Hello World

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Sharing is one of the best(*) things in the world. If one shares something somewhere with someone, it helps to make this world a better place.

 

* conditions apply : One shouldn’t share bad/ugly things.

 

I have started this blog to share some Mathematics e.g. solutions to CSIR-NET papers, Math GATE papers etc. So follow this blog for regular updates.

 

I have given full solutions to the questions asked in CSIR-NET papers, but before you see those solutions you should attempt the questions yourself if you want to learn Mathematics. Otherwise this is never useful to you.

 

Also I hope that YOU will also share your solutions or alternate solutions with all either by commenting on this blog or by E-mailing me.

 

Currently I have posted the solutions to Math CSIR-NET exams in parts.

 

The question papers are available here: June 2011, Dec-2011 .

 

More on the website csirhrdg.res.in

🙂 Have A Nice Day.

75 responses to “Hello World”

  1. Hi sir, thank u for ur help. I got codifence to clear the paper only after seeing ur webpage. I would like to inform that csir has released answer key for june 2012 in http://www.csirhrdg.res.in which will be available till august 14 th only. Hope this will be useful for u to help us further. Thank u again sir. Regards, kala.

    Reply

  2. Question 26 is wrong in booklet A of June 2012. So if I choose any of the four options, shall I get the marks?

    Reply

  6. Q84(net june-2011): A subgroup K of permutation group Sn is normal if it contain complete conjugate class of Sn,and you can see K contain complete conjugate class of S4 and A4.so K is normal in S4 and A4. Also for a finite group a subgroup is normal if [K ,H ] =2 and [K,H] =o(K)/o(H) =4/2 =2, therefore H is normal in K. So option 2 and 4 are correct.
    Also H does not contain complete conjugate of S4 hence H is not normal in S4.
    (conjugate class is number of different types of cycle in a permutation group)

    Reply

  8. sir i have filled in the form specialization code pure mathematics can i attempt questions from statistics in part c unit IV in exam

    Reply

  11. Hello Sir,
    I came across your blog and is is very useful. I would be very thankful to you Sir, if you kindly send me(bcskal@rediffmail.com) the PHYSICS question papers of last 3-years of CSIR-NET exams with answer keys. Thanks.

    Reply

      • Sir,
        To which books i refer mathematical science for csir net
        mathematical analysis:
        Algebra:
        Complex analysis
        Topology;
        PDE

        Kindly needful for us,i need your help sir
        awaiting reply,

      • This is my choice….urs may be different….as ‘everyone is unique’…..best of luck

        real analysis……1.malik & arora
        2.bartle & sherbert

        linear algebra…..1.schaum’s
        2.hoffman & kunze

        abstract algebra…1.herstein
        2.gallian

        complex analysis…1.brown & churchill
        2.schaum’s

        differential eq….1.ross
        2.m d raisinghania

        topology………..1.simmons
        2.munkers

        linear programming……any book.

  16. i have complete solutions of last 5 papers of csir mathematics and solution of Dec 2012
    also any body who want can contact me .its free of cost .

    Reply

  18. If S= { (x,y,z) \in R^3 : ax^2 + by^2 cz^2 = 1 , } then
    (a) compact and connected set
    (b) neither compact nor connected set
    (c) compact but not connected
    (d) connected but not compact

    Answer ?

    Reply

  24. kindly send me any materials in mathematical sciences which will be helpful for me for the coming CSIR NET Exam dec 2013..actually i am a little bit week in Abstract algebra in terms of solving problems but other papers is ok. plz send me materials whch do u think helpful for me..
    my E-mail id is
    pritamchetry76@gmail.com.
    PLEASE HELP ME..

    thanks….

    Reply

  28. Hi sir , please help me.

    Let V be the set of all bounded solutions of the ODE:
    u′′(t)−4u′(t)+3u(t)=0,t∈R. Then How can we prove V contains only the trivial function u≡0.
    Net June 2012 question number 42 in code A

    Reply

  32. A very useful blog for those who are preparing for csir net mathematics.
    sir please post the solutions for dec 2013 and june 2014 exams

    Reply

  36. Find the eigenvalues and the characteristic vectors of

    t1 : R x R –> R x R : (x,y) –> (2x – y, 0)

    t2 : R x R –> R x R : (x,y) –> (2x – y, x)

    t3 : R x R x R –> R x R x R: (x,y,z) –> (2x – y, 0, y +z)

    t4 : R x R x R –> R x R x R: (x,y,z) –> (0, 0,y)

    Reply

    • First, we calculate the eigenvalues r of t1
      The characteristic equation is
      |2-r -1|
      | | = 0 -r(2-r) = 0
      |0 0-r|
      The eigenvalues are r = 0 and r = 2
      For r=0 the characteristic vectors are the non trivial solutions of the
      system
      2x – y = 0
      0x +0y = 0
      The characteristic vectors are all the multiples of (1,2).
      For r=2 the characteristic vectors are the non trivial solutions of the
      system
      2x – y = 2x
      0x +0y = 2y
      This system is equivalent with 0x + y = 0
      The characteristic vectors are all the multiples of (1,0).

      You find the eigenvalues and characteristic vectors of t2 in the same way.

      Next, we calculate the eigenvalues r of t3
      The characteristic equation is
      |2-r -1 0 |
      |0 -r 0 | = 0 (r-1).r.(2-r) = 0
      |0 1 1-r|
      The eigenvalues are r = 0 , r = 1 and r = 2
      For r=0 the characteristic vectors are the non trivial solutions of the
      system
      2x – y + 0z = 0
      0x +0y + 0z = 0
      0x + y + z = 0
      This system is equivalent with
      2x – y = 0
      y + z = 0
      The characteristic vectors are all the multiples of (1,2,-2).
      For r=1 the characteristic vectors are the non trivial solutions of the
      system
      2x – y + 0z = x
      0x +0y + 0z = y
      0x + y + z = z
      This system is equivalent with
      x – y = 0
      y = 0
      The characteristic vectors are all the multiples of (0,0,1).
      For r=2 the characteristic vectors are the non trivial solutions of the
      system
      2x – y + 0z = 2x
      0x +0y + 0z = 2y
      0x + y + z = 2z
      This system is equivalent with
      y=0
      z=0
      The characteristic vectors are all the multiples of (1,0,0).
      You find the eigenvalues and characteristic vectors of t4 in the same way.

      Reply

  38. Sir, please send me csir net december 2011 mathematics paper answer key…
    Please sir send me as soon as possible

    Reply

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