Syllabus for General Aptitude (GA)
(COMMON TO ALL PAPERS)
Verbal Ability: English grammar, sentence completion, verbal analogies, word groups,
instructions, critical reasoning and verbal deduction.
Numerical Ability: Numerical computation, numerical estimation, numerical reasoning and data
Section 1: Mathematical Physics
Linear vector space: basis, orthogonality and completeness; matrices; vector
calculus; linear differential equations; elements of complex analysis: Cauchy-
Riemann conditions, Cauchy’s theorems, singularities, residue theorem and
applications; Laplace transforms, Fourier analysis; elementary ideas about tensors:
covariant and contravariant tensor, Levi-Civita and Christoffel symbols.
Section 2: Classical Mechanics
D’Alembert’s principle, cyclic coordinates, variational principle, Lagrange’s
equation of motion, central force and scattering problems, rigid body motion;
small oscillations, Hamilton’s formalisms; Poisson bracket; special theory of
relativity: Lorentz transformations, relativistic kinematics, mass‐energy equivalence.
Section 3: Electromagnetic Theory
Solutions of electrostatic and magnetostatic problems including boundary value
problems; dielectrics and conductors; Maxwell’s equations; scalar and vector
potentials; Coulomb and Lorentz gauges; Electromagnetic waves and their
reflection, refraction, interference, diffraction and polarization; Poynting vector,
Poynting theorem, energy and momentum of electromagnetic waves; radiation
from a moving charge.
Section 4: Quantum Mechanics
Postulates of quantum mechanics; uncertainty principle; Schrodinger equation;
one-, two- and three-dimensional potential problems; particle in a box, transmission
through one dimensional potential barriers, harmonic oscillator, hydrogen atom;
linear vectors and operators in Hilbert space; angular momentum and spin;
addition of angular momenta; time independent perturbation theory; elementary
Section 5: Thermodynamics and Statistical Physics
Laws of thermodynamics; macrostates and microstates; phase space; ensembles;
partition function, free energy, calculation of thermodynamic quantities; classical
and quantum statistics; degenerate Fermi gas; black body radiation and Planck’s
distribution law; Bose‐Einstein condensation; first and second order phase
transitions, phase equilibria, critical point.
Section 6: Atomic and Molecular Physics
Spectra of one‐ and many‐electron atoms; LS and jj coupling; hyperfine structure;
Zeeman and Stark effects; electric dipole transitions and selection rules; rotational
and vibrational spectra of diatomic molecules; electronic transition in diatomic
molecules, Franck‐Condon principle; Raman effect; NMR, ESR, X-ray spectra;
lasers: Einstein coefficients, population inversion, two and three level systems.
Section 7: Solid State Physics & Electronics
Elements of crystallography; diffraction methods for structure determination;
bonding in solids; lattice vibrations and thermal properties of solids; free electron
theory; band theory of solids: nearly free electron and tight binding models; metals,
semiconductors and insulators; conductivity, mobility and effective mass; optical,
dielectric and magnetic properties of solids; elements of superconductivity: Type-I
and Type II superconductors, Meissner effect, London equation.
Semiconductor devices: diodes, Bipolar Junction Transistors, Field Effect Transistors;
operational amplifiers: negative feedback circuits, active filters and oscillators;
regulated power supplies; basic digital logic circuits, sequential circuits, flip‐flops,
counters, registers, A/D and D/A conversion.
Section 8: Nuclear and Particle Physics
Nuclear radii and charge distributions, nuclear binding energy, Electric and
magnetic moments; nuclear models, liquid drop model: semi‐empirical mass
formula, Fermi gas model of nucleus, nuclear shell model; nuclear force and two
nucleon problem; alpha decay, beta‐decay, electromagnetic transitions in nuclei;
Rutherford scattering, nuclear reactions, conservation laws; fission and fusion;
particle accelerators and detectors; elementary particles, photons, baryons,
mesons and leptons; quark model.