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Let they meet each other at distance x from B and at time t and let the total distance of journey be l.
Let the speed of second man be u.
Speed of first man = 12
When they meet :
x = 12t and l - x = vt
Dividing these two : v/12 = (l - x)/x........(1)
The journey after meeting :
1st man would now cover l - x distance in 10/3 hours.
Hence l - x = 12(10/3) = 40............(2)
2nd would cover x distance in 24/5 hours.
Hence x = v(24/5).................(3)
From (1) v/12 = (l - x)/x = 40/x
x = 480/v
Put this in (3)
480/v = v(24/5)
v2 = 480(5/24) = 100
Hence v = 10 km/hr
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m1 = -b/a and m2 = b/a
tan  = | (m2 - m1) / 1 + m1 m2 |
= tan-1[{(b/a) - (-b/a)}/{1 + (b/a)(-b/a)}]
= tan-1{(2b/a)/(1 - b2/a2)}
= 2tan-1(b/a)
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Let x-axis be along the inclined plane and y-axis be perpendicular to it.
ax = -gsin300 and ay = -gcos300
Initial velocity : ux = u.cos(30+ ) uy = u.sin(30+)
Final velocity in x-direction is zero since it hits the plane perpendicularly.
0 = u.cos(30+) - (g.sin30)t
t = u.cos(30+)/(g.sin30) ............(1)
y-coordinate : y = u.sin(30+).t - (1/2)(gcos30)t2
When it hits the plane y = 0
t = 2u.sin(30+)/(g.cos30)..............(2)
From (1) and (2)
u.cos(30+)/(g.sin30) = 2u.sin(30+)/(g.cos30)
tan(30+) = ( 3)/2
= -300 + tan-1{( 3)/2)
where is the angle of projection with the inclined plane.
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Good Work Goutham.
Horizontal component of velocity is constant.
ucos600 = vcos300
v = u/3 = 20/3 m/s
Centripetal acceleration is given by v2/R = gcos300
R = v2/gcos300 = (20/3)2/(53) = 15.4 m
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Concentrate on your 11th studies and take down the notes provided in your coaching. Beside coaching use remaining time to study 11th portion. And after your exams are over just go through the notes and try to grasp the topics by giving more time.
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In this site there is a link named "Study Material". Click on this link and you'll get a list of various topics including Algebra.
Refer to that link and you will find the relations and their applications in examples written in very compact from.
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Ring-Chain Tautomerism : Tautomeric forms exist in substances possessing functional groups which can interact additively and which are so placed that intramolecular reaction leads to a stable cyclic system. The cyclic form usually predominates (especially if it contains five or six members).
Keto-Enol Tautomerism : In organic chemistry, keto-enol tautomerism refers to a chemical equilibrium between a keto form (a ketone or an aldehyde) and an enol. The enol and keto forms are said to be tautomers of each other. The interconversion of the two forms involves the movement of a proton and the shifting of bonding electrons; hence, the isomerism qualifies as tautomerism.
For more information refer :
http://www.answers.com/topic/tautomerism
http://en.wikipedia.org/wiki/Tautomer
http://en.wikipedia.org/wiki/Keto-enol_tautomerism
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M L Khanna is not that bad. You can solve some elementary problems from it just to have a start.
But I would suggest you to buy MCQ ( A Dasgupta ) which is really a good objective book. It contains a good set of problems. Must go through it.
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The phase lag  is given by tan = XL/R
tan = wL/R = 2 fL/R = 100
Hence time lag is given by :
t = (/2)T (T = time period)
t = [{tan-1(100)}/2](1/50)
This is approx. t = 1/200 = 0.005 sec
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When there is a will there is always a way.
Your marks in board exams reflect that you are a good student , then how can you think of leaving the preparation after 1 year. You still have a year left and one year is sufficient for a good student. Means you have to show dedication throughout the upcoming year and dont be depressed because there are many who have cleared JEE form your stage. Grasp 12th topics firmly and side by side give some time to 11th topics too. All the best.
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The questions asked in AIEEE are not that tough but what matters is the speed on that day which can be increased by practice and solving some mock tests.
Maths : Preferably practice coordinate geometry and calculus and after completion go for sequences,complex and vectors.
Physics : Practice electricity and magnetism, mechanics , modern physics in order. Even if u r left with some time go for optics, thermodynamics and waves in order.
Chemistry : Practice whole physical part, revise concepts of organic and inorganic every morning and practice them.
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Kepler's Law :
T2  R3
(T1/T2)2 = (R1/R2)3 = (R/4R)3
(T1/T2) = (R/4R)3/2 = (1/4)3/2 = 1/8
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Cv = 0.075 kcal/(kg.K)
Suppose the molecular wt. = M
Then Cv = (75M) cal/(mol.K)
Cv = R/( -1)
75M = 2/(5/3 - 1)
M = 0.04 kg
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Since and  are the roots of the equation ax2 + bx + c = 0
+ = -b/a = c/a
74 + 47 = 44(3+3)
= ()4(+)(2-+2)
= ()4(+){(+)2 - 3}
= (c/a)4(-b/a){(-b/a)2 - 3c/a}
= bc4(3ac - b2)/a7
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Octahedral void :
Let a small circle squeezed between the spheres in the void and let its centre (0,0).
Distance of centre of one of spheres form (0,0) = (R2 + R2) = (2)R
Also this is equal to R + r where r is the radius of small sphere in-between.
Hence R + r =(2)R
r = (2 - 1)R = 0.414R
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