Filter
JEE-Main
- Force and Inertia, Newton's First Law of motion; Momentum, Newton's Second Law of motion; Impulse; Newton's Third Law of motion.
- Law of conservation of linear momentum and its applications, Equilibrium of concurrent forces
- Static and Kinetic friction, laws of friction, rolling friction
- Dynamics of uniform circular motion: Centripetal force and its applications
- Centre of mass of a two-particle system, Centre of mass of a rigid body; Basic concepts of rotational motion;
- moment of a force, torque, angular momentum, conservation of angular momentum and its applications; moment of inertia, radius of gyration
- Values of moments of inertia for simple geometrical objects, parallel and perpendicular axes theorems and their applications
- Rigid body rotation, equations of rotational motion
- Equation of state of a perfect gas, work doneon compressing a gas
- Kinetic theory of gases - assumptions, concept of pressure
- Kinetic energy and temperature: rms speed of gas molecules; Degrees of freedom, Law of equipartition of energy
- applications to specific heat capacities of gases, Avogadro's number
- Periodic motion - period, frequency, displacement as a function of time. Periodic functions.
- Simple harmonic motion (S.H.M.) and its equation; phase
- oscillations of a spring -restoring force and force constant; energy in S.H.M. - kinetic and potential energies
- Simple pendulum - derivation of expression for its time period; Free, forced and damped oscillations, resonance
- Wave motion. Longitudinal and transverse waves, speed of a wave
- Displacement relation for a progressive wave.
- Principle of superposition of waves, reflection of waves, Standing waves in strings and organ pipes, fundamental mode and harmonics, Beats, Doppler effect in sound
- Electric charges: Conservation of charge, Coulomb's law-forces between two point charges, forces between multiple charges
- superposition principle and continuous charge distribution
- Electric field: Electric field due to a point charge, Electric field lines, Electric dipole, Electric field due to a dipole, Torque on a dipole in a uniform electric field.
- Electric flux, Gauss's law and its applications to find field due to infinitely long uniformly charged straight wire
- uniformly charged infinite plane sheet and uniformly charged thin spherical shell
- Electric potential and its calculation for a point charge, electric dipole and system of charges
- Equipotential surfaces, Electrical potential energy of a system of two point charges in an electrostatic field
- Conductors and insulators, Dielectrics and electric polarization, capacitor, combination of capacitors in series and in parallel
- capacitance of a parallel plate capacitor with and without dielectric medium between the plates, Energy stored in a capacitor
- Electric current, Drift velocity, Ohm's law, Electrical resistance
- V-I characteristics of Ohmic and nonohmic conductors, Electrical energy and power
- Electrical resistivity, Colour code for resistors; Series and parallel combinations of resistors; Temperature dependence of resistance
- Electric Cell and its Internal resistance, potential difference and emf of a cell, combination of cells in series and in parallel.
- Kirchhoff's laws and their applications. Wheatstone bridge, Metre bridge.
- Biot - Savart law and its application to current carrying circular loop.
- Ampere's law and its applications to infinitely long current carrying straight wire and solenoid
- Force on a moving charge in uniform magnetic and electric fields. Cyclotron
- Force on a current-carrying conductor in a uniform magnetic field.
- Force between two parallel currentcarrying conductors-definition of ampere
- Torque experienced by a current loop in uniform magnetic field; Moving coil galvanometer, its current sensitivity and conversion to ammeter and voltmeter
- Current loop as a magnetic dipole and its magnetic dipole moment.
- Bar magnet as an equivalent solenoid, magnetic field lines; Earth's magnetic field and magnetic elements
- Para-, dia- and ferro- magnetic substances
- Magnetic susceptibility and permeability, Hysteresis, Electromagnets and permanent magnets
- Electromagnetic induction; Faraday's law, induced emf and current; Lenz's Law, Eddy currents.
- Self and mutual inductance. Alternating currents, peak and rms value of alternating current/ voltage
- reactance and impedance; LCR series circuit, resonance; Quality factor, power in AC circuits, wattless current. AC generator and transformer
- Reflection and refraction of light at plane and spherical surfaces, mirror formula, Total internal reflection and its applications,
- Deviation and Dispersion of light by a prism, Lens Formula, Magnification, Power of a Lens
- Combination of thin lenses in contact, Microscope and Astronomical Telescope (reflecting and refracting) and their magnifyingpowers
- Wave optics: wavefront and Huygens principle
- Interference, Young's double slit experiment and expression for fringe width, coherent sources and sustained interference of light
- Diffraction due to a single slit, width of central maximum
- Resolving power of microscopes and astronomical telescopes, Polarisation, plane polarized light; Brewster's law
- Alpha-particle scattering experiment; Rutherford's model of atom; Bohr model, energy levels.
- Composition and size of nucleus, atomic masses, isotopes, isobars; isotones
- Radioactivityalpha, beta and gamma particles/rays and their properties; radioactive decay law
- Mass-energy relation, mass defect; binding energy per nucleon and its variation with mass number, nuclear fission and fusion
- Semiconductors; semiconductor diode: I-V characteristics in forward and reverse bias; diode as a rectifier; I-V characteristics of LED, photodiode, solar cell and Zener diode
- Zener diode as a voltage regulator. Junction transistor, transistor action, characteristics of a transistor
- Transistor as an amplifier (common emitter configuration) and oscillator. Logic gates (OR, AND, NOT, NAND and NOR). Transistor as a switch
- Vernier callipers-its use to measure internal and external diameter and depth of a vessel.
- Screw gauge-its use to determine thickness/ diameter of thin sheet/wire.
- Simple Pendulum-dissipation of energy by plotting a graph between square of amplitude and time.
- Metre Scale - mass of a given object by principle of moments.
- Young's modulus of elasticity of the material of a metallic wire
- Surface tension of water by capillary rise and effect of detergents
- Co-efficient of Viscosity of a given viscous liquid by measuring terminal velocity of a given spherical body
- Plotting a cooling curve for the relationship between the temperature of a hot body and time
- Speed of sound in air at room temperature using a resonance tube
- Resistivity of the material of a given wire using metre bridge.
- Resistance of a given wire using Ohm's law
- Matter and its nature,
- Dalton’s atomic theory; Concept of atom
- molecule, element and compound; Physical quantities and their measurements in Chemistry
- precision and accuracy, significant figures, S.I. Units, dimensional analysis
- Laws of chemical combination
- Atomic and molecular masses, mole concept, molar mass
- percentage composition, empirical and molecular formulae
- Chemical equations and stoichiometry
- Discovery of sub-atomic particles (electron, proton and neutron); Thomson and Rutherford atomic models and their limitations; Nature of electromagnetic radiation, photoelectric effect;
- Spectrum of hydrogen atom, Bohr model of hydrogen atom - its postulates, derivation of the relations for energy of the electron and radii of the different orbits, limitations of Bohr’s model
- Dual nature of matter, de-Broglie’s relationship, Heisenberg uncertainty principle
- Elementary ideas of quantum mechanics, quantum mechanical model of atom, its important features, ?? and ??2, concept of atomic orbitals as one electron wave functions; Variation of ?? and ??2 with r for 1s and 2s orbitals
- various quantum numbers (principal, angular momentum and magnetic quantum numbers) and their significance
- shapes of s, p and d - orbitals, electron spin and spin quantum number; Rules for filling electrons in orbitals aufbau principle
- Pauli’s exclusion principle and Hund’s rule, electronic configuration of elements, extra stability of half-filled and completely filled orbitals
- Different methods for expressing concentration of solution - molality, molarity, mole fraction, percentage (by volume and mass both)
- vapour pressure of solutions and Raoult’s Law Ideal and non-ideal solutions, vapour pressure - composition, plots for ideal and non-ideal solutions
- Colligative properties of dilute solutions - relative lowering of vapour pressure, depression of freezing point, elevation of boiling point and osmotic pressure
- Determination of molecular mass using colligative properties; Abnormal value of molar mass, van’t Hoff factor and its significance
- Electronic concepts of oxidation and reduction, redox reactions, oxidation number, rules for assigning oxidation number, balancing of redox reactions
- Electrolytic and metallic conduction, conductance in electrolytic solutions, specific and molar conductivities and their variation with concentration: Kohlrausch’s law and its applications.
- Electrochemical cells - Electrolytic and Galvanic cells, different types of electrodes, electrode potentials including standard electrode potential, half - cell and cell reactions, emf of a Galvanic cell and its measurement
- Nernst equation and its applications; Relationship between cell potential and Gibbs’ energy change; Dry cell and lead accumulator; Fuel cells; Corrosion and its prevention
- Rate of a chemical reaction, factors affecting the rate of reactions: concentration, temperature, pressure and catalyst
- elementary and complex reactions, order and molecularity of reactions, rate law, rate constant and its units, differential and integral forms of zero and first order reactions
- Characteristics of first order reactions and half - lives, effect of temperature on rate of reactions Arrhenius theory
- activation energy and its calculation, collision theory of bimolecular gaseous reactions (no derivation)
- Modes of occurrence of elements in nature, minerals, ores; Steps involved in the extraction of metals - concentration,
- reduction (chemical and electrolytic methods) and refining with special reference to the extraction of Al, Cu, Zn and Fe
- Thermodynamic and electrochemical principles involved in the extraction of metals
- Position of hydrogen in periodic table, isotopes, preparation, properties and uses of hydrogen; Physical and chemical properties of water and heavy water;
- Structure, preparation, reactions and uses of hydrogen peroxide; Classification of hydrides - ionic, covalent and interstitial; Hydrogen as a fuel
- General introduction, electronic configuration and general trends in physical and chemical properties of elements, anomalous properties of the first element of each group, diagonal relationships.
- Preparation and properties of some important compounds - sodium carbonate, sodium chloride, sodium hydroxide and sodium hydrogen carbonate; Industrial uses of lime, limestone, Plaster of Paris and cement; Biological significance of Na, K, Mg and Ca
- General Introduction:
- Preparation, properties and uses of boron and aluminium; Structure, properties and uses of borax, boric acid, diborane, boron trifluoride, aluminium chloride and alums.
- Tendency for catenation; Structure, properties and uses of allotropes and oxides of carbon, silicon tetrachloride, silicates, zeolites and silicones.
- Properties and uses of nitrogen and phosphorus; Allotrophic forms of phosphorus; Preparation, properties, structure and uses of ammonia, nitric acid, phosphine and phosphorus halides, (PCl3, PCl5); Structures of oxides and oxoacids of nitrogen and phospho
- Preparation, properties, structures and uses of dioxygen and ozone; Allotropic forms of sulphur; Preparation, properties, structures and uses of sulphur dioxide, sulphuric acid (including its industrial preparation); Structures of oxoacids of sulphur
- Preparation, properties and uses of chlorine and hydrochloric acid; Trends in the acidic nature of hydrogen halides; Structures of Interhalogen compounds and oxides and oxoacids of halogens
- Occurrence and uses of noble gases; Structures of fluorides and oxides of xenon
- Introduction to co-ordination compounds, Werner’s theory; ligands, co-ordination number, denticity, chelation;
- IUPAC nomenclature of mononuclear coordination compounds, isomerism; Bonding-Valence bond approach and basic ideas of Crystal field theory, colour and magnetic properties
- Importance of coordination compounds (in qualitative analysis, extraction of metals and in biological systems).
- Tetravalency of carbon; Shapes of simple molecules - hybridization (s and p); Classification of organic compounds based on functional groups: - C = C - , - C h C – and those containing halogens, oxygen, nitrogen and sulphur
- Homologous series; Isomerism - structural and stereoisomerism.
- Nomenclature (Trivial and IUPAC)
- Electronic displacement in a covalent bond
- Common types of organic reactions
- Detection of extra elements (N,S, halogens) in organic compounds; Detection of the following functional groups: hydroxyl (alcoholic and phenolic), carbonyl (aldehyde and ketone), carboxyl and amino groups in organic compounds
- Inorganic compounds, and Organic compounds
- Chemistry involved in the titrimetric excercises - Acids bases and the use of indicators
- Chemical principles involved in the qualitative salt analysis
- Chemical principles
- Complex numbers as ordered pairs of reals, Representation of complex numbers in the form a+ib and their representation in a plane
- Argand diagram, algebra of complex numbers, modulus and argument (or amplitude) of a complex number, square root of a complex number, triangle inequality, Quadratic equations in real and complex number system and their solutions
- Relation between roots and co-efficients, nature of roots, formation of quadratic equations with given roots
- Matrices, algebra of matrices, types of matrices, determinants and matrices of order two and three.
- Properties of determinants, evaluation of determinants, area of triangles using determinants.
- Adjoint and evaluation of inverse of a square matrix using determinants and elementary transformations
- Test of consistency and solution of simultaneous linear equations in two or three variables using determinants and matrices.
- Real - valued functions, algebra of functions, polynomials, rational, trigonometric, logarithmic and exponential functions, inverse functions.
- Graphs of simple functions. Limits, continuity and differentiability.
- Differentiation of the sum, difference, product and quotient of two functions.
- Differentiation of trigonometric, inverse trigonometric, logarithmic, exponential, composite and implicit functions; derivatives of order upto two.
- Rolle’s and Lagrange’s Mean Value Theorems.
- Applications of derivatives: Rate of change of quantities, monotonic - increasing and decreasing functions, Maxima and minima of functions of one variable, tangents and normals.
- Fundamental integrals involving algebraic, trigonometric, exponential and logarithmic functions. Integration by substitution, by parts and by partial fractions.
- Integration using trigonometric identities.
- Integral as limit of a sum. Fundamental Theorem of Calculus.
- Properties of definite integrals.
- Evaluation of definite integrals, determining areas of the regions bounded by simple curves in standard form.
- Coordinates of a point in space, distance between two points, section formula, direction ratios and direction cosines,
- angle between two intersecting lines. Skew lines, the shortest distance between them and its equation
- Equations of a line and a plane in different forms, intersection of a line and a plane, coplanar lines
- Measures of Dispersion: Calculation of mean, median, mode of grouped and ungrouped data.
- Calculation of standard deviation, variance and mean deviation for grouped and ungrouped data
- Probability: Probability of an event, addition and multiplication theorems of probability, Baye’s theorem, probability distribution of a random variate, Bernoulli trials and Binomial distribution.
Understanding of tautology, contradiction, converse and contrapositive. Doubts and Replies
- JEE-Main
- >
- Maths
- > Mathematical Reasoning
- > Understanding of tautology, contradiction, converse and contrapositive.
No Doubts in Understanding of tautology, contradiction, converse and contrapositive.
Ask Your Doubt in Understanding of tautology, contradiction, converse and contrapositive.
Recently ask Most Popular Doubt in Chapter "Mathematical Reasoning"
0
Votes
0
Answers
what are concepts are there in the mathematical reasoning?
Aditi Sawant
- about 11 years ago
- JEE-Main
- >
- Maths
- > Mathematical Reasoning
- > Understanding of tautology, contradiction, converse and contrapositive.
