UNIT 1: UNITS AND MEASUREMENT

Units for measurement, system of units S.I., fundamental and derived units. Dimensions and their applications.

UNIT 2: DESCRIPTION OF MOTION IN ONE DIMENSION

Motion in a straight line, uniform and non-uniform motion, their graphical representation. Uniformly accelerated motion, and its applications

UNIT 3: DESCRIPTION OF MOTION IN TWO AND THREE DIMENSIONS

Scalars and vectors, vector addition, a real number, zero vector and its properties. Resolution of vectors. Scalar and vector products, uniform circular motion and its applications projectile motion.

UNIT 4: LAWS OF MOTION

Force and inertia Newton s Laws of Motion. Conservation of linear momentum and its applications, rocket propulsion, friction laws of friction

UNIT 5 WORK, ENERGY AND POWER

Concept of work, energy and power. Energy kinetic and potential. Conservation of energy and its applications, Elastic collisions in one and two dimensions. Different forms of energy.

UNIT 6: ROTATIONAL MOTION AND MOMENT OF INERTIA

Centre of mass of a two-particle system. Centre of mass of a rigid body, general motion of a rigid body, nature of rotational motion, torque, angular momentum, its conservation and applications. Moment of Inertia, parallel and perpendicular axes theorem, expression of moment of inertia for ring, disc and sphere.

UNIT 7: GRAVITATION

Acceleration due to gravity, one and two-dimensional motion under gravity. Universal law of gravitation, variation in the acceleration due to gravity of the earth. Planetary motion, Keplers laws, artificial satellite geostationary satellite, gravitational potential energy near the surface of earth, gravitational potential and escape velocity

UNIT 8: SOLIDS AND FLUIDS

Inter-atomic and Inter-molecular forces, states of matter.

(A) Solids : Elastic properties, Hooks law, Youngs modulus, bulk modulus, modulus of rigidity.

(B) Liquids : Cohesion and adhesion. Surface energy and surface tension. Flow of fluids, Bernoullis theorem and its applications. Viscosity, Stokes Law, terminal velocity.

UNIT 9: OSCILLATIONS

Periodic motion, simple harmonic motion and its equation of motion, energy in S.H.M., Oscillations of a spring and simple pendulum.

UNIT 10: WAVES

speed of a wave, longitudinal and transverse waves, superposition of waves, progressive and standing waves, free and forced Oscillations, resonance, vibration of strings and air-columns, beats, Doppler effect.

UNIT 11: HEAT AND THERMODYNAMICS

Thermal expansion of solids, liquids and gases and their specific heats, Relationship between Cp and Cv for gases, first law of thermodynamics, thermodynamic processes. Second law of thermodynamics, Carnot cycle, efficiency of heat engines.

UNIT 12: TRANSFERENCE OF HEAT

Modes of transference of heat. Thermal conductivity. Black body radiations, Kirchoffs Law, Wiens law, Stefans law of radiation and Newtons law of cooling.

UNIT 13: ELECTROSTATICS

Electric charge its unit and conservation, Coulombs law, dielectric constant, electric field, lines of force, field due to dipole and its behaviour in a uniform electric field, electric flux, Gausss theorem and its applications. Electric potential, potential due to a point charge. Conductors and insulators, distribution of charge on conductors. Capacitance, parallel plate capacitor, combination of capacitors, energy of capacitor.

UNIT 14: CURRENT ELECTRICITY

Electric current and its unit, sources of energy, cells- primary and secondary, grouping of cells resistance of different materials, temperature dependence, specific resistivity, Ohms law, Kirchoffs law, series and parallel circuits. Wheatstone Bridge with their applications and potentiometer with their applications.

UNIT 15: THERMAL AND CHEMICAL EFFECTS OF CURRENTS

Heating effects of current, electric power, simple concept of thermo-electricity Seeback effect and thermocouple, Chemical effect of current Faradays laws of electrolysis.

UNIT 16: MAGNETIC EFFECTS OF CURRENTS

Oersteds experiment, Bio-Saverts law, magnetic field due to straight wire, circular loop and solenoid, force on a moving charge in a uniform magnetic field (Lorentz force), forces and torques on currents in a magnetic field, force between two current carrying wires, moving coil galvanometer and conversion to ammeter and voltmeter.

UNIT 17: MAGNETOSTATICS

Bar magnet, magnetic field, lines of force, torque on a bar magnet in a magnetic field, earths magnetic field, para, dia and ferro magnetism, magnetic induction, magnetic susceptibility.

UNIT 18: ELECTROMAGNETIC INDUCTION AND ALTERNATING CURRENTS

Induced e.m.f., Faradays Law, Lenzs Law, Self and Mutual Inductance, alternating currents, impedance and reactance, power In a.c. Circuits with L.C. And R Series Combination, resonant circuits. Transformer and A.C. generator.

UNIT 19: RAY OPTICS

Reflection and refraction of light at plane and curved surfaces, total internal reflection, optical fibre; deviation and dispersion of light by a prism; Lens formula, magnification and resolving power; microscope and telescope.

UNIT 20: WAVE OPTICS

Wave nature of light; Interference Youngs double slit experiment. Diffraction - diffraction due to a single slit. Elementary idea of polarization.

UNIT 21: ELECTROMAGNETIC WAVES

Electromagnetic waves and their characteristics, Electromagnetic wave spectrum from gamma to radio waves propagation of EM waves in atmosphere.

UNIT 22: ELECTRON AND PHOTONS

Charge on an electron, e/m for an electron, photoelectric effect and Einsteins equation of photoelectric effect.

UNIT 23: ATOMS, MOLECULES AND NUCLEI

Alpha - particles scattering experiment, Atomic masses, size of the nucleus; radioactivity; Alpha, beta and gamma particles/ rays and their properties, radioactive decay law, half life and mean life of radio-active nuclei, binding energy, mass energy relationship, nuclear fission and nuclear fusion.

UNIT 24: SOLIDS AND SEMI-CONDUCTORS DEVICES

Energy bands in solids, conductors, insulators and semi-conductors, pn junction, diodes, diode as rectifier, transistor action, transistor as an amplifier.

UNIT 1: Sets, Relations and Functions

Sets and their Representations, Union, intersection and complements of sets, and their algebraic properties, Relations, equivalence relations, mappings, one-one, into and onto mappings, composition of mappings.

UNIT 2: Complex Numbers

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. Cube roots of unity, triangle inequality.

UNIT 3: Matrices and Determinants

Determinants and matrices of order two and three, properties of determinants, Evaluation of determinants. Area of triangles using determinants, Addition and multiplication of matrices, adjoint and inverse of matrix. Test of consistency and solution of simultaneous linear equations using determinants and matrices

UNIT 4: Quadratic Equations

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; Symmetric functions of roots, equations reducible to quadratic equations application to practical problems

UNIT 5: Permutations and Combinations

Fundamental principle of counting; Permutation as an arrangement and combination as selection, Meaning of P(n,r) and C(n,r). Simple applications.

UNIT 6: Mathematical Induction and Its Applications

UNIT 7: Binomial Theorem and its Applications

Binomial Theorem for a positive integral index; general term and middle term; Binomial Theorem for any index. Properties of Binomial Co-efficients. Simple applications for approximations.

UNIT 8: Sequences and Series

Arithmetic, Geometric and Harmonic progressions. Insertion of Arithmetic Geometric and Harmonic means between two given numbers. Relation between A.M., G.M. and H.M.Special series: Σn, Σn2, Σn3 . Arithmetico-Geometric Series, Exponential and Logarithmic series.

UNIT 9: Differential Calculus

Polynomials, rational, trigonometric, logarithmic and exponential functions, Inverse functions. Graphs of simple functions. Limits, Continuity; 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. Applications of derivatives: Rate of change of quantities, monotonic - increasing and decreasing functions, Maxima and minima of functions of one variable, tangents and normals, Rolles and Lagranges Mean Value Theorems.

UNIT 10: Integral Calculus

Integral as an anti-derivative. 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. Properties of definite integrals. Evaluation of definite integrals; Determining areas of the regions bounded by simple curves.

UNIT 11: Differential Equations

Ordinary differential equations, their order and degree. Formation of differential equations. Solution of differential equations by the method of separation of variables. Solution of homogeneous and linear differential equations, and those of the type
d2y/dx2 = f(x)

UNIT 12: Two dimensional Geometry

Recall of Cartesian system of rectangular co-ordinates in a plane, distance formula, area of a triangle, condition for the collinearity of three points and section formula, centroid and in-centre of a triangle, locus and its equation, translation of axes, slope of a line, parallel and perpendicular lines, intercepts of a line on the coordinate axes.

The straight line and pair of straight lines

Various forms of equations of a line, intersection of lines, angles between two lines, conditions for concurrence of three lines, distance of a point from a line Equations of internal and external bisectors of angles between two lines, coordinates of centroid, orthocentre and circumcentre of a triangle, equation of family of lines passing through the point of intersection of two lines, homogeneous equation of second degree in x and y, angle between pair of lines through the origin, combined equation of the bisectors of the angles between a pair of lines, condition for the general second degree equation to represent a pair of lines, point of intersection and angle between two lines.

Circles and Family of Circles

Standard form of equation of a circle, general form of the equation of a circle, its radius and centre, equation of a circle in the parametric form, equation of a circle when the end points of a diameter are given, points of intersection of a line and a circle with the centre at the origin and condition for a line to be tangent to the circle, length of the tangent, equation of the tangent, equation of a family of circles through the intersection of two circles, condition for two intersecting circles to be orthogonal.

Conic Sections

Sections of cones, equations of conic sections (parabola, ellipse and hyperbola) in standard forms, condition for y = mx + c to be a tangent and point(s) of tangency.

UNIT 13: Three Dimensional Geometry

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, equation of a sphere, its centre and radius. Diameter form of the equation of a sphere.

UNIT 14: Vector Algebra

Vectors and Scalars, addition of vectors, components of a vector in two dimensions and three dimensional space, scalar and vector products, scalar and vector triple product. Application of vectors to plane geometry.

UNIT 15: Measures of Central Tendency and Dispersion

Calculation of Mean, median and mode of grouped and ungrouped data. Calculation of standard deviation, variance and mean deviation for grouped and ungrouped data.

UNIT 16: Probability

Probability of an event, addition and multiplication theorems of probability and their applications; Conditional probability; Bayes Theorem, Probability distribution of a random variate; Binomial and Poisson distributions and their properties.

UNIT 17: Trigonometry

Trigonometrical identities and equations. Inverse trigonometric functions and their properties. Properties of triangles, including centroid, incentre, circum- centre and orthocentre, solution of triangles. Heights and Distances

UNIT 18: Statics

Introduction, basic concepts and basic laws of mechanics, force, resultant of forces acting at a point, parallelogram law of forces, resolved parts of a force, Equilibrium of a particle under three concurrent forces, triangle law of forces and its converse, Lamis theorem and its converse, Two parallel forces, like and unlike parallel forces, couple and its moment.

UNIT 19: Dynamics

Speed and velocity, average speed, instantaneous speed, acceleration and retardation, resultant of two velocities. Motion of a particle along a line, moving with constant acceleration. Motion under gravity. Laws of motion, Projectile motion.