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https://cracku.in/cat/lesson/4/number-integral-solutions-video

In the last example given in this video, the question has asked the number of integral solutions but in the solution only positive integral solutions are found. Let me know if I am wrong.

what will be the maximum sum of 54, 52, 50...?
1 702
2 704
3 756
4
700

When will the tier 2 test series will be out ? I want to buy it and start practicing

The new variety of genetically modified (a)/crops is being extremely successful in (b)/curbing the usage of (c)/ pesticides and increasing the per unit output (d)/No error (e)

Here is (variety)- singular or plural?

A straight Line L is perpendicular to the line 5x-y =1 .The area of the traingle formed by the line L and coordinate axes is 5 Find the equation of the line 

i want concepts of reasoning

Should MUST always follow HAVE .Eg That MUST HAVE been really difficult for you.

since That is a singular why can't we use HAS in place of HAVE? 

I found something about MODALS in my google search but I didn't understand it.Please explain.

And one more doubt..

What is the difference between Doesn't and Don't..

Eg: He doesn't want to be killed..  but why doesn't ? why not don't...

What is the remainder when 8^8 is divided by 17? Plz mention the method.

CAT 2004 Question no.- 64..........In the first question germany might hav also played its 2nd game with pakistan also but in the solution provided you have considered new zealand & South Africa....y?

q28 di section cat 2007. How this question should be solved. By my method i am taking a lot of time. I am putting value in each of the option and then finding the percentage is there any way of eliminating the options?  Please refer question 28 of di section cat 2007