PULLA EDU APP JEE MAIN ADVANCED

                 CHAPTER 15 WAVES INTRODUCTION In day to day life we are familiar with different types of waves. All types waves transfer energy from one point to another without the bodily sovement of the particles of the medium. Generally there are three types of was. The most familiar type of waves are the mechanical waves. eg. waves sa streched string, water waves, sound waves, seismic waves etc. All these require a medium for propagation. Another type of waves are the electromagnetic waves. They do not require a medium to travel. eg. light, radio waves, x-rays, γ -rays etc. All these waves travels with the velocity of light. A third kind of wave is the matter waves . They are associated with matter. The matter waves can easily be detected in the case of very small particles like electrons, protons, neutrons, atoms and molecules etc. They arise in quantum mechanical description of matter. Matter waves associated with electrons are employe...

NEWTON'S UNIVERSAL LAW OF GRAVITATION Every body in the universe attracts every other body with a force  which is directly proportional to the product of their masses and versely proportional to the square of the distance between them.  Consider two masses mand m, separated by a distance, r. According to Newton's law of gravitation the force between the two masses directly proportional to the product of masses (m, m,) and inversely pro portional to the square of the distance (r). 1. or m, m, F Gm m where G is a constant called the gravitational constant. In S.I units, G 6.67 1o " Nm kg. The dimensional formula of G is (M 'L'T 1. The force on mbym can be written in vector form as F-- Gimmr, where is the unit vector from m to m2. The negative sign of gravitational force shows that it is an attractive force. Forces on the two masses are equal and opposite. F, =-F i.e. The force on 1" particle due to 2 particle = force on 2 particle due to 1"parti...

TRIGONOMETRY BASIC EQUATIONS  CHAPTER 3  TRIGONOMETRIC FUNCTIONS Angle Angle is a measure of rotation of a given ray about its  initial point.The original ray is called the initial side and  the final position of the ray is called the terminal side  of the angle. The point of rotation is called the vertex.   If the direction of rotation is anticlockwise,the angle is  said to be positive.If the direction is clockwise then the  angle is negative. If the ray rotates and come to its original position,we  say that it has completed one revolution. Two units of measurement of an angle 1.Degree measure If a rotation from the initial side to terminal side is  (1/360)th of a revolution,the angle is said to have one degree, written as 1o .One degree is divided into 60  minutes and one minute is divided into 60 seconds. 1 o=60’ 1 ’=60’’ 2.Radian measure    Angle subtended at the centre by an arc of length 1  unit in a unit circle...

HEAT AND TEMPERATURE Heat is form of energy. Heat is transferred between two(or more ) systems or system and its surroundings by virture of temperature difference.  Temperature is the degree of hotness.  SI unit of heat is Joule(J ) and that of temperature is kelvin (K)

PRESSURE In fluids, gases and liquids the molecules are free to move. On the way they collide with the walls of container and exert a force on the walls. The force is acting normal to the surface.  The force acting normal to surface per unit area is called pressure. It is scalar quantity.   Its dimensional formula is ML⁻¹T⁻². Its unit is Nm⁻² or Pascal (Pa).This unit is in honour of French scientist BLAISE PASCAL. Another common unit of pressure is atmosphere. The pressure exerted by atmosphere is at sea level is called one atmosphere.(atm) 1 atm=1.013*10⁵Pa properties of fluid pressure 1) The pressure will be equal at any point in the same horizontal level of a liquid at rest 2)The pressure will be the same in all directions at any point in liquid at റസ്റ്റ്‌ PASCAL'S LAW Blaise Pascal observed that pressure in a fluid at rest is the same in all directions, if we ignore the gravity. To establish this, consider an elementary volume of liquid which is in the form of right ...

Introduction Fluid is that which can flow. Liquids and gases are fluids. A fluid has no definite shape. It assumes the shape of container . Fluid can not withstand tangential stress or shearing stress on its surface. That is why they flow. The shearing stress of fluids is about one millionth of solids. The compressibility of solids and liquids are much lower when compared with gases. The main differences between the liquids and gases 1) Liquid is incompressible, while a gas is compressible 2)Liquid has  a free surface, while a gas has no free surface Common properties of liquids and gases 1) Liquids and gases can flow and 2) Liquids and gases can exert pressure on walls of container Thrust and pressure The force acting perpendicular to surface is called thrust. The trust per unit area is called pressure. BUOYANCY Consider a body immersed in a liquid. The thrust acting on bottom surface will be greater than thrust on top side. Thrust in upper surface is downwards and thrust on bott...

∫GMm/r^2 

Introduction MOLECULAR NATURE OF MATTER The scientific atomic theory is credited to John Dalton. Atomic theory is not the end of quest, but beginning. Atoms consists of nucleons and electrons. The nucleus itself is made up of protons and neutrons. The protons and neutrons are again made up of quarks. Quarks may not br the end of the story. There may be string like elementary entities. In this chapter, understanding the behavior of gases 

INTRODUCTION The kinectic theory was developed in the nineteenth century by Maxwell, Boltzman and other. It gives molecular interpretation of pressure and temperature of a gas it also explains gas laws and Avogadro's hypothesis. It correctly explains specific heat capacities of many gases. It help us to find molecular sizes and masses.

FACTORIALS The continued product of Iⁿ n natural number is called the "n!" n factorial ie; n!=1*2*3*....... 0!=1 n!=1*2*3........(n-2)(n-1)n n!=(n-1)!n factorial is defined only for whole numbers PERMUTATIONS A permutation of a set of elements is an arrangement of (all or part) elements in same order Eg: n=3 {a, b, c} 3P(3) abc           acb           bac           bca           cab           cba The number of permutationn of n things taken r at a time is the no. of ways of arranging n things taken r at  atime and denoted by P(nr)=ⁿPᵣ=nᵖr This is equivalent to the number of ways of filling up r vacent spaces in a line with n different objects Theorem If 0≤r≤n then ⁿPᵣ = (n)(n-1)(n-2)............(n-(r-1))                =(n)(n-1)(n-2)..............(n-r+1) Note o≤r≤n           npᵣ=n!/(n-r)!  ...

FUNDAMENTAL PRINCIPLE OF COUNTING  If an event can happen exactly m ways and following it a second event can happen in exactly in n ways, then the two events in succession can happen exactly in mn different ways 1.In a class there are 27 boys  and 14 girls. The teacher wants to select one boy and one girl to represent the class. In how many ways can the teacher make this selection? No of ways to select boys = 27 The teacher has to perform two operations 1.selecting one from 27 boys in 27 ways 2.selecting a girl from 14 girls. In total ways 27*14 ways =378 ways 2)  A flag contains 3 blocks with different colours. Each coloured differently. If there are 6 different colours. How many such designs are possible? 3)  How many numbers are there in between 100 and 1000 such 7 is in the unit place? 4)  How many three digit numbers are there with all digits distinct? PERMUTATIONS ; FACTORIALS, PERMUTATIONS 

In 1543 Nicolaus Copernicus stated that all planets move SUN in circular orbits with the sun at the centre. But Johannes Kepler (1571-1630)discarded this theory and proposed the elliptical orbits for planetary motion. He formulated three laws known as Kepler laws of planetary motion. 1) KEPLER FIRST LAW(LAW OF ELLIPTICAL ORBIT ) Every Planet revolves round the sun in elliptical orbits with sun at one of the foci. 2)KEPLER SECOND LAW (LAW OF EQUAL AREAS) The line joining the sun and plannets sweeps out equal areas in equal intervals of time.  i.e, the areal velocity swept by radius vector of ellipse is a contestant. 3) KEPLER THIRD LAW (HARMONIC LAW) The square of time period  of revolution of plannet around the sin is directly proportional to cube of mean distance between sun and plannet. The proof of first law involves borh calculus and geometry... It is beyond scope of plus one and jee EXPLANATION OF FIRST LAW Drawing an ellipse. The string has its ends fixed at ...