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The question isn't complete ... From which cylinder does the thred finally come out?? Top or bottom?

I am assuming the the string comes out of the bottom of the inner cylinder at the bottom

The horizontal component of the velocity is $v sin\alpha$

Let the velocity of the spool's center be ${v}_{T}$ and its angular velocity about the centre be $\omega$

For no slipping

${v}_{T} = R \omega$

Also

${v}_{T} - r\omega=vsin\alpha$

${v}_{T}-(r/R){v}_{T}=v sin \alpha$

${v}_{T}=(v sin \alpha)/(1-(r/R))$

Check at this site :

http://dce.ac.in/cee/CEEresult.php

This should give you some idea

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The average speed of the molecules increases ... not necesrily that of an individual molecule. Its a statistical result that the average speed of a collection of particles is directly proportional to temperature. Its not about individual particles. The speed of individual particales varies erratically owing to the random collisions they undergo with each other

There is no such software ... work hard, study well ... instead of posing such questions use your nickels to ask some serious doubt on any subject

Take up the NCERT books and finish them ... then move on to better books like HC verma, Arihant etc.

Another thing ... if you haven't taken coaching for any other reason than financial constraints .... well, its risky. If there are financial constraints ... then work hard and don't stop till its over

All the best

ompelx sope is analogus to slope in 2-D, but in argand plane ... refer to arihant for details

JOin Fiitjee or Narayana

Books:

NCERT first priority

Then do anything that your teachers suggest.

Depends on the state board. If its WB, Karnataka, Tamil nadu, Andhra ... then better go with KV ... for these boards literally don't teach anything

take up the NCERT books and finish them thoroughly ... then go for all the higher books and stuff. First prority should be finishing 11 and 12 NCERT books in the vaccations. that way youi'll have a broad overview of the syllabus and can identify potentially problematic areas ... after this you have all the time in the world to hone in on your skills

Good approach @shikhar_destructo

Good soution @riku

For 11th entrance test is in April that is few weeks after your 10th boards

For 12th entrance test is in October of your class 11th (that is it is 1 and a half year course)

For 12th pass entrance test is after IITJEE result day

Also one regular batch is made out of correspondence batch after their first test

The cutoff will be released by Jadavpur shortly ... plz wait till that time