elessar_iitkgp is right. There are 2 more extreme possibilities as well, as below

 

The following are the total possibilities (theoretically).

 

1. (X - 0) * (X - 0)

2. (X - 0) * (X - 1)

3. (X - 1) * (X - 0)  [same as 2 above. But enumerated for completeness)

4. (X - 1) * (X - 1)

5. (X - 0) * (X - ) [ one root being 0 and the other being infinity. one may argue

                             whether infinity can have a square or any exponent.The

                             moment v think of infinity as a concrete no, then it can. But

                              if it is an abstract entity, it cant. But then, it should not

                              have been used in calculations at all, if abstract and not

                             concrete.Hence, for the sake of completeness, the following

                             may need to be included in a maths-sense. 

                             Am I being  Polemical ? Perhaps, But then what is science

                             without its share of diversity of opinion.anyway. Remember

                             Bayesian vs classicists schools wrt Prob theory ? ]

 ]

6. (X - ) * (X - 0)

7. (X - ) * (X - )

yes. as below.

 

2b = a + c (a,b, c are in AP) : now suaring :

4b^2 = a^2 + c^2 + 2.a.c.      : Now dividing by 2

2b^2 = (a^2+c^2) /2 + (ac)     : multiply both sides by (a+C)

2b^2 * (a+c) = (a^2 + c^2)*(a+c) / 2 + (ac)*(a+c) : rearranging :

2b^2 * (a+c) = (a^2 + c^2)*(2b)/2     + (ac)*(a+c) : exapnding now

2b^2 * (a+c) = b.a^2 + b.c^2  + c.a^2 + a.c^2 : rewriting  again

2b^2 * (a+c) = b.a^2 + c. a^2 + b.c^2 + a. c^2 : Rearranging again

2b^2 * (a+c) = a^2 *(b+c)      + c^2 ( a+b) : Hence, QED

 

 

What will be a better choice  between  :

 

a. Btech in Petrol engg from ISMU, Dhanbad and Electr and computers in NIT, Suratkal and (b) Msc (chem-int) ISMU and Comp Sc in NIT Suratkal under the following parameters.

 

a. Scope for further studies b. Perceived brand equity of the institutions amongst academia / recruiters and c. Placements. rgds.

 

 

The following is a little lengthy. But, perhaps worth the effort, if you have some time on your hands.

 

My suggestion would be that you attend the counselling by AIEEE, if you are not too financially challenged. The reasons are as below..

 

a. First of all, in a session like this - AIEEE counselling -  you get to meet some of the brightest minds at your peer level (some of whom might be JEE qualifiers with perhaps, decent ranks but not having obtained a branch of aspiration,  would have preferred to look at other meritorious options like NIT's). The atmosphere is cerebral, electric and intellectually stimulating and the sheer experience of it is worth the expenditure. In fact, you donot get such an opportunity again, in your life, generally.

 

b. Secondly, even a rejection will be a meaningful if as much info. as can be gathered has been gathered - if financially or otherwise it is not a challenge- and the choice made thereafter. When there is an opportunity to gather some more personal experience on the other meritorius / competing choices, might as well gather the same, before you exercise your choice.

 

c. The AIEEE counselling process is different from the one by JEE. Am sure that there may be some in this forum who would have preferred a branch of their choice in an IIT in a different location to the branch they ended up receiving in a given location. ie.,  For eg Course A at  IIT- X over course B at IIT- Y, which they eventually ended up receiving.( Of course, one may argue saying that one should have been careful while filling up the choice sheet, but tell me honestly, who is careful beyond the 20th choice anyway). For eg., If there was a huge screen, displaying all the options available to each of the JEE qualifiers for his rank and below, I am sure many on this forum would agree that they might have looked at other options.

 

Now it brings us to another point before we summarise pointc.. Pl read on. Am not digressing but am analysing before synthesising.

 

d. In my view, each human being is a potential brand and life is an attempt by the potential brand (the human being) to emerge as a real brand. The shortest way to become a  brand is to be recognised by a popular brand in his / her area of interest and hence, one is able to appreciate the thirst of youngsters with an analytical bent of mind for an IIT seat. But then,  this is not the only way. There are individuals  who are bigger brands themselves than their alma mater and so are there individuals who never visited an institution but created many themselves.

 

Generally, an individual's attempt to emerge as a Real brand (from a potential one) depends upon his/her ability to integrate the qualities of as many big brands as possible, in his sphere of interest. Nothing man-made is perfect and since brands are man-made, they invariably suffer from human fallibilities. Thus, since, no Brand is perfect, the suggestible course of action for an individula is to integrate the upsides of as many big brands as possible,  while moderating the downsides of the given brand, by integrating complementary upsides of  another equally / reasonably good brand.

 

The only way to recognise the differences (whether the give difference is an upside or a downside, i leave to the reader)  across brands is to compare the systems and processes of the two brands. Now that you have been bestowed with such an opportunity why not make use of the same. 

 

e. Now the synthesis. The best way for somebody to emerge as a real brand from a potential one is to assimialte as many pluses of as many brands while downplaying the downsides.So if you can assimilate even one upside from a another meritorious system, perhaps you may emerge a better brand in that respect, even in comparison with the one you would die to associate with. 

 

So, would suggest that you go for the AIEEE counsellig, unless you are financially challenged. By the way, pl check up with your parents as well. Take it from me, they may or may not be well informed but no one will have your interest utmost in their hearts,  more than them. So if they donot mind and if u arent financially challeneged, I would suggest you go for the counselling.

 

f. Rather long. Am sure. Perhaps, a little trying. But thought I would share some wisdom from my own personal experiences. After all, the best lessons are learnt from the biggest of follies, are nt they.

 

g. Let me reveal my identity a bit now, to make it interesting. Am from the IIM's.

 

Warm Rgds and May GOD bless all of you. Take it from me I accidentally started viewing this blog and am really amazed by the talent that is sloshing about in these fora. If this is the sample of what young India is all about, am sure our country is in the hands of great individuals. Rgds.

Just see whether the following solution is adequate for Problem no 2

 

Rearranging the terms  :

 (x + 1)                =  1  -   (x-1) , squaring

x + 1                    =  1 +  (x-1)  - 2  (x - 1)

Cancelling and rearranging :

                    1      = - 2  (x -1 ) : solving

                 (x-1)   = - (1/2) {read as  minus (1/2) }

Retain only the minus root of  (x-1).

Solving for X ,w e get

                      X    = (5/4) , but  (x -1 ) = minus (1/2). ie + root is ignored.

 

This solution set satisfies the problem as given above

 

 (x +1) +  (x-1)    = Sqrt of (9/4) - (1/2) = 1. QED.

 

Is the above satisfacotry ?

 

 

Have proposed the following solution for Prob 2. See whether it is befitting.

 

Rearranging the terms, we get

 

(x+1)           = 1 -   (x-1)

Squaring

x + 1             = 1 + (x - 1)  - 2  (x - 1) : Cancelling

1                   = - 2  ( x -1 ) : rearranging :

  (x-1)           = - (1/2) (ie Minus (1/2)

 

With  (x - 1) being equal to minus (1/2), squaring and rearranging,

we get X = (5/4).ie X = (5/4) and (X + 1) = (9/4), but  (x -1 ) = minus (1/2) only

ie Plus (1/2) for  (x - 1) is not reckoned.

 

Thus with only the negative root of   (x-1) being taken at - (1/2) and with

X being (5/4), the solution set satisfies the problem as given above

 

 (x+1) +   (x -1) = 1 [ Sqrt of (9/4) - (1/2) =1 ]