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All
India Engineering/Architecture Entrance Examination 2009 |
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APPENDIX
– III
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Syllabus
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MATHEMATICS
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UNIT
1:
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SETS, RELATIONS AND
FUNCTIONS: |
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Sets
and their representation; Union, intersection and complement of sets and
their algebraic properties; Power set; Relation, Types of relations,
equivalence relations, functions;. one-one, into and onto functions,
composition of functions.
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UNIT
2:
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COMPLEX NUMBERS AND QUADRATIC EQUATIONS:
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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.
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UNIT
3:
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MATRICES AND
DETERMINANTS: |
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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.
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UNIT
4:
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PERMUTATIONS AND
COMBINATIONS: |
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Fundamental principle of counting, permutation as an
arrangement and combination as selection, Meaning of P (n,r) and C (n,r),
simple applications.
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UNIT
5:
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MATHEMATICAL INDUCTION: |
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Principle of Mathematical Induction and its simple applications. |
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UNIT
6:
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BINOMIAL THEOREM AND ITS SIMPLE APPLICATIONS: |
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Binomial theorem for a positive integral index, general term and middle
term, properties of Binomial coefficients and simple applications.
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UNIT
7:
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SEQUENCES AND SERIES: |
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Arithmetic and Geometric progressions, insertion of
arithmetic, geometric means between two given numbers. Relation between
A.M. and G.M. Sum upto n terms of special series: Sn, Sn2, Sn3.
Arithmetico - Geometric progression. |
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UNIT
8:
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LIMIT, CONTINUITY AND
DIFFERENTIABILITY: |
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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. |
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UNIT 9:
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INTEGRAL CALCULUS: |
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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.
Evaluation of simple integrals of the type
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.
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UNIT
10:
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Differential Equations: |
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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 of the type:
dy
-- + p (x) y = q (x)
dx |
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UNIT
11:
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CO-ORDINATE GEOMETRY: |
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Cartesian system of
rectangular co-ordinates in a plane, distance formula, section formula,
locus and its equation, translation of axes, slope of a line, parallel
and perpendicular lines, intercepts of a line on the coordinate axes.
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.
Circles, conic sections
Standard form of equation of a circle, general form of the equation of a
circle, its radius and centre, 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
a circle, equation of the tangent. 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.
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UNIT
12:
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Three Dimensional Geometry:
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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. |
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UNIT
13:
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Vector Algebra:
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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. |
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UNIT
14:
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STATISTICS AND PROBABILITY:
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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. |
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UNIT 15:
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Trigonometry:
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Trigonometrical
identities and equations. Trigonometrical functions. Inverse
trigonometrical functions and their properties. Heights and Distances.
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UNIT
16:
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MATHEMATICAL REASONING: |
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Statements, logical operations and, or, implies,
implied by, if and only if. Understanding of tautology, contradiction,
converse and contrapositive. |
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PHYSICS
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The syllabus contains two Sections - A
and B. Section - A pertains to the Theory Part having 80% weightage, while
Section - B contains Practical Component (Experimental Skills) having 20%
weightage. |
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SECTION A
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UNIT
1:
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PHYSICS AND MEASUREMENT
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Physics, technology and society, S I units,
Fundamental and derived units. Least count, accuracy and precision of
measuring instruments, Errors in measurement, Significant figures.
Dimensions of Physical quantities, dimensional analysis and its
applications. |
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UNIT
2:
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KINEMATICS |
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Frame of reference. Motion in a straight line:
Position-time graph, speed and velocity. Uniform and non-uniform motion,
average speed and instantaneous velocity Uniformly accelerated motion,
velocity-time, position- time graphs, relations for uniformly accelerated
motion.
Scalars and Vectors, Vector addition and Subtraction, Zero Vector,
Scalar and Vector products, Unit Vector, Resolution of a Vector.
Relative Velocity, Motion in a plane, Projectile Motion, Uniform
Circular Motion. |
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UNIT
3:
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LAWS
OF MOTION
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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. |
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UNIT 4:
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WORK,
ENERGY AND POWER
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Work done by a constant force and a variable force;
kinetic and potential energies, workenergy theorem, power.
Potential energy of a spring, conservation of mechanical energy,
conservative and nonconservative forces; Elastic and inelastic
collisions in one and two dimensions. |
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UNIT
5:
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ROTATIONAL MOTION
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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. |
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UNIT
6:
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GRAVITATION
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The universal law of
gravitation. Acceleration due to gravity and its variation with altitude
and depth. Kepler’s laws of planetary motion. Gravitational potential
energy; gravitational potential. Escape velocity. Orbital velocity of a
satellite. Geo-stationary satellites.
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UNIT
7:
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PROPERTIES OF SOLIDS
AND LIQUIDS
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Elastic behaviour, Stress-strain relationship, Hooke’s
Law, Young’s modulus, bulk modulus, modulus of rigidity. Pressure due to a
fluid column; Pascal’s law and its applications. Viscosity, Stokes’ law,
terminal velocity, streamline and turbulent flow, Reynolds number.
Bernoulli’s principle and its applications. Surface energy and surface
tension, angle of contact, application of surface tension - drops, bubbles
and capillary rise. Heat, temperature, thermal expansion; specific heat
capacity, calorimetry; change of state, latent heat. Heat transfer-
conduction, convection and radiation, Newton’s law of cooling.
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UNIT
8:
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THERMODYNAMICS
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Thermal
equilibrium, zeroth law of thermodynamics, concept of temperature. Heat,
work and internal energy. First law of thermodynamics. Second law of
thermodynamics: reversible and irreversible processes. Carnot engine and
its efficiency. |
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UNIT
9:
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KINETIC THEORY OF GASES |
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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; Mean free path,
Avogadro’s number. |
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UNIT
10:
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OSCILLATIONS AND WAVES
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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 |
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UNIT
11:
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ELECTROSTATICS
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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.
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UNIT
12:
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CURRENT ELECTRICITY
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Electric current, Drift velocity, Ohm’s law,
Electrical resistance, Resistances of different materials, 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. Potentiometer - principle and its applications. |
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UNIT
13:
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MAGNETIC EFFECTS OF CURRENT AND MAGNETISM
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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 current-carrying 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. |
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UNIT
14:
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ELECTROMAGNETIC
INDUCTION AND ALTERNATING CURRENTS
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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. |
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UNIT
15:
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ELECTROMAGNETIC WAVES
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Electromagnetic waves and their characteristics.
Transverse nature of electromagnetic waves.
Electromagnetic spectrum (radio waves, microwaves, infrared, visible,
ultraviolet, Xrays, gamma rays). Applications of e.m. waves. |
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UNIT 16:
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OPTICS
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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, Laws of reflection and
refraction using Huygen’s 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, uses of
plane polarized light and Polaroids. |
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UNIT 17:
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DUAL NATURE OF MATTER AND RADIATION
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Dual nature of radiation. Photoelectric effect, Hertz
and Lenard’s observations; Einstein’s photoelectric equation; particle
nature of light. Matter waves-wave nature of particle, de Broglie
relation. Davisson-Germer experiment. |
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UNIT 18:
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ATOMS AND NUCLEI
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Alpha-particle scattering experiment; Rutherford’s
model of atom; Bohr model, energy levels, hydrogen spectrum.
Composition and size of nucleus, atomic masses, isotopes, isobars;
isotones. Radioactivity-alpha, 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. |
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UNIT 19:
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ELECTRONIC DEVICES
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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. |
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UNIT 20:
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COMMUNICATION SYSTEMS
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Propagation of electromagnetic waves in the atmosphere; Sky and space wave
propagation, Need for modulation, Amplitude and Frequency Modulation,
Bandwidth of signals, Bandwidth of Transmission medium, Basic Elements of a
Communication System (Block Diagram only) |
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SECTION-B
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UNIT 21:
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EXPERIMENTAL SKILLS |
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Familiarity with the basic approach and
observations of the experiments and activities:
1. Vernier callipers-its use to measure internal and
external diameter and depth of a vessel.
2. Screw gauge-its use to
determine thickness/diameter of thin sheet/wire.
3. Simple
Pendulum-dissipation of energy by plotting a graph between square of
amplitude and time.
4. Metre Scale - mass of a given object by
principle of moments.
5. Young’s modulus of elasticity of the material
of a metallic wire.
6. Surface tension of water by capillary rise and
effect of detergents.
7. Co-efficient of Viscosity of a given viscous
liquid by measuring terminal velocity of a given spherical body.
8.
Plotting a cooling curve for the relationship between the temperature of a
hot body and time.
9. Speed of sound in air at room temperature using
a resonance tube. 10. Specific heat capacity of a given
(i) solid and
(ii) liquid by method of mixtures.
11. Resistivity of the material
of a given wire using metre bridge.
12. Resistance of a given wire
using Ohm’s law.
13. Potentiometer –
(i) Comparison of emf of two
primary cells.
(ii) Determination of internal resistance of a cell.
14. Resistance and figure of merit of a galvanometer by half
deflection method.
15. Focal length of:
(i) Convex mirror
(ii)
Concave mirror, and
(iii) Convex lens using parallax method.
16.
Plot of angle of deviation vs angle of incidence for a triangular prism.
17. Refractive index of a glass slab using a travelling microscope.
18. Characteristic curves of a p-n junction diode in forward and
reverse bias.
19. Characteristic curves of a Zener diode and finding
reverse break down voltage.
20. Characteristic curves of a transistor
and finding current gain and voltage gain.
21. Identification of
Diode, LED, Transistor, IC, Resistor, Capacitor from mixed collection of
such items.
22. Using multimeter to:
(i) Identify base of a
transistor
(ii) Distinguish between npn and pnp type transistor
(iii) See the unidirectional flow of current in case of a diode and an
LED.
(iv) Check the correctness or otherwise of a given electronic component
(diode, transistor or IC). |
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CHEMISTRY
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SECTION-A
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PHYSICAL CHEMISTRY
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UNIT
1:
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Some Basic conceptS IN CHEMISTRY
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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. |
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UNIT
2:
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States of Matter
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Classification of
matter into solid, liquid and gaseous states.
Gaseous State:
Measurable properties of gases; Gas laws - Boyle’s law, Charle’s law,
Graham’s law of diffusion, Avogadro’s law, Dalton’s law of partial
pressure; Concept of Absolute scale of temperature; Ideal gas equation,
Kinetic theory of gases (only postulates); Concept of average, root mean
square and most probable velocities; Real gases, deviation from Ideal
behaviour, compressibility factor, van der Waals equation, liquefaction
of gases, critical constants.
Liquid State:
Properties of liquids - vapour pressure, viscosity and surface tension
and effect of temperature on them (qualitative treatment only).
Solid State:
Classification of solids: molecular, ionic, covalent and metallic
solids, amorphous and crystalline solids (elementary idea); Bragg’s Law
and its applications; Unit cell and lattices, packing in solids (fcc,
bcc and hcp lattices), voids, calculations involving unit cell
parameters, imperfection in solids; Electrical, magnetic and dielectric
properties. |
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UNIT
3:
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Atomic Structure
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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;
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