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Circles and System of Circles
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IntroductionMost of the things that we see around us are circular. Sun, moon on full moon day bangle mery-go around, which you loved so much when you where a child; all happened to circles. Ever wondered how a circle can be represented mathematically; well no!!, then we will tell you in this chapter. Also we will take about tangent normulas, chords which we all have hear about. So let us prove deep in to circles.Definition: locus of a set of points equidistant from a fixed point Equation ofcircle -(x - h)2+ (y - k)2= r2x2h2- 2hx + y2- 2ky + k2- r2= 0x2+ y2+ 2gx + 2fy + C = 0CenterGenreal second degree equation-ax2+ by2+ 2hxy + 2yx +2fy +C = 0this equa
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on 27 Dec 2008 19:19:00 IST
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Solution of Triangles
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IntroductionEvery triangle has 3 angles and 3 sides. Given any 3 quantities out of 3 angles and 3 sides (at least one of which is a side) are given then remaining 3 can be found , which is termed as solution of the triangle. Many interesting relation among these quantities will be discussed in this section. Which formula is to be used where is a very important point here, as a use of wrong formula might lead to large calculations. So be prepared to see some very interesting stuff. Terminology Side
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on 27 Dec 2008 19:03:55 IST
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Trignometric Ratios and Identities
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Math: Trignometry ChapterThe word trignometry is devided from 2 greek words(1) Trigonon and(2) MeetronTrignon means triangle and metron means measure So, is science of measuning angle .A very interesting branch, it is used in almost all other branches of mathematic whether it be coordinatc goemetry or it be calculus.For a given anglein a right angle these ate six fossible ratios of 2 sides and hence there are 6 trignometric functions. These are extremely useful in simplefying many cliculations in mathematics. So lets stady these in more details.Trignometric functions:Let O be centre if cir
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on 27 Dec 2008 18:45:14 IST
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Functions and Graphs
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Functions:Let AB be two non empty sets & F is a relation which associates each elemenet of set A with unique element of set B, then F is c/d a function from A to B.Set A is called domain of F & B be the co domain of F.Set of elements of B, which are images of elements of set A is c/d range of F.F : AB ("F is function of A into B")If aA then element in B which is assigned to 'a' is called image of 'a' & denoted by F(a).let A = {a, b, c, d}, B = {1, 2, 3, 4, 5}So, F(a) = 2, F(b) = 3, F(c) = 5, F(d) = 1 Dumb Question: What is non empty set ?Ans: A set which contain at least one elementeg. A
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on 27 Dec 2008 18:17:16 IST
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Probability
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IntroductionDispute in 1654 led to the creation of a mathematical theory of prabability by two famous french mathematicians Blaise Pascal and Pierrede Fermet . First fundamental principles of prabobility theory were formulated for Ist time In popular dice game. Consisted in throwing a pair of dice 24 time, the problem was to decide whether or not to bet even money on occurrence of at least one "double six" during 24 throws. By gambling rule chevalier de mere believed it would be profitable but c caluclation shows just opposite .Dutch scientist christion Huygens in 1657 published the first book of probability
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on 27 Dec 2008 18:04:55 IST
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Matrics & Determinants
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IntroductionMatrices and determinants are very nice ways to vepresent bunch of number. matrices as well as determinants dlong with some very nice properties that each of then have, prove to be very useful in solving equations, finding area of polygons etc. Matrices a also find use in Linear Algebra which is beyond the scope of JEE syllabus.So, Let us study these in details.Matrices And DeterminantsMATRICESA rectangular away of elements or symbols.along sows and wlumns in colled a matricx .Equal MAtrices :- Two matrices are eqnal if they have the same order and each element of ove is equal to the corresponding of the other.Classification (Secondaty
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on 27 Dec 2008 17:49:36 IST
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Logarithms
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IntroductionDefinition:-We define log as, ay= x than y = logax. in logax. both x and a are positive ie. x > 0 and a > 0 and also a1.Dumb Question:- Why a cannot be 1 ?Ans:- Suppose a is 1 then let us attempt to y such that y = log1x.Now according to definition of log.1y= x.But no matter what power we raise to 1 the answer will be. 1 only so we will never never be able to find y.Hence a cannot be 1.Some important formulae:- (Formulaes marked with * are important. This is not be printed)1. logaa = 1.2. logany1 = 0.3. logca = logba.logcb.Why ?Let logba = x and logcb = ySo, by definition, a = bx..................................... (i)b = cy..............
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Complex Numbers
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IntroductionComplex number is one of the most important chapter for IIT - JEE. It is assumed to be one of the toughest chapter of syllabus, though it is not. We have discussed this chapter in as simple as we can . The tricks that are used here are uery simple & very useful , espedially the trignometric concepts & theory of equation dicussed here with co-ordinate geometry is quite useful. After going through a very new concept you will find it very interesting & challenging. We have tried our best possible way to make this chapter look easier & interesting
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on 27 Dec 2008 16:42:06 IST
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Nucleus
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IntroductionNucleus the central core of an atom is held together by a short -range force called nucleus force, which is also a potential source of energy called Nuclear energy. in this unit we will first understand the phenomenon of radioactivity and its explanation using bindingenergy concept. we will later study about the radioactive decay characteristcs which hold emmense temperaturein age estimation of old rocks etc.Nuclear Characterstics:(1) Nuclear mass: The total mass of nucleus in the nucleus is called as nucleus mass.Nuclear mass =mass of proton + mass of neutron.(2) Radius of Nucleus: Radius of Nucleus holds the relationshipwhere R0= 1.1 x 1
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on 27 Dec 2008 16:15:11 IST
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Bohrs Model and X-rays
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Neils Bohr gave forward his model of atom with answeres most of the flaws that Rutherford model had. This model introduced quantization principal and this model is regarded as first quantum mechanical model. We will explore in detail, this structure of atom. We will also look into X - ray formation which is a converse process of photoclectric effect and will examine Moreley's law in pantium. THE BOHR THEORY OF HYDROGE ATOM (AND HYDROGEN LIKE ATOM) Bohr gave following postulates for electron in hydrogen atom :- • An electron in an atom could resolve in certain stable orbits without the emission of radiant energy. • An elec
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on 27 Dec 2008 15:52:30 IST
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Electromagnetism
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Magnetics (Magnetic Field): Magnetic Force: The magnetic force ( on a charge q moving with velocity ina magnetic field is given both in magnetude and direction, by = q( x ) The Biot and Savart Law: Consider an infinitesinal element of length 'dl' of a wire carrying current I. The magnetre field d at P because of is given by the law: Magnetic field due to current in a straight line: (Secondary Information) at P due is = l = R cot, dl = - R cosec2d, r = R cosec
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on 27 Dec 2008 15:23:14 IST
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Wheatstone's Bridge
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ntroduction It works on the pricipal of Wheatstone bridge. It is so called because it uses a wire which is a metre long. The wire is made of uniform cross-section of a material with a high resistivity and low teemperature coefficient of resistance (e.g. manganin). The fig. 14.4 shows a simple from a Metre Bridge. The wire is streched along a metre scale between two brass or copper strips. The unknown resistance X and a known resistance R (resistance box) are connected between the gaps DF and HK, respectively. When the sliding contact (jockey) is at the position C, it divides the wire into two parts of resistance RAC and RCB; these resistanc
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on 27 Dec 2008 14:54:01 IST
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Electric Current
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IntroductionWe all must be families with the team electric current. We think who simple it is. But when even for a single moment we try to analyze actually what it is, how is it generated then we realize that team and making it so simpler to us. Now a days every single thing is an application of current and electricity.Conductor for and time is called electric currentWhere dq is the charge flown through a cross section area conductor in time dt. It is also called instantaneous current I this dt - 0.Where q is the charge flown in a finite time t. S.I unit of electric current is Ampere (A).Illustration
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on 27 Dec 2008 14:42:13 IST
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Capacitance And Capacitor
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The capacitance of any conductor is its capacity to store charge. As the quantity of charge on conductor is increased its potential also increases. Beyond a limit even if a small additional charge is given then it starts leaking. Hence Q µ V or Q = CV. Where C is called capacitance of the conductor. It depends upon geometrical shape and size of the conductor. If V = 1 volt, then Q = C, hence capacitance of any conductor will be numerically equivalent to that charge which makes its potential e
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on 27 Dec 2008 14:21:21 IST
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Electrostatics
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The study of electrostatic introduces us to the vast world by electricity, magnetism, current, working of circuits and charges. Right from the attraction between a proton and neutron to the working of large high voltage generator can be explained by the simple concepts of electrostatics, the most basic of phenomenon and yet the most interesting of all.Introduction: Electrostatic is the study of charges that are at rest and their interactions.Electric Charge: It is an intrinsic property of protons and electrons, proton and elec
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on 27 Dec 2008 13:49:41 IST
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Gas Laws
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Chemistry: Physical Chemistry The Gas Laws started .... in 1643 A.C. with invention of the barometer and continued until 1873 with the Vancer Waal's Equation. The gas law led to numerous concepts include the mole, temperatur, formula weight, absolute kinetic energy & stoichiometric coefficients. Gas laws were put forward by mainly three process. John Dalton, Robert Boyle, Jacques Charles. Modern kinetic molecules theory started with Bennoulli's suggestion in 1734 that pressure exerted by a gas on walls of its containes is sum of many collisions by individual molecules. THese gas laws have very significant role in practical life.
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on 27 Dec 2008 13:28:38 IST
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Calorimetry And Thermal Expansion
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Calorimetry can be considered to be the earliest known principal of Heat and Thermodynamics.This was the introduction of the widely used principal of Conservation of Energy to mankind.Thermal Expansion too find a great importance in engineering application.Its knowledge should also be imported for efficient working of various machines.Calorimetry and Thermas Expansion:-Calorimetry:-Heat:-It is a form of energy which determines the change in thermas state of a body.Heat flows from a body which has a higher temp. to the body which has lower temp.Specific Heat:- Quantity of heat in calories required to raise the temp. of 1 gm. of that substance by 1C.thermal Equilibr
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on 27 Dec 2008 13:17:50 IST
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Heat Transfer
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IntroductionHeat Transfer helps us to understand various aspects for the transfer of heat through various materials(solids, liquid and gasses) through various known process such as conduction, convection, radiation etc.So, it finds a great use in engineering applications.Heat is transferred from higher temperature to lower temperature. [secondary information]There are three different ways in which heat can be transferred:1. Conduction:- it is process by which heat can be transferred in solids.2. Convection:- it is aprocess by which heat is transferred in fluides (gaseous &liquid)3. Radiation:- it is a process in which the heat is transferr
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on 27 Dec 2008 13:02:04 IST
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Geometric Optics
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OPTICS is study of propagation of light. In Geometric optics we are just concerned about, what the path of light is when it gets reflected or refracted. While dealing with Geometric optics we consider light rays to e paraxial i.e. which re very near to each other and thus a lot of assumptions could be encorprarted. In this unit we answer why a coin placed in water appear to be little bit raised above and many such phenomenom.REFLECION: When a ray of light is incident at a point on the surface, the surface throus party or whally the incident energy back into the medium of incidence. This phanomenon is called reflection.Surface that causes reflection are known a
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on 27 Dec 2008 12:43:53 IST
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Fluid Mechanics
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IntroductionFluids that include liquids and gases play a vital role in our daily lives as we breathe and drink them. Cars run on fluid (Petrol, diesel), Oceans and rivers are full of fluid (water), battery, AC’s, refrigerators too contain fluids (CFC’s etc) DEFINITIONA fluid is a substance that can flow and conform to the boundaries of any container containing it. This is because fluid can not sustain a force that is tangential to its surface. More over fluid flows because it can not with stand a shearing stress. DENSITYTo find the density r of a fluid at any point, we isolate a small volume elem
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