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This is the rough work I did during the interview, the question were added in a separate post (  as I did not want to reveal hints in the original post (perhaps open the questions side by side to make sense of the following rough work)

CSA prof 1 (not everything is correct in my solution): 



CSA prof 2 (not everything is complete in my rough work):

Feel free to ask in the comments, I am sure, some of the answers are not complete as the prof. just asked to explain some bits instead of writing everything down. 

posted Aug 25, 2020 in Interview Experience 1,611 views


Can you please explain what happened after $k \geqslant \frac{a^{2}+ b^{2} + 2ab}{a^{2} + b^{2}}$ in the third problem of the second image.


Yeah, I was struggling and told him that I don't think it can be simplified any further. Then I said if $k$ were 1, it can never be $true$ . Then I said if $k$ were 2, then..$2ab <= a^2 + b^2$ ,  the professor then said, I will give you a hint now, take it to the other side. I said okay, then it became $(a-b)^2 >= 0$  which was always $true$. So, for $k=2$ , the inequality is always correct. 

On the rhs (a + b)^2 should become (a^2 + b^2 + 2ab). Why have you written (a^2 + b^2)? Not able to understand.

@nvs16 It was a different question, the first line was a simple question, where the answer was for any $k$ greater than equal to $1$, the inequality holds. So, then the professor asked me to change the problem to $a^2 + b^2 + 2ab <= k(a^2 + b^2) $ .. its a different problem, I have written it in the post as well , perhaps you missed it. There is no perfect demarcation in the rough work I did hence I can understand the confusion though

How is this possible .. $k*(a+b)^2 = k*(a^2+b^2)$
@Priyansh Singh, k on both sides? why?

he did like this above

$a^2+b^2+2ab \leqslant k(a+b)^2$ 

$a^2+b^2+2ab \leqslant k(a^2+b^2)$


now look at only RHS in the equation how the square got split inside ?

They are two very different problems.


First problem was so easy that it didn't need any calculation. Second one starting on the second line is harder.
I got gate score of 611 and rank 1855 I have OBC reservation and CGPA 8.77. Do you think can I get a a call for Mtech research CDS or CSA
@sampathpro20 Don't remember the stats, maybe checkout last years cut off ranks. It should be close to that.