Saturday, 21 November 2015

WAY TO SUCCESS 4

JEE Advanced  2014 Syllabus  for Physics

General:   Units and dimensions,  dimensional  analysis;  least count,  significant  figures;  Methods of measurement   and error analysis  for physical  quantities  pertaining  to the following experiments:    Experiments  based  on using Vernier  calipers  and screw gauge (micrometer),
Determination   of g using simple  pendulum,  Young's  modulus  by Searle's  method,  Specific  heat of a liquid using calorimeter,  focal length  of a concave  mirror and a convex  lens using u-v method,  Speed  of sound  using resonance  column,  Verification  of Ohm's  law using voltmeter and ammeter,  and specific  resistance  of the material  of a wire using meter bridge and post office box.

Mechanics:    Kinematics  in one and two dimensions  (Cartesian  coordinates  only), projectiles; Uniform  Circular  motion;  Relative  velocity.
Newton's  laws of motion;  Inertial and uniformly  accelerated  frames  of reference;  Static and dynamic  friction;  Kinetic and potential  energy;  Work  and power; Conservation   of linear momentum  and mechanical  energy.

Systems  of particles;  Centre  of mass  and its motion;  Impulse;  Elastic and inelastic  collisions.
    Law of gravitation;  Gravitational  potential  and field; Acceleration   due to gravity;  Motion of    planets  and satellites  in circular  orbits;  Escape velocity.
   Rigid body, moment  of inertia, parallel  and perpendicular   axes theorems,  moment  of inertia     of uniform  bodies with simple  geometrical  shapes;  Angular  momentum;   Torque;   Conservation   of angular momentum;   Dynamics  of rigid bodies with fixed axis of rotation;   Rolling without  slipping of rings,  cylinders  and spheres;  Equilibrium  of rigid bodies;   Collision  of point masses  with rigid bodies.

Pressure  in a fluid;  Pascal's  law; Buoyancy;  Surface  energy  and surface  tension,  capillary  rise; Viscosity  (Poiseuille's  equation  excluded),  Stoke's  law; Terminal  velocity,  Streamline  flow, equation  of continuity,  Bernoulli's  theorem  and its applications.

Wave  motion  (plane waves  only), longitudinal  and transverse  waves,  superposition  of waves; Progressive  and stationary  waves;  Vibration  of strings  and air columns;Resonance;    Beats; Speed  of sound  in gases;  Doppler effect (in sound).

Thermal  physics:  Thermal  expansion  of solids, liquids  and gases;  Calorimetry,   latent heat;  Heat conduction  in one dimension;  Elementary  concepts  of convection  and radiation;  Newton's  law of cooling;  Ideal gas laws; Specific  heats (CV and Cp for mono atomic  and diatomic  gases); Isothermal  and adiabatic  processes,  bulk modulus  of gases;  Equivalence  of heat and work;  First law of thermodynamics   and its applications  (only for ideal gases);   Black body  radiation:
absorptive  and emissive  powers;  Kirchhoff's  law; Wien's  displacement  law, Stefan's  law.

  Electricity    and  Magnetism:   Coulomb's  law; Electric  field and potential;  Electrical   potential energy  of a system  of point charges  and of electrical  dipoles  in a uniform   electrostatic  field; Electric  field lines; Flux of electric field; Gauss's  law and its application   in  simple cases,  such as, to find field due to infinitely  long straight  wire, uniformly  charged   infinite plane sheet and  uniformly  charged  thin spherical  shell.

Capacitance;   Parallel plate capacitor  with and without  dielectrics;  Capacitors  in series  and parallel;  Energy  stored  in a capacitor.

Electric  current;  Ohm's  law; Series and parallel  arrangements   of resistances  and cells; Kirchhoff's   laws and simple  applications;  Heating  effect of current.

Biot-Savart's    law and Ampere's  law; Magnetic  field near a current-carrying   straight  wire, along the  axis of a circular coil and inside a long straight  solenoid;  Force on a moving  charge and on a current-carrying   wire in a uniform  magnetic  field.

Magnetic  moment  of a current  loop; Effect of a uniform  magnetic  field on a current  loop; Moving coil galvanometer,   voltmeter,  ammeter  and their conversions.

Electromagnetic   induction:  Faraday's  law, Lenz's  law; Self and mutual  inductance;  RC, LR and
LC circuits with D.C. and A.C. sources.

Optics Rectilinear  propagation  of light; Reflection  and refraction  at plane and spherical surfaces;  Total internal  reflection;  Deviation  and dispersion  of light by a prism;  Thin lenses; Combinations   of mirrors and thin lenses;  Magnification.

Wave  nature  of light: Huygens's  principle,  interference   limited to Young's  double-slit  experiment.

Modern   Physics:   Atomic  nucleus;  Alpha,  beta and gamma  radiations;  Law of radioactive
decay;   Decay constant;  Half-life and mean life; Binding  energy and its calculation;  Fission and fusion  processes;   Energy calculation  in these  processes.


Photoelectric  effect;  Bohr's theory of hydrogen-like   atoms;  Characteristic  and continuous  X-rays, Moseley's  law; de Broglie wavelength  of matter wave

Saturday, 14 November 2015


Way to Success - IIT - 3


SYLLABUS FOR JEE - 2016


                                                 Mathematics Syllabus

Algebra
Algebra of complex numbers, addition, multiplication, conjugation, polar representation, properties of modulus and principal argument, triangle inequality, cube roots of unity, geometric interpretations.
Quadratic equations with real coefficients, relations between roots and coefficients, formation of quadratic equations with given roots, symmetric functions of roots.
Arithmetic, geometric and harmonic progressions, arithmetic, geometric and harmonic means, sums of finite arithmetic and geometric progressions, infinite geometric series, sums of squares and cubes of the first n natural numbers.
Logarithms and their properties.
Permutations and combinations, Binomial theorem for a positive integral index, properties of binomial coefficients.
Matrices as a rectangular array of real numbers, equality of matrices, addition, multiplication by a scalar and product of matrices, transpose of a matrix, determinant of a square matrix of order up to three, inverse of a square matrix of order up to three, properties of these matrix operations, diagonal, symmetric and skew-symmetric matrices and their properties, solutions of simultaneous linear equations in two or three variables.
Addition and multiplication rules of probability, conditional probability, independence of events, computation of probability of events using permutations and combinations.
                                                                        Trigonometry
Trigonometric functions, their periodicity and graphs, addition and subtraction formulae, formulae involving multiple and sub-multiple angles, general solution of trigonometric equations.
Relations between sides and angles of a triangle, sine rule, cosine rule, half-angle formula and the area of a triangle, inverse trigonometric functions (principal value only).
       Analytical geometry
                      Two dimensions
Cartesian coordinates, distance between two points, section formulae, shift of origin.
Equation of a straight line in various forms, angle between two lines, distance of a point from a line. Lines through the point of intersection of two given lines, equation of the bisector of the angle between two lines, concurrency of lines, centroid, orthocentre, in centre and circum centre of a triangle.
Equation of a circle in various forms, equations of tangent, normal and chord.
Parametric equations of a circle, intersection of a circle with a straight line or a circle, equation of a circle through the points of intersection of two circles and those of a circle and a straight line.
Equations of a parabola, ellipse and hyperbola in standard form, their foci, directrices and eccentricity, parametric equations, equations of tangent and normal.
Locus Problems.
                  Three dimensions:
Direction cosines and direction ratios, equation of a straight line in space, equation of a plane, distance of a point from a plane.
                 Differential calculus
Real valued functions of a real variable, into, onto and one-to-one functions, sum, difference, product and quotient of two functions, composite functions, absolute value, polynomial, rational, trigonometric, exponential and logarithmic functions.
Limit and continuity of a function, limit and continuity of the sum, difference, product and quotient of two functions, l'Hospital rule of evaluation of limits of functions.
Even and odd functions, inverse of a function, continuity of composite functions, intermediate value property of continuous functions.
Derivative of a function, derivative of the sum, difference, product and quotient of two functions, chain rule, derivatives of polynomial, rational, trigonometric, inverse trigonometric, exponential and logarithmic functions.
Derivatives of implicit functions, derivatives up to order two, geometrical interpretation of the derivative, tangents and normals, increasing and decreasing functions, maximum and minimum values of a function, applications of Rolle's Theorem and Lagrange's Mean Value Theorem.
                Integral calculus
Integration as the inverse process of differentiation, indefinite integrals of standard functions, definite integrals and their properties, application of the Fundamental Theorem of Integral Calculus.
Integration by parts, integration by the methods of substitution and partial fractions, application of definite integrals to the determination of areas involving simple curves.
Formation of ordinary differential equations, solution of homogeneous differential equations, variables separable method, linear first order differential equations.


                 Vectors
Addition of vectors, scalar multiplication, scalar products, dot and cross products, scalar triple products and their geometrical interpretations.