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)

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.

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

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  • karthik
    Posted at 09:36h, 27 March Reply

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

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

    books for csir net

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

      Could you be a bit more specific?

      • v
        Posted at 14:42h, 07 July Reply

        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 Reply

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

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

    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 Reply

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

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

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

  • shrey
    Posted at 13:06h, 20 October Reply

    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 Reply

      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 Reply

    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 Reply

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

  • santosh
    Posted at 19:35h, 22 November Reply

    i t was very useful thanks.

  • Arkamouli Debnath
    Posted at 17:42h, 23 January Reply

    I have secured 25(or 26,still in doubt) in the Nbhm IPHd scholarship exam out of 40.
    Do you believe I’ll be called for interview?

  • Devibala
    Posted at 23:19h, 18 March Reply

    Can you tell me the books which you have followed for written exam?

  • Shakti kumar
    Posted at 09:20h, 30 May Reply

    Hii i did email neeraj but his email address is not correct. I want to crack nbhm exam for master’s can you plz tell me about all the books 📚 and tricks too..

  • Krishnan
    Posted at 18:28h, 24 July Reply

    Hey, I’m Krishnan , I’m currently studying in final year of bsc and I would complete my graduation around June next year (2019) when is the exam for i-phd held ? Please do guide me on this
    Thank you.

  • aarav
    Posted at 02:11h, 06 June Reply

    Hello Sir, I am a student of Delhi University(BSC. HONS. Mathematics) and my last five semester marks average is 8.3 cgpa and also I am a Inspire Scholarship holder and got all of my 3 instalments of graduation . but Now I want to take leave of 1 year because I wants try to crack iit jam exam from mathematics , So please to tell me,

    1.)May I apply for NBHM after a gap of 1 year and also what is the difficulty label of that exam and for instalments process it takes how much time.

    2)for Inspire Scholarship of PG , office takes only admission in any college or also want some percentages in 1st year of PG.

    3) If you know any other better option please to provide.

    4)And what are the placements scale in iit after PG .

    Pls to help me you can also WhatsApp me at number removed.

    • Manjil Saikia
      Posted at 17:57h, 25 July Reply

      Hi, the answers to the best of our knowledge are as follows:

      1. You can apply for NBHM after a gap year, the exam is at the same level if not more difficult as CSIR NET, IIT JAM, etc. Due to difference of structure it is not really possible to say about this exactly.
      2. You will need to give your marks for renewal of scholarship.
      3. You should also try for TIFR, CMI, ISI as well.
      4. It depends on what course you want to pursue.

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