could about the Tex filter and understand tat this is a display problem

#2 having understood #1 above, you of course would ignore what you were told by Sakshi because it was misleading and inaccurate

#3 If you want to use the Moodle TeX filter, then in addition to turning it on (and moving it up in the order of the filters applied if you have many) you also have to make sure it is working, which is not necessarily a trivial task

#4 Unfortunately, though you indicate you read all about the TeX filter, you do not post the requisite response from using all the options of texdebug.php, which means that no one who does understand how the Tex filter works can give you much in the way of assistance.

#5, If you wish to TURN OFF the TeX filter and use MathJax, then YOU CAN add the requisite material to your AdditionalHTML. Mauno has posted a txt file with the lines you would need to invoke MathJax and jsxgraph elsewhere... here is a file he posted that contains just a stanza for MathJax - edit as per MathJax.org https://moodle.org/pluginfile.php/139/mod_forum/attachment/1046910/mathjax.txt ... or you can go to MathJax.org and study the use of MathJax via cdn and insert a Hub statement that suits you (MathJax allows for additional flexability in using display vs inline math, as well as asciimathml if you handle tokens appropriately.)

#6 If you don't wish to use MathJax (a mistake I think, in the circumstances) then reread the material of texdebug, turn on debugging, run through all the tests, and post results, first check to make sure that you have the necessary binaries in their correct location and the correct perms on the proper files.

#7 as you no doubt noted, there are some issues when using TeX in some question forms. To determine whether it is a display issue or a feature of the question format, test the display of the TeX not on a question but in a web resource