APPSC Asst Controller Legal Metrology, Syllabus
GENERAL STUDIES AND MENTAL ABILITY
S yllabus:
1 . General Science – Contemporary developments in Science and Technology and their implications
i ncluding matters of every day observation and experience, as may be expected of a well-educated
person who has not made a special study of any scientific discipline.
2. Current events of national and international importance.
3. H istory of India – emphasis will be on broad general understanding of the subject in its social,
eco nomic, cultural and political aspects with a focus on AP Indian National Movement.
4. World Geography and Geography of India with a focus on AP.
5. Indian polity and Economy – including the country’s political system- rural development – Planning
a nd economic reforms in India.
6. Mental ability – reasoning and inferences.
PHYSICS
1. Mechanic s and Relativeity:
Newtons law s of motion, force and potential energy, conservative force. Conservation
laws – collis ions – impact parameter, scattering cross-section Laboratory and Centre of mass
reference fr ames. Transformations between them. Rutherford scatterering. Motion of a rocket.
Rigid body dynamics – Moment of inertia of simple regular bodies, rotating frames of reference –
coriolis fo rce. Angular momentum, torque, precession of a top, gyroscope. Central forces –
motion u nder inverse square law – gravitational force, Kepler’s laws. Motion of satellites. Motion
of fluids – streamline and turbulent flow. Bernoulli’s equation with simple applications – Reynolds
number.
Galelean re lativity, special theory of relativity – Time duration and length contraction
Michelson – Morley experiment, Lorentz transformations, addition of velocities, variation of mass
with velocity – mass energy equivalence.
2. Waves and Oscillations:
Oscillations, Simple harmonic motion, progressive and stationary waves. Damped
harmonic Oscillator, Forced oscillations and resonance. Wave equation, harmonic solutions.
Plane and spherical waves, superposition of waves and beats, phase velocity, group velocity,
Doppler effect.
3. Thermal Physics:
Laws of ther modynamics, carnot’s cycle. Isothermal and adiabatic processes.
Thermodynamic potentials, Maxwells relations. Claussius – clapeyrons equation joule – Thomson
effect. Kine tic theory of gases. Maxwell’s velocity distribution, equipartion theorem, specific heat
of gases. Mean free path. Brownian motion, specific heat of solids – Einstein and
Debye’sthe ories. Black body radiation Wien’s, Rayleigh-jeans and plancks laws. Solar constant,
Sahas theory of thermal ionization – stellar spectra, production of low temperature – adiabatic
demagnetiz ation – negative temperature. Vander waals equation, critical constants.
4. Optics:
Huygens principle interference, young’s experiment interference in thin films, Newton’s
rings. Mich elson’s interferometer. Diffraction – Fresnel and Fraunhoffer diffraction. Diffraction by
straight edge, circular and rectangular apperture, single and double slits, plane grating,
Dispersive power Resolving power, Rayleighs criterion. X-ray diffraction and Bragg’s law.
Polarisation – Plane, Polarisation by reflection, circular, elleptic polarisation, double refraction,
Nicol pris m, quarter and half wave plates. Laser principle – spontaneous and stimulated emission
of Radiation. He-Ne, Ruby and semiconductor diode lasers. Coherence. Diffraction as Fourier
transform ation. Holography and applications.
5. Elect ricity and Magnetism:
Coulomb’s Law, Electric field, Gauss’s Law, electric potential. Poissons and Laplace
equatio ns and solutions for homogeneous dielectric, uncharged conducting sphere in a uniform
field, p oint charge and infinite conducting plane. Magnetic shell, magnetic induction and field
streng th Biot savarts law and applications. Electromagnetic induction, Faradays and Lenz’s laws.
Self a nd mutual inductance, induction coil and transformer.
Alter nating currents L-R, C-R, L-C-R circuits. Series and parallel resonance, Q-factor.
Elec tromagnetic waves – Maxwells equations. Transverse nature of e-m waves, pointing vector.
Ma gnetic materials – Dia, para, ferro, antiferro and ferri magnetism (Qualitative features
on ly). Langevin’s theory of paramagnetism, Weiss theory of ferromagnetism. Ferro magnetic
D omains Hysterisis, Nuclear magnetism. Dielectric materials – Capacitative with dielectric
m aterial as medium; electric polarisation; electronic, ionic, electric polarisabilities and their
v ariations with temperature.
6. Moder n Physics:
Bohr’s m odel, sommerfeld extension. Explanation of atomic spectra. Stern-Gerlach
experime nt, space quantization, electron spin, vector atom model, spectral terms, fine structure
of spectr al lines. J-J and L-S coupling schemes. Pauli’s exclusion principle, spectral terms of two
equivale nt and non-euqivalent electorns, Zeeman, Paschenback effects, Stark effect.
Charact eristic X-rays, Moseley’s Law. Gross and fine structure of Band spectra, Raman effect.
Black b ody radiation, Wien, Rayleigh Jeans and Planck’s Laws of radiation. Photo
electric effect and Einstein’s Explanation, Compton effect, de Broglie hypothesis. Wave-particle
duality , uncertainity principle, Schrodinger equation, eigen functions and eigen values. Physical
mean ing of eigen function, Solution of Schoedinger equation for 1) particle in a box 2) potential
step 3) harmonic oscillator 4) hydrogen atom.
Rad ioactivity – alpha, beta and gamma rays, Gammow’s theory of alpha decay. Laws of
rad ioactivity. Radioactive equilibrium. Aritificial radioactivity – Rutherfords experiment, discovery
of Neutron. Mass spectrometers. Nuclear binding energy, semi-emperical mass formula.
N uclear fission, nuclear reactors. Nuclear fusion, fusion cycles. Elementary particles and their
c lassification. Strong, Weak and elector-magnetic interactions. Particle accelerators – Cyclotron
and linear accelerators. Basic experimental ideas of superconductivity.
7. Electronics :
Band theory o f solids – Conductors, insulators and semi conductors. Intrinsic and extrinsic
semi conduct ors; p-n junction diode, forward and reverse bias. Diode as a rectifier. Transistor –
different configurations of transistor, Transister parameter amplifier. Transistor oscillator.
Modulation and detection. Transistor receiver. Basic principle of television. Digital principles –
Logic gates – AND, OR NOT, XOR gates – truth tables.
MATHEMATICS
Alg ebra:
Gr oups – subgroups – normal subgroups – quotient groups – homomorphism and
isomorphism theorems – cyclic groups – permutation groups – Cayleay’s theorem.
R ings – subrings – integral domain – fields – ideals quotient ring – maximal and prime
i deals – Euclidean rings – polynomial rings – Unique factorization domains – principal ideal
domains.
Lin ear Algebra:
Ve ctor spaces – subspaces – linear independence and dependence – Bases and
di mension – Finite – dimensional vector spaces and their properties.
Li near transformations – Rank and nullity of a linear transformation – Cayley – Hamilton
th eorem – Matrix of a linear transformation – eigen values and eigen vectors – Canonical forms.
I nner product spaces – Orthonormal basis – Quadratic forms.
Different ial equations:
Order an d degree of a differential equation – Formation of a differential equation –
Different ial equations of first order and first degree – Linear differential equations with constant
and vari able coefficients – Total differential equations.
Formation of partial differential equations – Equations of first order – Charpit’s methods.
Geometry:
General equation of second degree in two variables – Tracing of conics.
Plane, straight lines in space – sphere – Cone.
Curves in space – curvature – Torsion – Seret – Frenet formulae.
Real Analysis:
Real number syste m R – Open and closed sets in R- Compact sets – sequences in R and
their convergence – Series of real numbers – Tests of convergence – absolute and conditional
convergence – re arrangements of series.
Limits and contin uity of a real valued function properties of continuous functions –
Differentiation – Mean value theorems – Applications.
Riemann integration – conditions for Reimann integrability – improper integrals.
Complex Analysis:
Complex numbers and their geometric representation – limits and continuity of functions
of a Complex variable – Analytic functions – Couchy Riemann equations – Complex integration –
Canchy’s theorem – Canchy’s integral formula – Power series – Taylor’s and Laurent’s series –
Types of singularities – Calculus of residues and application to evaluation of definite integrals.
Vector calculus:
Differentiation of a vector va lued function – Gradient of a scalar function – Divergence
and curl of a vector function in Cartesian and polar coordinates.
Green’s theorem – Gauss a nd Stoke’s theorems and their applications to evaluation of
double and triple integrals.
a) Transform Calculus: Laplace T ransforms – Inverse Laplace transforms – solving
differential equations using Lapla ce transforms.
Fourier and Hankel transforms.
b) Numerical Analysis: transcendental a nd Polynomial equations – Regula Falsi method
– Newton Raphson method Interpolation – numerical differentiation – numerical
intergration – Runga Kutta method.
c) Number Theory: Fundamental theorem of arithmetic – congruences and their
applications – Fermat’s and Wilson’s theorems – solution of linear congruences –
Chinese remainder theorem.
d) Linear Programming: Formation of linear programming problem – Graphical solution
– Dual problem – simplex method – Transportation problem
i ncluding matters of every day observation and experience, as may be expected of a well-educated
person who has not made a special study of any scientific discipline.
2. Current events of national and international importance.
3. H istory of India – emphasis will be on broad general understanding of the subject in its social,
eco nomic, cultural and political aspects with a focus on AP Indian National Movement.
4. World Geography and Geography of India with a focus on AP.
5. Indian polity and Economy – including the country’s political system- rural development – Planning
a nd economic reforms in India.
6. Mental ability – reasoning and inferences.
PHYSICS
1. Mechanic s and Relativeity:
Newtons law s of motion, force and potential energy, conservative force. Conservation
laws – collis ions – impact parameter, scattering cross-section Laboratory and Centre of mass
reference fr ames. Transformations between them. Rutherford scatterering. Motion of a rocket.
Rigid body dynamics – Moment of inertia of simple regular bodies, rotating frames of reference –
coriolis fo rce. Angular momentum, torque, precession of a top, gyroscope. Central forces –
motion u nder inverse square law – gravitational force, Kepler’s laws. Motion of satellites. Motion
of fluids – streamline and turbulent flow. Bernoulli’s equation with simple applications – Reynolds
number.
Galelean re lativity, special theory of relativity – Time duration and length contraction
Michelson – Morley experiment, Lorentz transformations, addition of velocities, variation of mass
with velocity – mass energy equivalence.
2. Waves and Oscillations:
Oscillations, Simple harmonic motion, progressive and stationary waves. Damped
harmonic Oscillator, Forced oscillations and resonance. Wave equation, harmonic solutions.
Plane and spherical waves, superposition of waves and beats, phase velocity, group velocity,
Doppler effect.
3. Thermal Physics:
Laws of ther modynamics, carnot’s cycle. Isothermal and adiabatic processes.
Thermodynamic potentials, Maxwells relations. Claussius – clapeyrons equation joule – Thomson
effect. Kine tic theory of gases. Maxwell’s velocity distribution, equipartion theorem, specific heat
of gases. Mean free path. Brownian motion, specific heat of solids – Einstein and
Debye’sthe ories. Black body radiation Wien’s, Rayleigh-jeans and plancks laws. Solar constant,
Sahas theory of thermal ionization – stellar spectra, production of low temperature – adiabatic
demagnetiz ation – negative temperature. Vander waals equation, critical constants.
4. Optics:
Huygens principle interference, young’s experiment interference in thin films, Newton’s
rings. Mich elson’s interferometer. Diffraction – Fresnel and Fraunhoffer diffraction. Diffraction by
straight edge, circular and rectangular apperture, single and double slits, plane grating,
Dispersive power Resolving power, Rayleighs criterion. X-ray diffraction and Bragg’s law.
Polarisation – Plane, Polarisation by reflection, circular, elleptic polarisation, double refraction,
Nicol pris m, quarter and half wave plates. Laser principle – spontaneous and stimulated emission
of Radiation. He-Ne, Ruby and semiconductor diode lasers. Coherence. Diffraction as Fourier
transform ation. Holography and applications.
5. Elect ricity and Magnetism:
Coulomb’s Law, Electric field, Gauss’s Law, electric potential. Poissons and Laplace
equatio ns and solutions for homogeneous dielectric, uncharged conducting sphere in a uniform
field, p oint charge and infinite conducting plane. Magnetic shell, magnetic induction and field
streng th Biot savarts law and applications. Electromagnetic induction, Faradays and Lenz’s laws.
Self a nd mutual inductance, induction coil and transformer.
Alter nating currents L-R, C-R, L-C-R circuits. Series and parallel resonance, Q-factor.
Elec tromagnetic waves – Maxwells equations. Transverse nature of e-m waves, pointing vector.
Ma gnetic materials – Dia, para, ferro, antiferro and ferri magnetism (Qualitative features
on ly). Langevin’s theory of paramagnetism, Weiss theory of ferromagnetism. Ferro magnetic
D omains Hysterisis, Nuclear magnetism. Dielectric materials – Capacitative with dielectric
m aterial as medium; electric polarisation; electronic, ionic, electric polarisabilities and their
v ariations with temperature.
6. Moder n Physics:
Bohr’s m odel, sommerfeld extension. Explanation of atomic spectra. Stern-Gerlach
experime nt, space quantization, electron spin, vector atom model, spectral terms, fine structure
of spectr al lines. J-J and L-S coupling schemes. Pauli’s exclusion principle, spectral terms of two
equivale nt and non-euqivalent electorns, Zeeman, Paschenback effects, Stark effect.
Charact eristic X-rays, Moseley’s Law. Gross and fine structure of Band spectra, Raman effect.
Black b ody radiation, Wien, Rayleigh Jeans and Planck’s Laws of radiation. Photo
electric effect and Einstein’s Explanation, Compton effect, de Broglie hypothesis. Wave-particle
duality , uncertainity principle, Schrodinger equation, eigen functions and eigen values. Physical
mean ing of eigen function, Solution of Schoedinger equation for 1) particle in a box 2) potential
step 3) harmonic oscillator 4) hydrogen atom.
Rad ioactivity – alpha, beta and gamma rays, Gammow’s theory of alpha decay. Laws of
rad ioactivity. Radioactive equilibrium. Aritificial radioactivity – Rutherfords experiment, discovery
of Neutron. Mass spectrometers. Nuclear binding energy, semi-emperical mass formula.
N uclear fission, nuclear reactors. Nuclear fusion, fusion cycles. Elementary particles and their
c lassification. Strong, Weak and elector-magnetic interactions. Particle accelerators – Cyclotron
and linear accelerators. Basic experimental ideas of superconductivity.
7. Electronics :
Band theory o f solids – Conductors, insulators and semi conductors. Intrinsic and extrinsic
semi conduct ors; p-n junction diode, forward and reverse bias. Diode as a rectifier. Transistor –
different configurations of transistor, Transister parameter amplifier. Transistor oscillator.
Modulation and detection. Transistor receiver. Basic principle of television. Digital principles –
Logic gates – AND, OR NOT, XOR gates – truth tables.
MATHEMATICS
Alg ebra:
Gr oups – subgroups – normal subgroups – quotient groups – homomorphism and
isomorphism theorems – cyclic groups – permutation groups – Cayleay’s theorem.
R ings – subrings – integral domain – fields – ideals quotient ring – maximal and prime
i deals – Euclidean rings – polynomial rings – Unique factorization domains – principal ideal
domains.
Lin ear Algebra:
Ve ctor spaces – subspaces – linear independence and dependence – Bases and
di mension – Finite – dimensional vector spaces and their properties.
Li near transformations – Rank and nullity of a linear transformation – Cayley – Hamilton
th eorem – Matrix of a linear transformation – eigen values and eigen vectors – Canonical forms.
I nner product spaces – Orthonormal basis – Quadratic forms.
Different ial equations:
Order an d degree of a differential equation – Formation of a differential equation –
Different ial equations of first order and first degree – Linear differential equations with constant
and vari able coefficients – Total differential equations.
Formation of partial differential equations – Equations of first order – Charpit’s methods.
Geometry:
General equation of second degree in two variables – Tracing of conics.
Plane, straight lines in space – sphere – Cone.
Curves in space – curvature – Torsion – Seret – Frenet formulae.
Real Analysis:
Real number syste m R – Open and closed sets in R- Compact sets – sequences in R and
their convergence – Series of real numbers – Tests of convergence – absolute and conditional
convergence – re arrangements of series.
Limits and contin uity of a real valued function properties of continuous functions –
Differentiation – Mean value theorems – Applications.
Riemann integration – conditions for Reimann integrability – improper integrals.
Complex Analysis:
Complex numbers and their geometric representation – limits and continuity of functions
of a Complex variable – Analytic functions – Couchy Riemann equations – Complex integration –
Canchy’s theorem – Canchy’s integral formula – Power series – Taylor’s and Laurent’s series –
Types of singularities – Calculus of residues and application to evaluation of definite integrals.
Vector calculus:
Differentiation of a vector va lued function – Gradient of a scalar function – Divergence
and curl of a vector function in Cartesian and polar coordinates.
Green’s theorem – Gauss a nd Stoke’s theorems and their applications to evaluation of
double and triple integrals.
a) Transform Calculus: Laplace T ransforms – Inverse Laplace transforms – solving
differential equations using Lapla ce transforms.
Fourier and Hankel transforms.
b) Numerical Analysis: transcendental a nd Polynomial equations – Regula Falsi method
– Newton Raphson method Interpolation – numerical differentiation – numerical
intergration – Runga Kutta method.
c) Number Theory: Fundamental theorem of arithmetic – congruences and their
applications – Fermat’s and Wilson’s theorems – solution of linear congruences –
Chinese remainder theorem.
d) Linear Programming: Formation of linear programming problem – Graphical solution
– Dual problem – simplex method – Transportation problem
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