M....mischevious R.....reliable..... U......unique....(as every individual is) N......naughty..... A.....adorable.....admirable.... L .......luvin'

Certainly spidey sir I remember I know you are big brother !! I matched it with you .

Generally I do keep away from this sort of discussions however I am telling this to you from the bottom of my heart

Trust me this is the most wonderful intimacy I have seen here !

Marrying isn't a good option at all ............you could have accumulated the tears over the last 2 weeks .....and tried dipping yourselves in it ! ( skinny dipping is more enjoyable than marrying ) and you are going for civil engineering in IIT Guwahati ........whatever branch he gets tell him to go for NIT Silchar .......trust me you two will remain close and hence will be at peace ( distance between the two is not much ) + you will be in IIT Guwahati so you may help him out in some cases + next year if he qualifies you will get him in your insti! who knows!!

You said you don't like idly daily : "OMG!!!!! how bad! But I will get 280 in AIEEE... So I will get good group in NIT (hopefully) I am ready even for Bits pilani or goa or NIT south india. I dont like idly daily but its okay."

So here are a few statistics obtained about you :

I.P = 59.92.4.220

Country = India

State = Tamil Nadu

City = Chennai

Latitude = 13.0830

Longitude = 80.2830

Interesting isnt it!! Profile says Delhi !! Miss. Mansivini ; sorry if the gender is "actually " wrong !

Good luck !

Happy Birthday Mrunal !!

As she says she is M....mischevious R.....reliable..... U......unique....(as every individual is) N......naughty..... A.....adorable.....admirable.... L .......luvin'

So friends wish her on her birthday

May God bless you ..........Have a fabulous year ahead !!!

Sorry for allignment problems

Nice problem dude ,

ax ² + by²+ 2hxy + 2gx + 2fy + c = 0 ...........................................1

Condition for a pair of straight lines is

abc + 2fgh - af ² - bg ²- ch ² = 0 .................................................2

Now , let the point of intersection on the y axis be ( 0,t )

Now , $\partial$ S / $\partial$ x = 2ax + 2hy + 2g = 0

$\partial$ S / $\partial$ y = 0 = 2hx + 2by + 2f = 0

So ht + g = 0 , bt + f = 0 [ as x = 0 , it lies on the Y axis ]

So , now we have hf = bg ................................................................3

The equation of Y axis is x = 0

Now solving this and the equation of pair of lines, we get

Now the given equation is , ax ² + by²+ 2hxy + 2gx + 2fy + c = 0

So putting x = 0 , we have by ² + 2fy + c = 0

So , they intersect at one point , hence they should be having only 1 root

So applying that , ( D = 0 ) , we have f² = bc ...............................4

So we have from eqn 3 , fh = bg

or fgh = bg ² ........................................................................................5

Now look at 2 ,

we have abc + 2fgh - af ² - bg ²- ch ² = 0

So using 4 and 5

abc + 2fgh - fgh - abc - ch² = 0

So we have ch ² = fgh

So the following things can be deduced

fgh = ch² = bg²

and 2fgh = bg ²+ ch²

Too difficult to understand your options!!

Hence solved

[ P.S : I didnt find your question in my AIEEE 10 MOCK TESTs BOOK .~ Arihant Publishers I have question papers and solutions upto 2006 as I bought it in Class 11.Moreover its not copy pasted , impossible to find such a detailed solution in those books ! ]

1050 = 2 * 3 * 5 * 5 * 7

Now we have been given x1 , x2 , x3 , x4 , x5

now 2 or 3 or 7 , so number of ways = 5 ³ ways

So we have 5 to deal with

Now we can have 2 * 3 * 7 * 25 * 1 or 2 * 3 * 7 * 5 * 5

So number of ways of arranging the 5 s are 5 C1 + 5 C2 = 15

So total number of ways = 5³ * 15 = 125 * 15 = 1875

No I think its a hyperbola

x + i y = z = 1 - t + i

(t² + t + 1)

So

we have to eliminate t

x = 1 - t

Hence t = 1 - x

y =

(t² + t +1)

y² = t² + t + 1

or y ² = (1 - x) ² + 1- x + 2 = 1 - 2x + x² + 3 - x = x² + 4 - 3x

or y² = (x - 3/2 )²+ 7/4

So y² - (x - 3/2)² = 7/4

which represents a hyperbola .

Attention again ,

I am back with my BJ job

A very very Happy Birthday to Ramya.

May God shower all His blessings on you .May you have an

excellent year ahead, brimming with success and joys !!

(

P.S : We already know that you have made it big to the big

brother institute) still hold your momentum and may you rock in

all your coming exams .......

I only hope your maths don't get any stronger ....it will hurt us a lot

So come on friends leave your comments and wish her.....

1 / 1 - cos x + 2 i sin x

= 1/ (2 sin ² x/2 + 4 i sin x/2 cos x/2 )

= 1/ (2 sin x/2 ) . 1/( sin x/2 + 2 i cos x/2 )

= 1/ (2 sin x/2 ) . (sin x/2 - 2i cos x/2) / ( sin ²x/2 + 4 cos² x/2 )

= ( 1 - 2 i cot x/2 ) / ( 2 sin ² x/2 + 8 cos ² x/2)

= ( 1 - 2i cot x/2 ) / ( 5 + 3 cos x )

1st problem is nice I will tell you the general way of solving these problems

It is the type of problems where

x ^m ( a + bxⁿ )^p ,

Now here you have m = - 3 , n = 1 , p = 2

In these type of problems you have, (m+1)/n = an integer , so you can try putting

( a + b x ⁿ ) part = t ^k where k is the denominator of the fraction p

now replace it as said and you will see its easy ,

It now reduces to

2 t dt / t ( t² + 1 ) = 2

dt / (t ²+ 1)³

Now make required substitutions and get the answer.....this is the approach.

Look at who's answering .........the potential rank 1 guy !! sorry dada.....haven't ever been able to solve 100 problems together ...in 2 hours ( honest confession ) . I am an ordinary guy.

However ( with a few known problems like these ) went pretty close! + this year 20 objective questions where you need to put in some explanation. + because of leakage, paper should be tougher
( statistics ).

Odds are heavily stacked against us.

Yeah Karthik absolutely , WBJEE 2006 was postponed by a month due to votes and man the paper was a mini IIT paper.User Feynman qualified in those unfriendly bouncy conditions

and not only did he qualify , he got < 20 rank !!!

Now paper is going to be tougher certainly.
Its now going to be seen when the test is going to be scheduled.

Go through this links given below and see for yourself the news in details.

http://www.telegraphindia.com/1080420/jsp/frontpage/story_9161988.jsp

http://www.telegraphindia.com/1080420/jsp/bengal/story_9161626.jsp

http://www.hindu.com/2008/04/20/stories/2008042055420800.htm

http://timesofindia.indiatimes.com/Kolkata/Papers_leaked_no_JEE_today/articleshow/2964897.cms

http://www.expressindia.com/latest-news/JEE-postponed-after-leaked-papers-reach-market/299230/

Due to question paper leakage .

............WBJEE has been postponed for

atleast 1 month

check this link and go to etv bangla watch the streaming video of :

amar bangla headlines

http://www.etv.co.in/etv-d4/index1.php

If I am not wrong this book is far better and has more beautiful problems than Irodov......even i needed it.....got the book from didi's shelf. However please respond if anyone knows it.

Solution is A x² + B y² = 1

or differential equation of all conics whose axes coincide with the axes of co ordinates.

Courtesy : hard disk which rests above shoulders between ears underneath hair......
(I am not bald

)

solve for yourself and get the answer! Trust me dude this is the only way to be able to solve 100 problems in 2 hours.

The position of instantaneous axis of rotation should be (l/2 sin

, l/2 cos

)

l/2 = x ( see in figure)

Now applying conservation of mechanical energy ,

Decrease in potential energy of the rod = increase in rotational energy about instantaneous axis of rotation

m g l/2 ( 1 - sin

) = 1/2 I

²

Now I = m l²/ 12 + m x ² = ml ² / 12 + ml ² /4 = ml ² /3

So now putting the value of I ,
we have

mg l/2 ( 1 - sin

) = 1/2 ( m l ²/ 3 )

²

So

² = 3g ( 1 - sin

) / l

So

=

3g / l ( 1 - sin

)

I think answer is as given by Ramyani didi

.I hope thats a nishpap solution.

Sorry for daring to touch mechanics section even after guys like Anchitsaini being around.

D.C.Pandey seems to be a good book.But better books are available.

Happy Birthday Mrunal !!

As she says she is M....mischevious R.....reliable..... U......unique....(as every individual is) N......naughty..... A.....adorable.....admirable.... L .......luvin'

So friends wish her on her birthday May God bless you ..........Have a fabulous year ahead !!!

Sorry for allignment problems

So friends wish her on her birthday

May God bless you ..........Have a fabulous year ahead !!!