Every student is in a race to score well during their higher and senior secondary years. Anything less than 90% is a curse in today’s competitive world. So, not only students but parents also, have changed their mindsets to such an extent that coaching classes are a must have for every student during their 11th and 12th standards, especially science students.
Are coaching centres a necessity? Do they feed off every Indian family’s need for preparing their kids for entrance examinations, especially for science-related courses? Do they attempt to create an aptitude for the field by forcing subjects on students?
Yes, coaching centres have their pros. But if this is the case, then why do many people flunk the competitive exams even after joining these coaching institutes?
It’s the pressure of scoring exceptionally well on the students that is imposed from the very early days. So in this chaos of what to do and what not do, Direct Admission has a brilliant product named Kota Online Coaching Program (KOCP).
KOCP is an educational tool developed by Direct Admission featuring education faculty of KOTA which possess an experience of more than 30 years. The KOCP kit includes video lectures that are accessible online. This was an initiative taken by the company in aid of students who intend to crack national level competitive exams inclusive of JEE, NEET and CBSE. To dodge the problem of inefficient internet connectivity, the video lectures are also made available offline in the form of DVD, USB, SD card and Tablet. Kota Online Coaching Program (KOCP) combines the best faculty of Kota, their teaching methodologies, their experience and bring it to the comfort of your own home. You can access it via CD Rom, USB Drives, Pen drives and watch it at your own fixed schedule. You are also provided with the contact number of the concerned authorities to clear your doubts the very same day via telephonic discussion or other electronic correspondences.
The advanced technology used in fabricating the entire kit allows its user to steer the video speed through the course of its streaming. To dodge the problem of inefficient internet connectivity, the video lectures are also made available offline in the form of DVD, USB, SD card and Tablet.
Direct admission has successfully sold more than 1500 copies since the launch of KOCP in December, 2016.
Advantages of Online Coaching
- No travelling. Saves time and money both. Parents can assess the performance of child at home itself.
- Quality teachers (IIT qualified and experienced). Many IITians, NITians, Doctors (Medical interns) who can’t join coaching institutes physically are using online platform to prepare students for exams like IIT JEE and AIPMT (NEET).
- The classes take place in the evening time, mostly between 8 p.m – 10 p.m (our preferred timings). Students already finished with their School work and other stuff before this.
- Free demo class to each student in online mode so that they can understand the platform and if they are comfortable then only they should join a course. Any technical issue on student’s side will be taken care in the technical orientation before the class.
- Personal attention and monitoring are the hallmarks of online coaching. We are having not more than 20 (Max 25) students in a batch that allows our teachers to carefully monitor the progress of each student.
- With students from every part of the country and outside India (NRIs) also, online coaching allows better global benchmarking and analysis reports.
Attractive Scholarships, Regular counselling, continuous online help from subject and exam experts, Customized sessions are some of the key advantages of Online Coaching.
KOCP: IIT JEE Coaching
Basic Information About the IITs and their Joint Entrance Exam The Indian Institutes of Technology (IITs) are the most prestigious institutes in India that offer engineering and technological education of internationally recognized standard of excellence. The IITs offer courses at their Mumbai, Delhi, Guwahati, Kanpur, Kharagpur, Madras, Roorkee campuses and also at the Institute of Technology, Banaras Hindu University (BHU), Varanasi and Indian School of Mines, Dhanbad. From the year 2008 onwards, eight new IITs have been set up across the country by the Union HRD Ministry. These new IITs are located in the states of Rajasthan (Jodhpur), Bihar (Patna), Andhra Pradesh (Hyderabad), Himachal Pradesh (Mandi), Orissa (Bhubaneshwar), Madhya Pradesh (Indore), Gujarat (Gandhinagar) and Punjab (Rupnagar), which has increased the total number of IITs to 15.
Students coming out of the IITs are known to have acquired professional excellence in life. Be it a matter of getting admissions for further studies in most prestigious Universities abroad, or getting employment in any reputed organisations in the world, IITians are always in top demand.
Every year, the IITs conduct a Joint Entrance Examination (JEE) to select candidates for the 4-year B.Tech, B.Pharm, 5-year B.Arch, Integrated M.Sc. and M.Tech courses.
Pattern of the IIT JEE
At present, the IIT JEE is a single – stage objective type examination consisting of two papers of three hours duration each to test comprehension & analytical ability of candidates. Both papers, Paper-1 and Paper-2 will each have three separate sections on Physics, Chemistry & Mathematics. All questions will be of Objective Type, designed to test aptitude, comprehension and analytical ability of the candidates
Eligibility for the IIT JEE
- Candidates appearing in (10+2) or equivalent qualifying examination, must secure at least 60%(55% for SC/ST and PD) marks in aggregate in their respective Board Examination.
- A student can have only two attempts to write the JEE in the year in which he or she passes the XIIth standard examination and/or in the following year.
- Candidates who join any of the IITs, IT-BHU, Varanasi, and ISM, Dhanbad through JEE will not be permitted to appear for JEE in future
New selection process of IITs
- One entrance exam for admission to IITs, NITs and IIITs
- The new JEE will consist of 2 Tests viz. Main Test and Advanced Test which will test problem solving ability in basic science subjects – Physics, Chemistry and Mathematics. Both Tests will be of 3 hours duration each.
- Only the Top 1,50,000 candidates (including all categories) based on performance in JEE (Mains) will qualify to appear in the JEE (Advanced) examination, which will rank candidates for admissions to IITs, provided the candidates are among the top 20% high scorers of their respective boards in class XII examination.
As the above selection pattern gives a substantial importance to the Std. XII Board marks, it is very essential that every student prepares well not only for the proposed JEE, but for Std. XII also.
Our IIT JEE courses are elite in their perfectionism & proficiency and they lead the students to the peak of their preparation while simultaneously covering the school syllabus (CBSE & other Boards). The curriculum is revised frequently to keep pace with the fast changing competitive environment. The faculty is a blend of rich academic experience and vast knowledge. The series of periodic tests are identical to the pattern of various competitive engineering examinations and give ample practice to the aspirants for the same.
Getting a first-hand feel of studying in a rigorously competitive environment, our students further develop their ability of problem solving skills and demonstrate superior performance. Every test attempted by the students gives them a clear idea of their understanding of the topic, strengths and weaknesses, ranking amongst the aspirants from across India. By being a part of the on-going year round curriculum, they adapt themselves well to the pattern of paper and are successful in the examination with ease. Besides delivering knowledge we encourage and motivate our students to make most of their abilities by boosting their confidence.
DIRECT ADMISSION’s KOCP is wholly committed to imparting career based education and students have the benefit of our expertise and knowledge every day throughout the year. From our core curriculum of preparatory studies to the detailed subject analysis through tests, our students have an access to all that is required to be successful in IIT JEE (Main+Advanced).
This is a highly systematic, comprehensive and relevant Study Material Package. This course is designed meticulously for efficient learning. If the student goes through the SMP thoroughly then it helps develop sound understanding of fundamental, a methodological approach to problem solving.
The best brains compete to get an admission to this two-year legendary course offered by us. The course, unmatched in its rigour and precision, raises you to the very zenith of your preparation. The stimulating atmosphere of the institute, small batches (yes-we believe in quality) and one to one interaction with the instructor ensure that every rough edge is smoothened, every small doubt is cleared, that’s why most of our toppers are from this course. More importantly, we train you to think analytically, we give you a systematic approach to problem solving – a must for IIT-JEE. If you think you are bright, if you think you are capable, if you think that you can make it to the top, this course is precisely for you.
Crack JEE with Experienced Faculties of Kota All Courses of KOCP are focused and simplified for JEE Main & JEE Advanced to bring to students an easy and analytical methodology towards physics, chemistry and Mathematics.
Course Details JEE ADV + 11 STD.
- Excellent School Education, Board examination & All round development
- JEE (Main + Advanced) preparation
- This is two year school integrated program to develop step by step strong foundation of concepts & fundamentals, and also to sharpen question solving, smart thinking and reasoning skills to ensure success.
For the JEE Advanced exam, one has to start the preparations right from class 11. A high level of dedication and effort needs to be put in, from the very beginning. The questions asked in the JEE Advanced exam are almost equally from the Class 11 and Class 12 syllabus. There are many students who take it easy in 11th standard after the stressful 10th board exams, but it is almost impossible to cover up the lost preparation in 12th standard. So, in order to secure a good rank in the examination, students must begin an in-depth and structured preparation of the exam syllabi right from the 11th standard.
While cracking the JEE Main is relatively easier and based mainly on the NCERT content, the JEE Advanced requires a rigorous practice of the basics as well as relatively advanced practice problems from several reference books of both class 11th and 12th syllabus.
Important Topics from Class 11 Mathematics
A major section of the JEE Advanced Mathematics syllabus is based on the class 11 Mathematics content. The topics of 11th syllabus Mathematics that cover almost 50% of the JEE Advanced Mathematics question papers are listed below:
- Relations and functions
- Trigonometric functions
- Complex numbers
- Quadratic equations
- Linear inequalities
- Permutations and Combinations
- Binomial Theorem
- Sequences and series
- Straight lines
- Conic section
- Three-dimensional geometry
- Limits, derivatives and continuity of functions (including L’Hospital rule)
Since the above-mentioned topics form the base of any Mathematics problem, it is crucial to have a routine practice of sums of different levels of difficulty on a regular basis. For example, not understanding limits and derivatives will make solving problems of differentiation and integration very difficult. This topic forms approximately 30% of the class 12th Maths syllabus.
Of the above-mentioned topics, relations and functions, trigonometry and probability need to be studied more extensively.
Important Topics from Class 11 Physics
Understanding the concepts of Physics may prove to be challenging, especially if not studied with absolute concentration and focus right from the very first chapter of the class 11th syllabus. In general, the physics portion of the JEE advanced question paper is considered to be the toughest of all the three sections, thereby necessitating special attention and a considerable amount of practice of various types of problems.
The topics of 11th syllabus Physics that get high coverage in the JEE advanced examination are listed below:
- Kinematics (motion in a straight line and plane)
- Newton’s laws of motion, law of conservation of linear momentum
- Different types of friction
- Circular motion
- Work, power and energy; non-conservative forces
- Elastic, inelastic and non-elastic collision
- Mechanical properties of solids (stress, strain, elastic energy)
- Mechanical properties of fluids (streamline and turbulence, surface energy and surface tension)
- Rotational mechanics
- Thermal properties of matter
- Behaviour of perfect gases
- Waves and oscillations
Make a clear note of all the formulas in a categorical manner during the exam preparations. It is very important to follow several reference books for physics and practice as many sums as possible in order to gain confidence in the problem-solving process. It will enable a better understanding of application-based problem solving.
Important Topics from Class 11 Chemistry
The most basic concepts of organic chemistry are taught in the class 11thsyllabus. As the class 11th Chemistry syllabus is a major step-up from the contents of class 10th Chemistry, it is of utmost importance to study 11th Organic Chemistry.
Understanding the concepts of Physical Chemistry is relatively easier. However, it is the rudimentary knowledge of chemistry, which is required for understanding complicated concepts of Chemistry. The numerical concepts of Physical chemistry and their applications are often put to the test in the JEE Advanced. If properly answered, it can easily add to the JEE scores of a candidate. The topics of 11th Inorganic Chemistry need regular revision in order to score better in the JEE advanced.
The topics of 11th syllabus Chemistry, which are included in the JEE advanced syllabus, are listed below:
- Structure of Atom and other basic concepts of Chemistry+
- Molecular structure and Chemical Bonding
- Classification of elements and periodicity of properties
- Thermodynamics and Equilibrium
- Gases and liquids
- Redox reactions
- s-and p- block elements
- Organic Chemistry and Hydrocarbons
- Environmental Chemistry
Course Details for 12th + JEE Adv
This is one year course to develop strong foundation of concepts and their application. This course also sharpens question solving and reasoning skills of student. In addition to JEE (Adv) preparation, complete school syllabus, Physics & Chemistry Practical and English are also covered for excellent performance in school examination also.
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 Verniercalipers 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.Linear and angular simple harmonic motions.Hooke’s law, Young’s modulus.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 monoatomic 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); Blackbody 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: Huygen’s principle, interference limited to Young’s double-slit experiment.
- Modern physics:Atomic nucleus; α, β and γ 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 waves
CHEMISTRY SYLLABUS FOR JEE ADVANCED 2016:
- General topics:Concept of atoms and molecules; Dalton’s atomic theory; Mole concept; Chemical formulae; Balanced chemical equations; Calculations (based on mole concept) involving common oxidation-reduction, neutralisation, and displacement reactions; Concentration in terms of mole fraction, molarity, molality and normality.
- Concept of atoms and molecules:Dalton’s atomic theory; Mole concept; Chemical formulae; Balanced chemical equations; Calculations (based on mole concept) involving common oxidation-reduction, neutralisation, and displacement reactions; Concentration in terms of mole fraction, molarity, molality and normality.
- Gaseous and liquid states:Absolute scale of temperature, ideal gas equation; Deviation from ideality, van der Waals equation; Kinetic theory of gases, average, root mean square and most probable velocities and their relation with temperature; Law of partial pressures; Vapour pressure; Diffusion of gases.
- Atomic structure and chemical bonding:Bohr model, spectrum of hydrogen atom, quantum numbers; Wave-particle duality, de Broglie hypothesis; Uncertainty principle; Qualitative quantum mechanical picture of hydrogen atom, shapes of s, p and d orbitals; Electronic configurations of elements (up to atomic number 36); Aufbau principle; Pauli’s exclusion principle and Hund’s rule; Orbital overlap and covalent bond; Hybridisation involving s, p and d orbitals only; Orbital energy diagrams for homonuclear diatomic species; Hydrogen bond; Polarity in molecules, dipole moment (qualitative aspects only); VSEPR model and shapes of molecules (linear, angular, triangular, square planar, pyramidal, square pyramidal, trigonalbipyramidal, tetrahedral and octahedral).
- Energetic:First law of thermodynamics; Internal energy, work and heat, pressure-volume work; Enthalpy, Hess’s law; Heat of reaction, fusion and vapourization; Second law of thermodynamics; Entropy; Free energy; Criterion of spontaneity.
- Chemical equilibrium:Law of mass action; Equilibrium constant, Le Chatelier’s principle (effect of concentration, temperature and pressure); Significance of ΔG and ΔG0 in chemical equilibrium; Solubility product, common ion effect, pH and buffer solutions; Acids and bases (Bronsted and Lewis concepts); Hydrolysis of salts.
- Electro chemistry:Electrochemical cells and cell reactions; Standard electrode potentials; Nernst equation and its relation to ΔG; Electrochemical series, emf of galvanic cells; Faraday’s laws of electrolysis; Electrolytic conductance, specific, equivalent and molar conductivity, Kohlrausch’s law; Concentration cells.
- Chemical kinetics:Rates of chemical reactions; Order of reactions; Rate constant; First order reactions; Temperature dependence of rate constant (Arrhenius equation).
- Solid state:Classification of solids, crystalline state, seven crystal systems (cell parameters a, b, c, α, β, γ), close packed structure of solids (cubic), packing in fcc, bcc and hcp lattices; Nearest neighbours, ionic radii, simple ionic compounds, point defects.
- Solutions:Raoult’s law; Molecular weight determination from lowering of vapour pressure, elevation of boiling point and depression of freezing point.
- Surface chemistry:Elementary concepts of adsorption (excluding adsorption isotherms); Colloids: types, methods of preparation and general properties; Elementary ideas of emulsions, surfactants and micelles (only definitions and examples).
- Nuclear chemistry:Radioactivity: isotopes and isobars; Properties of α, β and γ rays; Kinetics of radioactive decay (decay series excluded), carbon dating; Stability of nuclei with respect to proton-neutron ratio; Brief discussion on fission and fusion reactions.
- Preparation and properties of compounds:Oxides, peroxides, hydroxides, carbonates, bicarbonates, chlorides and sulphates of sodium, potassium, magnesium and calcium; Boron: diborane, boric acid and borax; Aluminium: alumina, aluminium chloride and alums; Carbon: oxides and oxyacid (carbonic acid); Silicon: silicones, silicates and silicon carbide; Nitrogen: oxides, oxyacids and ammonia; Phosphorus: oxides, oxyacids (phosphorus acid, phosphoric acid) and phosphine; Oxygen: ozone and hydrogen peroxide; Sulphur: hydrogen sulphide, oxides, sulphurous acid, sulphuric acid and sodium thiosulphate; Halogens: hydrohalic acids, oxides and oxyacids of chlorine, bleaching powder; Xenon fluorides.
- Transition elements:Definition, general characteristics, oxidation states and their stabilities, colour (excluding the details of electronic transitions) and calculation of spin-only magnetic moment; Coordination compounds: nomenclature of mononuclear coordination compounds, cis–transand ionisation isomerisms, hybridization and geometries of mononuclear coordination compounds (linear, tetrahedral, square planar and octahedral).
- Ores and minerals:Commonly occurring ores and minerals of iron, copper, tin, lead, magnesium, aluminium, zinc and silver.
- Extractive metallurgy:Chemical principles and reactions only (industrial details excluded); Carbon reduction method (iron and tin); Self reduction method (copper and lead); Electrolytic reduction method (magnesium and aluminium); Cyanide process (silver and gold).
- Principles of qualitative analysis:Groups I to V (only Ag+, Hg2+, Cu2+, Pb2+, Bi3+, Fe3+, Cr3+, Al3+, Ca2+, Ba2+, Zn2+, Mn2+ and Mg2+); Nitrate, halides (excluding fluoride), sulphate and sulphide.
- Concepts:Hybridisation of carbon; σ and π-bonds; Shapes of simple organic molecules; Structural and geometrical isomerism; Optical isomerism of compounds containing up to two asymmetric centres, (R,S and E,Z nomenclature excluded); IUPAC nomenclature of simple organic compounds (only hydrocarbons, mono-functional and bi-functional compounds); Conformations of ethane and butane (Newman projections); Resonance and hyperconjugation; Keto-enoltautomerism; Determination of empirical and molecular formulae of simple compounds (only combustion method); Hydrogen bonds: definition and their effects on physical properties of alcohols and carboxylic acids; Inductive and resonance effects on acidity and basicity of organic acids and bases; Polarity and inductive effects in alkyl halides; Reactive intermediates produced during homolytic and heterolytic bond cleavage; Formation, structure and stability of carbocations, carbanions and free radicals.
- Preparation, properties and reaction of alkanes:Homologous series, physical properties of alkanes (melting points, boiling points and density); Combustion and halogenation of alkanes; Preparation of alkanes by Wurtz reaction and decarboxylation reactions.
- Preparation, properties and reaction of alkenes and alkynes:Physical properties of alkenes and alkynes (boiling points, density and dipole moments); Acidity of alkynes; Acid catalysed hydration of alkenes and alkynes (excluding the stereochemistry of addition and elimination); Reactions of alkenes with KMnO4 and ozone; Reduction of alkenes and alkynes; Preparation of alkenes and alkynes by elimination reactions; Electrophilic addition reactions of alkenes with X2, HX, HOX and H2O (X=halogen); Addition reactions of alkynes; Metal acetylides.
- Reaction of Benzene:Structure and aromaticity; Electrophilic substitution reactions: halogenation, nitration, sulphonation, Friedel-Crafts alkylation and acylation; Effect of o-, m- and p-directing groups in monosubstituted benzenes.
- Phenols:Acidity, electrophilic substitution reactions (halogenation, nitration and sulphonation); Reimer-Tieman reaction, Kolbe reaction.
- Characteristic reactions of the following (including those mentioned above):Alkyl halides: rearrangement reactions of alkyl carbocation, Grignard reactions, nucleophilic substitution reactions; Alcohols: esterification, dehydration and oxidation, reaction with sodium, phosphorus halides, ZnCl2/concentrated HCl, conversion of alcohols into aldehydes and ketones; Ethers: Preparation by Williamson’s Synthesis; Aldehydes and Ketones: oxidation, reduction, oxime and hydrazone formation; aldol condensation, Perkin reaction; Cannizzaro reaction; haloform reaction and nucleophilic addition reactions (Grignard addition); Carboxylic acids: formation of esters, acid chlorides and amides, ester hydrolysis; Amines: basicity of substituted anilines and aliphatic amines, preparation from nitro compounds, reaction with nitrous acid, azo coupling reaction of diazonium salts of aromatic amines, Sandmeyer and related reactions of diazonium salts; carbylamine reaction; Haloarenes: nucleophilic aromatic substitution in haloarenes and substituted haloarenes (excluding Benzyne mechanism and Cine substitution).
- Carbohydrates:Classification; mono- and di-saccharides (glucose and sucrose); Oxidation, reduction, glycoside formation and hydrolysis of sucrose.
- Amino acids and peptides:General structure (only primary structure for peptides) and physical properties.
- Properties and uses of polymers:Natural rubber, cellulose, nylon, teflon and PVC.
- Practical organic chemistry:Detection of elements (N, S, halogens); Detection and identification of the following functional groups: hydroxyl (alcoholic and phenolic), carbonyl (aldehyde and ketone), carboxyl, amino and nitro; Chemical methods of separation of mono-functional organic compounds from binary mixtures.
MATHEMATICS SYLLABUS FOR JEE ADVANCED –
- 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, Bayes Theorem, 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, incentre and circumcentre 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, 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, 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, separation of variables method, linear first order differential equations.
- Vectors: Addition of vectors, scalar multiplication, dot and cross products, scalar triple products and their geometrical interpretations.