Units for measurement, system of units S.I., fundamental and derived units. Dimensions and their applications.
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
Description Of Motion In Two Dimensions
Scalars and vectors, Uniform circular motion and its applications, Projectile motion.
Laws Of Motion
Force and inertia- Newton's Laws of Motion. Conservation of linear momentum and its applications, rocket propulsion, friction laws of friction
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.
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.
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, Kepler's laws, artificial satellite geostationary satellite, gravitational potential energy near the surface of earth, gravitational potential and escape velocity.
Oscillations & Waves
Periodic motion, simple harmonic motion and its equation of motion, energy in S.H.M. Oscillations of a spring and simple pendulum. Wave motion, 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.
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. Modes of transference of heat. Thermal conductivity. Black body radiations, Kirchoff s Law, Wien's Law, Stefan's law of radiation and Newton's law of cooling.
Electric charge its unit and conservation. Coulomb's law, dielectric constant, electric field, lines of force, field due to dipole and its behaviour in a uniform electric field, electric flux, Gauss's 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.
Electric current and its unit, sources of energy, cells- primary and secondary, grouping of cells resistance of different materials, temperature dependence, specific resistivity Ohm's law, Kirchoff s law, series and parallel circuits. Wheatstone Bridge with their applications and potentiometer with their applications.
Magnetic Effects Of Currents
Oersted's experiment, Bio-Savert's 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.
Electromagnetic Induction And Alternating Currents
Induced e.m.f., Faraday's Law, Lenz's 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.
Reflection and refraction of light at plane and curved surfaces, total internal reflection, optical fibre; deviation and dispersion of light by a prsim; Lens formula, magnification and resolving power; microscope and telescope.
Wave nature of light; Interference Young's double slit experiment. Diffraction diffraction due to a single slit. Elementary idea of polarization.
Solids And Semi-Conductors Devices
Energy bands in a solids, conductors, insulators and semi-conductors, n junction, diodes, diode as rectifier, transistor action, transistor as an amplifier.
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 numbers. Cube roots of unity, triangle inequality.
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.
Quadratic equations in real and complex number system and their solutions. Relation between roots and coefficients, nature of roots, formation of quadratic equations with given roots; Symmetric functions of roots, equations reducible to quadratic equations-application to practical problems.
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.
Binomial Theorem And Its Applications
Binomial Theorem for a positive integral index; general term and middle term: Binomial Theorem foranyindex. Properties of Binomial coefficient. Simple applications for approximations.
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: ?n, ?n2, ?n3. Arithmetico - Geometric Series, Exponential and Logarithmic series.
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 offunctions of one variable, tangents and normals, Rolle's and Lagrange's Mean Value Theorems.
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.
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 d^y dx3=f(x)
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, paralleland perpendicular lines, intercepts of a line of 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 intemaland 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 tines, 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 forthe 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, generalform 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 0' .he 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
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.
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 tine 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.
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.
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.
Trigonometrical identities and equations, Inverse trigonometric functions and their properties. Properties of triangles, including centroid, incentre circum-centre and ortho-centre, solution of triangles. Heights and Distances.
Iterative methods of solving equations: False position, Newton Raphson, Numerical Integration Rule: Trapizoidal and Simpsons Rule.