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- 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.
Maths Doubts and Replies
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if B is a symmetric matrix then AB* teanspose of A is a
Avinash
- about 10 years ago
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10
Answers
the set of all natural number x such that 4x+9<30 is equal to
Akhil
- over 10 years ago
