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I strongly believe that the question is
sin²4x+cos⁴x = 2sin4x cos²x

Assuming that this is the question, I follow as follows:
Use the following relation
sin4x = 2* sin2x * cos2x,
cos⁴x=(cos²x)²cos²x = (cos2x + 1)/2

The given equation turns to:
(2sc)²+( (c+1)/2 )² = 2 * (2sc) * (c+1)/2, where s = sin2x and c= cos2x
So,
( (2sc)-(c+1)/2 )²=0
So,
2sc = (c+1)/2
Now square on both side,
substitute, sin²x = 1- cos²x
Then u get a quadratic in (c²)
Solve for c²Rest routine..... remember c = cos2x not cosx

U can find this derivation in almost all standard text books. I hope even ur school text book has this.

It would be too tidious to type in the whole derivation.

The equation i1+i2+i3 = -i can be proved usind advanced maths, which u haven't yet seen. So, for the time being, the equation i1+i2+i3 = -i cannot be proved.

But y do u want to prove it?
You get the total current leaving A is 5i+i1+i2+i3. But u don't know a way by which u can find i1+i2+i3. So, go for an alternate method. look from out the circuit. What ever current enters A has to leave A. (as no charge can be stored a a point). So, we conclude that current leaving A is 4i. So, we are getting an answer passing trough a tunnel hiding from 3 monsters i1,i2 and i3.

If u go directly towards the monsters, u have to either give up and loose, or fight against them to win. To fight against them, u need weapons (advanced maths), which are not yet trained to use. So, try escaping it...... Its not a joke... I dont write this to entertain u.... This will be the case with any tough problem u encounter. Follow the same rule.

As far as BE studies is concerned, u will be muggin only a week before the exam...
So u have ample time to prepare for JEE.
U can go for a good correspondence course. FIITJEE's RSM is ideal.

These are the common questions which prevail in almost all students who start preparing for IITJEE. Here are few suggestions:

Never get behind ur teacher, Go along with ur teacher. Use this christmas holidays to reach him.
Read something before teacher discusses it in the class. it helps a lot, as every thing seems to be familiar. Consider 2 lectures: A lecture on "Importance of drinking water" and a lecture on "Chronic Fatigue Syndrome". Which one will be more interesting? he one which is more familiar to u. So, get familiar with topic before teacher discusses it. i don't ask u to read the whole chapter.

Regarding the night study. Doctors always suggest not to go for night outs... But when we prepare for IITJEE time will not at all be sufficient so, we will be forced to put night outs. When I was preparing for JEE, I never used to sleep during nights. Our classes used to be from 4.30am to 11am. So, I used to sleep from 1pm to 5pm. and then back to study till 3.30 am......... U can achieve high goals only when u work so hard... And remember hard work always gives fruitful results. So, study in what ever time u find it convenient.

Next about sessions. Most of the people start reading... after 30 mins, they log in to Orkut... then once again back to studies in 10mins... once again on computer games after 30 mins.... once again back to study... then for a time pass, quarrel with younger sister, and then studies.......and then on some thing else....
Few people do support studies in sessions... but as for as JEE prepn is concerned, u need to go deep into the subject. This can be attained only on long study hours. Have long study hours. Avoid sms, orkut, chatting etc during ur study. Of course fruits and juices in between study hours are always helpful. Even ask ur parents not to disturb u for the next 2 hrs or so...

Then the MOST IMPORTANT THING:
Fix priorities. make a list of activities u have to do on a typical day. Rank the activities based on their importance... For most of u, the first thing will be JEE prepn. On any day, go to priority 2, only after u are done with a certain targeted amount of priority1 is done. Ensure that at least top 2 things are done before u go to bed. Dont include food in the list, and say that u r going to eat only after u r done with JEE prepn... food is essential. So, dont include essential and inevitable things in the list. If u properly follow this rule, then u will be 400% more efficient than u were before

Then, day dreaming:
Dont day dream during study. Its a common weakness. What ever u dream, sitting in ur chair with HC verma in front of u, is not going to happen unless u study. And remember that u r not going to gain any thing from day dreaming.
Of course day dreaming is inevitable. But try to avoid it as much as possible. When u find ur self in a dream, where u get AIR 1 in JEE, just cut off the dream and start studies. A conscious effort is necessary to avoid day dreaming.

Dont try to complete every book in ur personal library...
ur teacher gives u a list of books to purchase. They dont expect u to mug up all the books. And u cant do that in 2 years, even if they insist on it.... So many books are need for reference, but not for mugging them fully. Select a book which u feel convenient with. Stick to the book and don't go to another book unless u complete this. Of course u may have to refer to other books to clarify doubts.

Fix deadlines for various things. For example, u may say, I have to complete permutations and combinations by this Saturday. but don't over estimate ur self which fixing deadlines. Leave urself in peace by having some buffer time to complete any thing. ie., if u expect to complete a chapter in 3 days, give ur self 4 days. And one important thing, don't try making long schedules starting from tomorrow to the day of JEE. make schedule weekly, or monthly as there will always be few factors which badly effect ur schedule...

Now, comin to the subject part.... the ideal way to go with any typical chapter is as follows: First go through the thoery part. As u read theory, keep solving inchapter examples. Once done with the theory part, then close the book, explain the chapter to the mosquito resting and sipping peacfully on ur hand in ur own words. By explaining the chapter to walls, u gain clarity. Now, once again quickly scan through the chapter. Once u r done with, then go to solved examples. Solved examples are not meant to be read as a novel. Read the question. Understand it.. and then close the book... try solving it on ur own... try for quite some time... if u are able to solve the problem, then compare it with the given solution. See which solution is elegant. if ur solution is elegant, then award ur self a medal. If the solution given in the book is elegant, then try to point out what key step made a difference. If both solutions are same, then see how the solution is presented. Not only solving is important, but also presenting is, as far as subjective exams are concerened... believe me, there are chances of getting back the main exam in JEE-2009. So be well prepared. If u are not able to solve, then go through the solution and check y weren't u able to. Then go to unsolved problems. Every day, make a list of doubts u get. Dont immediately ask a teascher to clarify them. Keep going though doubts for few days and try to solve them. Over a week, at least half of them will be solved. Now, ask ur teacher to clarify the remaining doubts.

Last but not least THE MANTRA:
The only mantra which determines ur rank is PRACTICE.
It is the strike rate that matters in an exam, not the no of questions u attempt By strike rate, i mean the fraction of questions u solve CORRECTLY. For better strike rate, u will have to practice problem every day. Solve at lease 20 MCQs from each of the subject every day. Make it a habit. Then attend as many
mock exams as u can. They are always helpful. Also take the mock exams seriously.
Finally,

PRACTICE...... PRACTICE...... PRACTICE...... PRACTICE...... PRACTICE...... PRACTICE...... PRACTICE...... PRACTICE...... PRACTICE...... PRACTICE...... PRACTICE...... PRACTICE......

A whole sequence of books can be written on this topic, which may result in a ten volume book package (each having nearly 300 pages...)

But as far as the techniques for IITJEE are concerned,
Integral calculus by Shanti Narayan will be of great help.
If u want to learn just the techniques without proofs, the FIITJEE material and Arihant series book will also be helpful.

To be frank, I never heard of such terms.
After looking at this question, I rushed to our library to check with reference books on matrices. I didn't find any info abt these.
Then I tried Googling. The results shown by google were all related to cryptography (consider it as a hybrid of maths and computer science). So, u may not nee dto know these terms at least till u complete ur B-tech.
So, "Just leave it"(Courtesy: NIKE)

I would like to ask one question out of curiosity.... Where did u come accross these terms?

An attempt can be definitely made. But, we need the following info,
radius of sphere,
size and shape of hole,
angle at which the ray is incident.
Once we have these details, we can start of trying to find the probability. Once u enter the dragon (the problem), u find that there will be a large no of reflection taking place. No more can u handle the problem with ur pen and paper, u will need the computer to solve it.
So, u need a computer to solve the problem.

A well established theory is developed to solve such problems. U dont need that theory atleast now.

One very famous similar problem is as follows:
When Gandhi ji was shot, he said "Hey Ram!". During that time, few air molecules came out of his mouth. What is the probability that 3 of those air molecules are right now in ur lungs?

Doesn't the problem sound impressive???

The result can be mathematically derived. But, I am sure, u cant even understand abc's of the derivation, as they involve advanced fluid mechanics theorems and complex maths.
So, lets try to derive the result intuitively.

Adhesive force can be considered as attraction force on liquid by walls.
Cohesive force can be considered as repulsive force on liquid by walls.

If attraction is more, liquid try to move towards walls. hence it tries to be in contact with walls as much as possible. So, lower miniscus will be formed, to increase the area of contact of liquid with walls.

By the same reasoning, upper miniscus will be formed when cohesive forces dominate, to reduce the area of contact.

Hence there will be no miniscus, when these 2 forces cancel each other.
So, no miniscus will be formed, when adhesive and cohesive forces are equal.

U are expected to at least remember logarithms of 2 and 3.
Log 10 is 1.
Express the number in terms of 2,3 and 10. (Most of the cases this works.)
Suppose we need to find log 75,
then we do as follows:
75=3*25=3*10*10/(2*2)
So,
log 75 = log3 + 2log10 - 2log2.

Another case could be approximating log.
Consider an MCQ with any pair of its options differ by atleast 1.
Say, the options are a) 5.62 b) 3.2 c) 7.9 d) 21.4
How approximate the nu,ber to nearest power of 10. Suppose, you need to find log (621453), 621453 is between 100000 and 1000000.
So, log (621453) must lie bet 5 and 6.
So, option A.

If neither of the above 2 cases is true, then definitely, logarithms will be given. If not, beleive me, the question will be deleted for evaluation.

prerequisites

i. You must complete your Class XII under the 10+2 system or its equivalent with a minimum of 50 per cent marks in Mathematics and Physics.

ii. You must be minimum 16 years of age to be eligible for a Private Pilot License and 17 for a Commercial Pilot License.

iii. Your vision in one eye must be perfect. In general medical terminology, it is called 6/6 eyesight. In the other eye, you could have an imperfection of 6/9, which must be correctable to 6/6.

iv. General physical fitness is mandatory. You must be free of any disease that can hamper normal function.

The route to being a commercial pilot

First, zero in on a good flying club.

Then you begin the stepwise training process.

~ Student Pilot License

i. You must appear for a written theory examination in Air Regulations, Aviation Meteorology and Air Navigation and Air Technical.

ii. You must obtain a medical certificate of fitness from doctors designated by the Director General of Civil Aviation. Only two bodies in India -- Air Force Central Medical Establishment in New Delhi and the Institute of Aviation Medicine, Bangalore -- are authorised to give you a medical fitness certificate.

iii. You have to get a security clearance.

iv. You will need to appear for an oral examination and an aptitude test.

v. If the medical clearance comes through and you clear the exams, you will be granted the SPL.

Damages: You must furnish a bank guarantee of Rs 10,000.

~ Private Pilot Licence

i. Post attaining the SPL, you will be assigned an instructor to start flying lessons. You will be taught the basics of flying and your instructor will accompany you on flights.

ii. After about 15 hours of flying with an instructor, ie dual flying, you can fly solo and go cross-country as well.

iii. To obtain a Private Pilot License, you have to fly a minimum of 60 hours. Of this, at least 20 hours should be solo flying and 5 hours should be cross-country flights.

iv. You will also need to appear for the written theory examinations in subjects like Air Regulations, Aviation Meteorology, Air Navigation, Aircraft Engines and Seamanship.

v. You will need to obtain the medical fitness certificate from the AFCME or IAM.

vi. You must be at least 17 years old.

viii. You must have passed Class XII or equivalent exam with Physics, Maths and Chemistry as your subjects.

Damages: The per hour cost of flying is quite steep: about Rs 3,500.

To get a PPL, you need at least 60 hours of flying. Thus the total cost of obtaining a PPL will be a cool Rs 2 lakh (Rs 200,000)!

~ Commercial Pilot License

This license is the most important license to become a commercial pilot.

i. The age bracket for getting a CPL is between 18 years and 30 years.

ii. You need a minimum of 250 hours of flying to get this license. Of this, 150 hours have to be solo flying, 25 hours of cross-country flying, 10 hours of instrument flying (which means you rely only on the plane's instruments for flying without looking at the horizon or external assistance), and 5 hours of flying in the night.

iii. A medical certificate from ACFME or IAM and theory tests in Air Regulations, Aviation Meteorology, Air Navigation, Technical and Planning are other important parts of the process.

iv. You can get the Private Helicopter License if you complete 40 hours of flight training with 15 hours of solo flying. Written exams on basic aviation subjects have to be taken.

v. To get a Commercial Helicopter Pilot License, you need 60 hours of flight training as well as appear for a written exam.

vi. Helicopter pilots are hired by public and private sector corporates as well as security agencies.

Damages: A steep Rs 9 lakh (Rs 900,000). For a Commercial Helicopter Pilot License, the cost could go up to Rs 13 lakh (Rs 1.3 million)!

~ Airline Transport Pilot's License

The above mentioned licenses can only allow you to fly as a co-pilot. If you want to take over as captain, you need the Airline Transport Pilot's License, which is the highest aviation license available.

Along with clearing written papers, you also need to clock a total of 1,500 flying hours and take medical tests.

Damages: It costs Rs 30,000 to Rs 40,000 per hour. Often, the airline you work for may sponsor the training costs.

Additional training and information

Once you get the CPL, you may want to go in for multi engine training.

After seven to 10 hours of multi engine training on a certain aircraft, your license will carry an endorsement of the aircraft you have flown.

All the above licenses need to be renewed regularly. You must adhere strictly to medical tests.

Fly one hour after your license expires, and you will be banned from flying ever again!

Medical conditions and regular exam clearances notwithstanding, a pilot can continue in this career till 61 years.

These days, you could even try for a scholarship. Please visit www.scholarshipsindia.com for details.

Damages: Multi engine flight training is very expensive and can cost anything between Rs 15,000 and Rs 25,000 per hour.

List of Flying Clubs in India

~State-owned

Indira Gandhi Rashtriya Udan Akademi, Rae Bareilly, Uttar Pradesh
Andhra Pradesh Aviation Academy, Hyderabad, Andhra Pradesh
Amritsar Aviation Club, Amritsar, Punjab
Bihar Flying Institute, Patna, Bihar
Bombay Flying Club, Mumbai, Maharashtra
Gujarat Flying Club, Vadodara, Gujarat
Government. Flying Training Institute, Bhubaneshwar, Orissa
Government Flying Training Institute, Kolkata, West Bengal
Government. Flying Training School, Bangalore, Karnataka
Haryana Institute of Civil Aviation, Karnal, Haryana
Haryana Institute of Civil Aviation, Hissar, Haryana
Haryana Institute of Civil Aviation, Pinjore, Haryana
Ludhiana Aviation Club, Ludhiana, Punjab
Madhya Pradesh Flying Club, Indore, Madhya Pradesh
Madhya Pradesh Flying Club, Bhopal, Madhya Pradesh
Madras Flying Club, Chennai, Tamil Nadu
Northern India Flying Club, Jallandhar, Punjab
Patiala Aviation Club, Patiala, Punjab
Rajasthan State Flying School, Jaipur, Rajasthan
UP State Flying Training Institute, Kanpur, Uttar Pradesh
Andaman & Nicobar Flying Training Institute, Port Blair, Andaman & Nicobar Islands
Assam Flying Club, Guwahati, Assam
Banasthali Vidyapith Gliding and Flying Club, Coimbatore, Tamil Nadu
Aviation Training Academy, Coimbatore, Tamil Nadu
Delhi Flying Club, New Delhi
Kerala Aviation Training Centre, Thiruvananthapuram, Kerala
Nagpur Flying Club, Nagpur, Maharashtra
Jamshedpur Cooperative Flying Club, Jamshedpur, Jharkhand

~ Private

Ahmedabad Aviation and Aeronautics, Ahmedabad, Gujarat
Academy of Carver Aviation, Belgaum, Karnataka
Flytech Aviation Academy, Hyderabad, Andhra Pradesh
Garg Aviation, Kanpur, Uttar Pradesh
HAL Rotary Wing Academy, Bangalore, Karnataka
Rajputana Aviation Academy, Kota, Rajasthan
Orient Flight School, Pondicherry
Wings Aviation, Hyderabad, Andhra Pradesh
Yash Air, Indore, Madhya Pradesh
Frank Airways, Indore, Madhya Pradesh
Bangalore Aeronautics and Technical Services, Bangalore, Karnataka

Useful resources:

http://www.dgca.nic.in/flyclub/flyclub.pdf
http://www.urbancookie.com/Life/adventure/flyingclub.html

Institute Name

:

New Flight Services (India) Ltd, Indore

Address

:

"NEWFLIGHT" #B/108, Ambikapuri Extension, AirPort Road, Indore -452005, MP

Phone

:

0091731 6450535 / 6452650

Fax

:

0091731 4044650

E-Mail

:

Contact I

Web Site

:

www.newflight.co.in

Institute Details

:

The most trusted name in Aviation Training . For more details visit www.newflight.co.in or www.newflight.20m.com

Courses Offered

:

CPL [ Commercial Pilot Training in Philippines / USA / Australia & Sri Lanka ],
International Aviation Management,
Airline Passenger Services,
Cabin Crew & in-Flight Services

Admission

:

Admissions are subject to a personal interview at Indore

For Admission & Enrollment procedure, you may contact directly to,

The Admission Officer
New Flight Services
108 Ambikapuri Extn. , Airport Road, Indore 452 005 INDIA
T : 0091-731-4044650, 6450535
M : +91-93297 37330
F : 91- 731- 4044650

Institute Name

:

Blue Diamond Aviation, Pune

Address

:

S-28/29/30 Super Mall, Opp Dorabjee Enclave, Salunke Vihar Road, Wanawadi, Pune 411040 (India)

Phone

:

+91-20-65203745

Fax

:

+91-20-26835920

Mobile

:

+91-9890005636

E-Mail

:

Contact I

Web Site

:

www.bdapune.com

Institution Details

:

Blue Diamond Aviation, Pune is a professional organisastion conducting regular ground school classes for Commercial Pilots Licence. Students are channelised for flying training in India or abroad.

Courses Offered

:

Courses are of 12 weeks duration with 5 hrs of classroom teaching per day (Monday to Saturday)
Subjects taught include:

Air Regulations
Air Navigation
Aviation Meteorology
Technical (General) - Theory of Flight, Flight Instruments, Radio Aids, Engines(Piston & Jet)
Technical (Specific) - Specific to the type of aircraft being flown

Eligibility

:

Education - Minimum 10 + 2 with Maths and Physics for CPL (for PPL only 10th pass)
Age - Minimum 16 years for PPL and 17 years for CPL on date of joining Ground School
Medical - Class II medical conducted by DGCA approved medical practitioner
Class I medical at AFCME (Delhi), IAM (Bangalore) or 5 AFH (Jorhat)
(This is required for CPL & ATPL only)

Institute Name

:

Asiatic International Aviation Academy, Indore

Address

:

108 AMBIKAPURI EXTN. , Airport Road,, Indore

Phone

:

0091731 6450535 / 6452650

Fax

:

0091731 4044650

Mobile

:

919229237330

E-Mail

:

Contact I

Web Site

:

www.aeroasia.co.in

Institution Details

:

The most trusted name in Aviation Training . For more details visit www.aeroasia.co.in or www.pptc.20m.com

Courses Offered

:

CPL [ Commercial Pilot Training in Philippines / USA / Australia & Sri Lanka ],
International Aviation Management,
Airline Passenger Services,
Cabin Crew & in-Flight Services
Admissions are subject to a personal interview at Indore
Admission Seminars soon in Kota, Delhi, Mumbai & Banglore
For Admission & Enrollment procedure, you may contact directly to,
The Admission Officer
Asiatic International Aviation Corporation
108 AMBIKAPURI EXTN. , Airport Road, Indore 452 005 INDIA
T : 0091-731-4044650
T : +91-731-6450535
M : +91-92292 37330
F : 91- 731- 4044650
W : www.aeroasia.co.in,
www.indianairways.org,
E : csg@asia.com
m : asiaticair@hotmail.com
Y : asiaticair@yahoo.com
Skype : capt.shekhar.gupta
Ham : VU2CSG

Delhi

Anugrah Allied Aviation Services (p) Ltd.
C-33,2nd Floor,
Amar Colony Market,
Lajpat Nagar-4
New Delhi-110024
Phone: 011-55644543
Website: www.falconairways.com
Email: Contact Us
Courses offered:
Pilot training (Flying clubs)
Provide excellent guidance for flying Training in India and Canada, Best Guidance for ground Excellent Course for Ground Staff and Customer care, and Pilots/Airhosstesses.
Minimum Eligibility: 10+2
Delhi Flying Club Ltd
Safdarjung Airport, New Delhi 110003
Phone : 4635080, 4618325
Courses offered :
a) Mech. E. Diploma in Mechanical Engineering ( 3 years)
Eligibility: Sr. Secondary School Certificate English, Physics, Maths and Chemistry
b) RT/R ( Aero Mobile- svc) - ( Six to Eight weeks)
c) Radio Officer ( 2 years)
d) Associate Membership exam (Approximate 3 years)
Faculty of Flight Safety Services, Delhi Flying Club Ltd.
a) Endorsement Courses for CPL Holders ( 6 weeks)
b) Flight Despatcher's Course ( 12 weeks)
c) Cabin Attendants Course ( 4 weeks)
Eligibility: 10+2 passed for all the above courses
School of Aviation Science and Technology, Delhi Flying Club Ltd.
a) Abinito B.A.M.E.C/aircraft Maintenance Engineers Licence Training Programme ( 3 1/2 years)
Eligibility : Sr. School Certificate or equivalent with English, Physics, Chemistry and Maths with 60% marks in aggregate or B.Sc pass with 55% marks in aggregate
Age: Maximum 20 years
b) On- the-Job Practical Training Programme ( 1 year/ 6 months)
Eligibility: Sr. School Certificate or equivalent with with English, Physics, Chemistry and Maths

Assam

Assam Flying Club, Guwahati Airport, Guwahati, Assam 781007

Bihar

Bihar Flying Institute, Civil Aerodrome, Patna, Bihar

Gujarat

Gujarat Flying Club, Civil Aerodrome, Hasni Road, Baroda 390006

Haryana

Karnal Avaiation Club, Kunjpura Road, Karnal
Hissar Aviation Club, Textile Road, Sirsa Bypass, Hissar
Pinjore Aviation Club, Civil Aerodrome, Ambala 134102

Maharashtra

American Flyers (India) Pvt.Ltd, 37, Virwani Industrial Estate, Western Express Highway, Goregaon, Mumbai 400063
PH: 022-8748042, Fax: 91-22-8750533
Courses: Professional Aviation / Aviation Management
Bombay Flying Club, Juhu Aerodrome, Santa Cruz west, Mumbai 400049
Indian Aviation Academy, Mumbai
7/8 Rushabh Complex, Opposite Fun Republic Cinema, Oshivara, Andheri (West)
Phone : 009122 - 26749058, 26740041
E-Mail : Contact us
Web Site : www.indianaviationacademy.com
Courses :
Pilot Training
Eligibility : Minimum 10 + 2 with English, Physics and Mathematics
Nagpur Flying club, Sonegaon Aerodrome, Nagpur

Madhya Pradesh

MP Flying Club, Bhopal Civil Aerodrome, Bhopal
Flying Club, Civil Aerodrome, Indore
Academy Of Aerospace & Aviation, 401,Shiba Complex,Regal Chauraha, Indore
Web Site: www.aaaindore.com
E-Mail : Contact Us
Phone : +91-731-5004458, 5043397
Courses :
Aviation Science of Engineering Foundation.
Duration - 4 Semester.
Eligibility: 10th Math., Science, English.
Commercial Pilot (CPL);
Duration -8 Semester.
Elgibility -10+2 / I.Sc. Phy., Chem. & Math. Min. 50% Marks.

Orissa

Govt. Aviation Training Institute, Civil Aerodrome, Bhubaneswar

Punjab

Ludhiana Aviation Club, Civil Aerodrome, P.O Sahnewal, Ludhiana
Patiala Aviation Club, Patiala, Punjab 147001
Northern India Flying School, Jalandhar Cantt 144005
Amritsar Aviation Club, PO Rajasansi, Amritsar Aerodrome, Amritsar

Rajasthan

Rajasthan State Flying School, Saganer Airport, Jaipur

Uttar Pradesh

Govt. Flying Club, Aerodrome, Faziabad
Govt. Flying Club, Aerodrome, Lucknow
Aviations Limited, hangar No. 3,Civil Aerodrome, Kanpur
Courses: PPL. Commercial Pilot Licence

West Bengal

Flying Training Institute, Behala, Kolkata 700060
Bats Aviation Academy
Course: Flying Training Course
Eligibility: Pass in 10+2 or equivalent with Physics, Maths and Chemistry or equivalent.
Hostel facilities is available

Andhra Pradesh

Flytech Aviation Academy, 102, A1-Kausar Road No. 10, West Marredpally, Secunderabad 500026, Andhra Pradesh
Phone : (91)-040-55496900. Fax (91)-040-27807664
E-mail: Contact Us, Website: http://www.flytechaviation.com
Courses: 1. Commercial Pilot Licence, 2. Aircraft Maintenance Engineering, 3.Airhostess Flight pursers
Eligibility: 10+2 or equivalent
Age: 16 years and above
Hostel facilities is available

Chennai

Orient Flight School , P.Box No. 1306, 40, G.S.T Road, Chennai 600016
Ph: 2341389 Fax: 044-2342170
Courses: Commercial Pilot Licence, PPL, Instrument rating, Multi-Engine Endorsement
Eligibility: 10+2 with Maths with Physics and sound Knowledge of English.
Age : MInimum 18 years for CPL and 17 years for PPL
Hostel facilities are available

Jamshedpur

Tata Nagar Aviation Private Limited, 2 North East, Circuit House Area, Jamshedpur 831001
Ph: 0657-425975, Fax: 0657-407594
Course: Commercial Pilot Licence Course
Eligibility: 10+2 with Physics and Maths

Well, it's valid doubt. U say when u superimpose, the currents are i,i,i and 2i.
U say the last current is 2i, by adding currents in both cases. But what abt the first thre currents? U r just considering the first case. there will be a significant contribution by the second case, even in the other three branches, of course, we can't find their exact magnitudes.
So, the net currents will be i+i1, i+i2, i+i3 and i+i, where i1, i2 and i3 are currents in 3 branches emerging from A other than AB due to the second case
so, the net current will be 5i+i1+i2+i3. Here u don't know the value of i1, i2 and i3. So, we cant say the answer.. Infact, i1+i2+i3 will turn out to be (-i), making the net current to 4i.

Hope every thing is clear now.

Hello Biki,

I understand ur confusion.

First to get started, let me make the principle of super position more clear.

In principle of super position, u take 2 things happening independently. (1 thing is independent of other. Any of these can exist without the existance of the other.).
U just take only first thing, observe the effect. Now take only second thing observe.
Principle of superposition says, the observation u make due to existence of both will be sum of the observations u make due existence of each of the things alone.

Now, lets get started.....
take the grid, trow in a current 4i into the grid at any grid point. (remember we are not goin to collect this current from the adjacent grid point.).Since the grid is symmetric, current divides equally that is., i, i, i, i.
Now, take a different case, take out current 4i from any grid point. (once agoin, we are not inputting current any where). So, what ever current u draw, has to be collected symmetrically. So, i, i, i, i.
Now club these 2 cases, so I am sending current 4i through A and collect 4i through B.

Forget about V and -V u were talking about. The current passing through wire B is 2i. So, potential difference accross A and B is 2i *r

Now, let the equivalent resistence be R.

So, replace the whole grid by a resistance R between A and B.
I am sending current 4i at one end and collecting the same current from the other end. (now there is no more grid, so, dont think about i,i,i,i and i. Just think abt outside 4i). So the potential difference accross A and B is R*4i
Therefore, 4i*R=2i*r
which implies R = r/2