Experiences at an NBHM MSc Scholarship Interview

Hi, this is record of my Interview held in month of Nov'13 for NBHM MSc Scholarship. After clearing the written exam held in Sept'13 I was called to appear for Interview at Punjab University. The written exam was easy and  I did all problems in Analysis , and I think my score was 22/30. Since I had given many interviews before this so I had the idea how things happens in the interview,I prepared Real Analysis quite well. I also looked at some topics from my Integrated PhD 1st sem mainly Topology.
So I was called for Interview in Morning at 9 and my name was there in the list at last position.

Early in the morning I saw my two IISER's professor Prof Passi and Dr.Amit there in the panel. After that I waited for my turn and entered the room at 4.20pm.

Everyone welcomed me in the room and there were 5 on the panel.(I don't know everyone's name sitting in the panel so I'll use Sir and Mam at places)

Dr Amit- Welcome Neeraj, (he jokes) abhi tak to kafi questions pata chal gye honge ki kya-kya puch rhe hai?( Till now you must have heard many problems which we have asked from others?)
Me- No sir , I haven't talked with others too much!

Mam- So what is your area of interest?
Me-Real Analysis.

Prof Passi- Since you said Analysis let me ask an interesting problem, first write down on the board  (\sqrt{2})^2 and tell its value?
Me- ( I got surprised , couldn't figure out why is he asking such an easy question!) Sir its 2!

Prof Passi- Now what is  2^{\sqrt{2}}?
Me-( I have seen this before but couldn't recall anything)

Prof Passi- What can you say about its nature whether it is rational or irrational, or any other detail?You'll be able do it only if you've seen it before!

Me- Yes sir I've seen it( gave it a thought but was not getting anything)

READ:   ৰামানুজন - গণিতজ্ঞ আৰু মানুহজন : অধ্যায় D : অৰ্থনৈতিক পৰ্যাপ্ততা

Prof Passi-( After sometime) okay leave it let's move on.

Mam- What do you mean by uniform continuous function?
Me- ( Gave the definition)

Mam- Is  f(x)= \frac{|x|}{1+|x|} uniform continuous on  \mathbb{R}?
Me-( Did it by considering  |f(x)-f(y)|)

Mam- Do you know any other shorter way?
Me-( Thinking for some other method)

Mam-( after a while) what about  lim_{x\to \infty}f(x) and lim_{x \to -\infty} f(x)
Me-(immediately) Oh yes since  f(x) is continuous on  \mathbb{R} and both these limits exists  f(x) must be uniform continuous!

Mam- Yes correct! Is  (sin x)^2 uniform continuous on  \mathbb{R}
Me- yes, since its derivative is bounded on $ mathbb{R}$

Mam- Is  sin x^2 uniform ?
Me- No, consider two sequences  x_n=\sqrt{2n \pi} and  y_n=\sqrt{2n \pi+\frac{\pi}{2}} , now  x_n-y_n \to 0 as  n\to \infty but  f(x_n)-f(y_n) n\rightarrow 0 as  n \to \infty

(After this sir started)

Sir- Have you done Topology?
Me- Yes sir.

Sir-What do you mean by Topology?
Me-( Gave its definition)

Sir- What do you mean by Hausdorff space?
Me-(Gave its definition)

Sir-Is  \mathbb{R}^2 Hausdorff with metric topology?
Me-(This was an easy one) Yes sir any two distinct points can be separated by  two disjoint discs.

Sir- Is  \mathbb{R} with cofinite topology Hausdorff?
Me-(thought for a while) No, for  x \neq y suppose  \exists U_x, U_y disjoint nbds of  x,y respectively, since  U_x \cap U_y=\phi \implies U_y \subset\mathbb{R} \setminus U_x and this is not possible since  U_y is infinite while  \mathbb{R} \setminus U_x is finite.

Mam-If  X is finite , what is cofinite topology on it ?
Me-(immediately without thinking thinking much) Indiscrete.

Mam- Think again!
Me- It'll be discrete since  X \setminus U is always finite always for any open set  U

Prof Gurmeet-Write down all the non isomorphic groups upto order 10
Me-(I was not sure whether I remember all of them or not, but wrote them all in the end)

Prof- Okay you can leave now

My Interview lasted for only 20 mins and before me they were taking interviews upto 50 mins, may be they were tired since I was last one or may be any other thing. But the good thing is that I cleared the interview 🙂
I noticed that interviews in North Zone for NBHM are relatively easy than other parts of India, through this post I'd like to help other students interested in taking the exam you can comment or contact me for any help.

READ:   Math Olympiad Problem Sheet

 [Neeraj is now an Integrated PhD student at the Centre for Applicable Mathematics, TIFR, Bangalore.]

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Neeraj Singh Bhauryal

13 Comments
  • karthik
    Posted at 09:36h, 27 March

    Can you tell me what books should be followed for the written examination?

  • krishnapal singh
    Posted at 12:51h, 07 June

    books for csir net

    • Gonit Sora
      Posted at 19:01h, 11 June

      Could you be a bit more specific?

      • v
        Posted at 14:42h, 07 July

        could you please ask neeraj bhai on what books can be referred and what all topics have to be concentrated inorder to write this exam?

        • Gonit Sora
          Posted at 21:14h, 12 July

          We have forwarded your email to the author. Sorry for the delay.

  • Vincy Anandi
    Posted at 14:33h, 07 July

    Hi Neeraj bhai... I am going to write this years NBHM scholarship for msc students.Could you please give me a suggestion on what all books and topics in particular I should concentrate?...Thank You

  • Gaurav Rajan Bopardikar
    Posted at 22:47h, 16 July

    Is it easy to prepare for iit jam maths in 4 months?

    • Gonit Sora
      Posted at 19:07h, 28 July

      If your concepts are clear then with four months of problem solving, we believe it is possible.

  • shrey
    Posted at 13:06h, 20 October

    Hi,
    I am called in for interview this year. Can you give me an idea of what sort of questions should I expect in the interview? I was thinking of revising everything I did fir the written test in addition to solving the paper. Can you recommend anything else?

    • Gonit Sora
      Posted at 14:47h, 14 November

      Hi, yes, that is an excellent idea. Try to go beyond the stage for the written test. We would urge you to thoroughly revise your preparation for the written stage once again. Best of luck.

  • Mho
    Posted at 23:25h, 04 November

    I don't know whether it's only me; but the MathJax commands are really in dilapidated condition. I'm noticing `\` is missing in each of them e.g. `mathbb` instead of `\mathbb` etcetera. Nevertheless, a big thanks to share your experience.

    • Gonit Sora
      Posted at 14:55h, 14 November

      Hi, thank you for pointing the error, it has been rectified now.

  • santosh
    Posted at 19:35h, 22 November

    i t was very useful thanks.