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IIT Kanpur has always been known for its research work and academics. If you are comparing BS in Chemistry at IIT Kanpur with its dual degree equivalent in Bits Pilani, then take IIT Kanpur. However if you are getting a better branch at Bits Pilani/Hyderabad/Goa, then go there without hesitation
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Take NTU .. defnitely better than any IIT
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Yes you can have a branch change from any branch to any other branch . The deciding factors (in IITs) is your CGPA after first year, institute policy and no. of seats
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I would say barring NIT-Warangal and NIT-Trichy that too only cse/ece/eee branches other than these three branches at these two NITs the new IITs are much better than them
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I am assuming f(x) is a polynomial. Then f(1) gives the sum of all coefficients. f(-1) gives the sum of even powered coefficients minus the sum of odd power coefficients. So f(1) + f(-1) gives twice the sum of even power coefficents , So the required answer is 0.5*(f(1) + f(-1))
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yes it is 40... if he draws 38 then they can be all blue and red .. and only black socks will remain .. so drawing 2 more will definitely ensure that he has a pair of black socks
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Subtracting both equations we get 
where m,n are integers. B is smallest positive, when m=n=1 and we take - sign for pi/12 So, smallest positive value of B is 
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iit guwahati ece > iit kanpur civil > iit-roorkee chemical > iit-roorkee civil > iit hyd cse > bits pilani cse
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Your possible options will be CSE @ IIT Kgp/ Guwahati/ Roorkee, EE at IIT Kgp/Guwahati/ Roorkee, Chemical @ IIT B, D, K, M, Kgp Civil @ IIT B, D
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If you are after job , then petroleum engg at ISM Dhanbad is quite good.. other wise take Chem @ BITS Pilani
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You give your preference list and they check from the top. The topmost branch/IIT that is available to you will be given to you
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Definitely Chemical Engg. at NIT Warangal.
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Please re-read Rolle's Theorem properly
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IIT Kanpur , Second yr. feel free to nudge
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Yes generally Mathematics and Computing is a tough branch but it is manageable and it has its advantages in getting a job rather than B.Sc/M.Sc. in any subject. If you want a job only then Mathematics and Computing is your best option. However, if you are not after jobs then M.Sc. integrated will be ur best option (dont take M.Sc. Chem though)
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@Sushobhan : I am not too sure whether guys will know in 12th whether they like a particular branch or not nor will they get to know/like it if they see the courses offered in a particular branch. There are many misconceptions about what a particular branch is like. ....................... @Dhruv : Well as Sushobhan has said before, both branches are equally good and it will depend on your ability to concentrate for another year knowing that many of your friends will have graduated. Also doing an M.Tech. is valid only in India. Institutions abroad do NOT recognise the M.Tech. qualification in a dual degree course. So I would have preferred Mech. B.Tech.
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Your rank is good enough to get quite a lot of good courses in old IITs (mainly in Kanpur, Kgp, Guwahati, Roorkee.... you can get Aerospace @ IIT-K and also Materials science and metallurgy and you can also get Chemical at IIT-Kgp, Guwahati, Roorkee...
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I would suggest that you take electrical at kgp because not only it is a core branch but also as kgp has the best campus and i am sure that campus life prepares you more for a job rather than acads. Also you might want to look at some courses at IIT-K as IIT-K will not be offering dual degree courses from this year onwards although the intake will be same. So some branches which you could not get earlier may become available to you.
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Branch change at any iit is a difficult prospect. So whichever branch you go to, dont go in expectation that you can change your branch after the first year. Branch change criterion at IIT Kanpur is much more tougher than any other IIT because neither does IIT Kanpur allow students getting straight 10.0 in their first year the option of changing branch without restriction(as most other IITs do) and nor does it allow any extra intake in any branch. (Eg : IIT-Kgp allows 10% extra of the no. of students allotted to a branch but IIT-K does not allow this). Yes at IIT-K you have the option of applying for branch change at the end of your 2nd, 3rd or 4th semester, but it is solely decided on the CGPA obtained until the 2nd semester ends. The CGPA after 3rd or 4th sem has no effect on your application. Further even in 2nd year 3/5 courses in a sem are common for all students so you wont miss out on much and you do have the option for applying for extra courses.
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