Algebra: Complex number as an ordered pair of real numbers; real and imaginary parts, absolute value, the graphical representation of complex numbers, triangle inequality, complex conjugate co-ordinates, roots of a complex number. Theory of quadratic equations and expressions; the relation between roots and coefficients. Arithmetic, geometric and harmonic progressions. Permutations and combinations. Elementary applications of mathematical induction. Binomial theorem. Determinants of order two and three and their elementary properties.
Trigonometry: De Moivre's theorem and its applications; hyperbolic and inverse hyperbolic functions,
separation of real and imaginary parts of a complex quantity.
Vector Algebra: Addition of vectors, multiplication by a scalar; scalar product, cross product and scalar triple product
with geometrical applications.
Probability: Probability; sum and product laws; conditional probability.
Calculus: Functions; into, onto and one-one function, polynomial, rational, trigonometric, logarithmic and
exponential functions.The notion of limit and continuity of a function, a derivative of a function at a point; derivatives of the sum, difference,
product and quotient of functions, derivatives of composite functions, implicit functions and inverse
trigonometrical, logarithmic and exponential functions. Logarithmic differentiation. Geometrical interpretation
of derivative; successive differentiation, tangents, and normals. Sign of the derivative and monotonicity.
Maximum and minimum values of a function.Integration as the inverse process of differentiation; integration by parts and by substitutions; definite integral and its application for the determination of areas (simple cases), properties of definite integrals.
Introduction and Measurement: Dimensions of a physical quantity, uses of dimensional analysis, Errors in measurement.
Dynamics of a Particle: Newton's laws, motion in one, two and three dimensions, relative motion, inertial
frames, circular motion, spring force, gravitational force, the law of gravitation, variation of gravity with altitude, escape velocity, satellite motion, work, kinetic and potential energies, conservation of energy, momentum, and angular momentum, elastic collisions in one and two dimensions.
Dynamics of a System of Particles: Centre of mass, motion under external forces, rigid bodies, rotation of a
rigid body about a fixed axis, torque, angular acceleration, angular momentum, a moment of inertia, the radius of gyration, kinetic energy of rotation, combined translational and rotational motions, parallel and perpendicular axes theorems, a moment of inertia of a ring, disc, cylinder, and sphere.
Simple Harmonic Motion: Basic equation, displacement, velocity and acceleration, graphical and mathematical representation, kinetic and potential energies, Lissajous figures, simple pendulum, compound pendulum as a rigid oscillating body. Mass-spring system, damped harmonic oscillations, forced oscillations and resonance.
Intermolecular Forces: Attractive and repulsive forces, three states of matter, ionic, covalent, Van der Waals and metallic bondings, surface tension, the angle of contact, capillarity, the pressure difference across a spherical film, determination of surface tension by capillary rise and Jaeger's methods, elasticity, Hooke's law, Young's modulus, shear and bulk moduli.
Kinetic Theory of Gases: Basic postulates, derivation of an expression for pressure exerted by an ideal gas, interpretation of temperature, equipartition of energy, specific heats of monoatomic and diatomic gases.
First Law of Thermodynamics: Dependence of work and heat on the path, internal energy, isothermal, isobaric, isochoric and adiabatic processes, specific heats of an ideal gas, Mayer's relation.
Radiation: Black-body, Kirchhoff's law, Stefan's law, Newton's law of cooling, black-body spectrum, Wien's law.
Wave Motion: Progressive waves, superposition principle, beats, stationary waves, the vibration of strings, air columns, resonance, Doppler's principle and its applications to sound and light waves.
Nature of Light: Light as wave motion, plane and spherical waves, Huygen's principle, reflection and refraction at a plane surface, electromagnetic nature of light waves, quantum nature of light, coherent sources; Fresnel's biprism, measurement of wavelength, Fresnel's half -period zones, rectilinear propagation of light, diffraction at a circular obstacle, aperture and a slit for plane waves.
Electrostatics: Conservation and quantization of charge, Coulomb's law, electric field, superposition principle, electric flux, Gauss's law and its applications in simple cases, electric potential and potential difference, electric field and potential due to a dipole, capacitance, capacitors in series and parallel, the energy stored in a capacitor.
Electric Circuits: Kirchhoff's laws, Wheat-stone bridge and its applications, potentiometer and its applications.
Magnetic Field: Biot-Savart and Ampere's laws, magnetic field along the axis of a current carrying circular coil, inside a toroid , due to a straight wire, magnetic moment of a current loop, force on a moving charge and on a current carrying wire in a magnetic field, moving coil galvanometer, voltmeter, ammeter, electromagnetic induction, Faraday's and Lenz's laws, self and mutual inductances, transformer, the energy stored in an inductor.
Alternating Current Circuits: Rotating coil in a magnetic field, ac, arms and peak values, phase relations between voltage and current in a resistor, inductor, capacitor and their series combinations, impedance and reactance (definitions only), instantaneous and average power in ac circuits, power factor, wattless current and choke coil.
Modern Physics: Photons, photoelectric effect, Bohr's theory of hydrogen-like atoms, X- says production and properties, de Broglie hypothesis, Davisson, and Germer experiment, Thomson's experiment, explanation of Bohr's orbits, uncertainty principle. radioactivity, nature of alpha, beta and gamma rays, laws of disintegration, half and mean lives, atomic nucleus, binding energy, nuclear energy by fission and fusion.
Electronics: Thermionic emission, work function, diode rectification and triode amplification, bands in solids (descriptive ideas only), conductors, semiconductors and insulators, intrinsic and extrinsic semiconductors, pn junction and its rectification properties.
Development of Classical Model of an Atom: Bohr model of an atom, calculation of the radius of the Bohr's orbit, quantisation of electronic energy levels, Spectral evidence for quantisation, the introductory concept of four quantum numbers, Pauli's exclusion principle, Hund's rule, Aufbau principle, the concept of the spatial distributions of s and p orbitals. Isotopes.
The Periodic Law: a Long form of the Periodic Table. Electronic configuration and the Periodic Table. Periodicity in properties, elementary ideas about ionization potential, electron affinity, electronegativity and atomic radii. The position of hydrogen.
The Theory of Chemical Bonding: The ionic bond, characteristic properties of ionic compounds. The covalent bond. The introductory concept of overlapping of orbitals, σ, and π bonds, Co-ordinate bond. Oxidation number. Characteristic properties of covalent compounds, hybridization as illustrated by common molecules like NH3, H2O, CH4, C2H4, and C2H2.
Chemical Equilibrium and Ionic Equilibria: Generalised expression of the law of mass action and its applications. Arrhenius theory, evidence in favour of dissociation theory, ionic product of water, hydrolysis, the relation between hydrolysis constant, ionic product of water and dissociation constant, solubility product and its applications to analytical chemistry.
Chemical Kinetics: Order and Molecularity of reaction. Photochemical reactions. The expression of first and second order reactions.
Acids and Bases: Hydrogen and hydroxyl ions in aqueous solution, Lewis concept of acids, dissociation of acids, pH value, Buffer solution, Theory of indicators for acid-alkali titrations, choice of indicators for
acid-alkali titrations.Oxidation-reduction, ion electron concept. Solid and liquid state of matter, Crystalline and
amorphous solids, Four types of crystalline solids, crystal lattice and unit cell. Types of solutions, properties of solutions, osmosis and osmotic pressure, preparation and properties of colloidal solutions.
Metals: Nature of metallic state. The metallic bond. The occurrence of metals in nature. The general principle of metallurgy as illustrated by methods used for the extraction of iron, copper, aluminium, and silver from various types of ores. Preparation and properties of heavy water, ozone, and hydrogen peroxide.
s-Block Elements: General characteristics, Trends in a variation of properties in the periodic table of alkali and alkaline earth metals.
d-Block Elements: General characteristics, the Elementary idea about paramagnetism and diamagnetism, different oxidation states of transition elements as illustrated by chromium, manganese, and iron. Classification of organic compounds, nomenclature, Homologous series. Functional groups; Isomerism (position, chain, functional, metamerism). Petroleum as the commercial source of hydrocarbon and organic chemicals, petroleum refining practice, octane number.
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What is the Physics syllabus for the REAP exam?
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What is the mathematics syllabus for the REAP exam?
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