Note :-

1. All questions carry equal marks.
2. There will be Negative Marking.
3. Medium of Competitive Exam: Bilingual in English & Hindi.

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Syllabus : Physics-II

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1. Mathematical Methods of Physics
   1. Dimensional analysis; Vector algebra and vector calculus; Linear algebra, matrices,
   2. Cayley Hamilton theorem, eigen value problems; Linear differential equations;
   3. Special functions (Hermite, Bessel, Laguerre and Legendre); Fourier series, Fourier and Laplace transforms;
   4. Elements of complex analysis; Elementary ideas about tensors;
   5. Introductory group theory; Elements of computational techniques: roots of functions, interpolation, extrapolation, integration by trapezoid and Simpson's rule,
   6. solution of first order differential equations using Runge-Kutta method; Finite difference methods;
   7. Elementary probability theory, random variables, binomial, Poisson and normal distributions.

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2. Classical Mechanics
   1. Newton's laws; Phase space dynamics, stability analysis;
   2. Central-force motion; Kepler's laws, Gravitational field and potentials;
   3. Two-body collisions, scattering in laboratory and centre-of-mass frames;
   4. Rigid body dynamics, Angular momentum, moment of inertia tensor, non-inertial frames and pseudoforces;
   5. Variational principle, Lagrangian and Hamiltonian formalisms and equations of motion;
   6. Poisson brackets and canonical transformations; Symmetry, invariance and conservation laws, cyclic coordinates;
   7. Periodic motion, small oscillations and normal modes; Damped harmonic oscillations, Driven harmonic oscillations;
   8. Waves in media, Superposition of waves; Special theory of relativity, Lorentz transformations, relativistic kinematics and mass-energy equivalence.
   9. Kinematics of moving fluids: Bernouli's theorem, Viscosity, Surface tension.

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3. Quantum Mechanics
   1. Wave-particle duality; Wave functions in coordinate and momentum representations;
   2. Commutators and Heisenberg's uncertainty principle; Matrix representation; Dirac's bra and ket notation;
   3. Schroedinger equation (time-dependent and time-independent);
   4. Eigen value problems such as particle-in-a-box, harmonic oscillator, etc.; Tunneling through a barrier;
   5. Motion in a central potential; Orbital angular momentum, Angular momentum algebra, spin;
   6. Addition of angular momenta; Hydrogen atom, spin-orbit coupling, fine structure;
   7. Time-independent perturbation theory and applications; Variational method; WKB approximation;
   8. Time dependent perturbation theory and Fermi's Golden Rule; Selection rules; Semi-classical theory of radiation;
   9. Elementary theory of scattering, phase shifts, partial waves, Born approximation;
   10. Identical particles, Pauli's exclusion principle, spin-statistics connection;
   11. Relativistic quantum mechanics: Klein Gordon and Dirac equations.

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4. Thermodynamic and Statistical Physics
   1. Laws of thermodynamics and their consequences; Thermodynamic potentials,
   2. Production of low temperature and its applications; Maxwell relations;
   3. Chemical potential, phase equilibria; Phase space, micro- and macro states;
   4. Micro canonical, canonical and grand-canonical ensembles and partition functions;
   5. Free Energy and connection with thermodynamic quantities;
   6. First and second-order phase transitions; Classical and quantum statistics, ideal Fermi and Bose gases;
   7. Principle of detailed balance; Blackbody radiation and Planck's distribution law;
   8. Bose-Einstein condensation; Random walk and Brownian motion;
   9. Introduction to non-equilibrium processes; Diffusion equation.

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5. Nuclear and Particle Physics
   1. Basic nuclear properties: size, shape, charge distribution, spin and parity;
   2. Binding energy, semi-empirical mass formula; Liquid drop model; Fission and fusion;
   3. Nature of the nuclear force, form of nucleon-nucleon potential;
   4. Charge-independence and charge-symmetry of nuclear forces; Isospin; Deuteron problem;
   5. Evidence of shell structure, single- particle shell model, its validity and limitations;
   6. Rotational spectra; Elementary ideas of alpha, beta and gamma decays and their selection rules;
   7. Nuclear reactions, reaction mechanisms, compound nuclei and direct reactions;
   8. Classification of fundamental forces; Elementary particles (quarks, baryons, mesons, leptons);
   9. Spin and parity assignments, isospin, strangeness; Gell-Mann-Nishijima formula; C, P, and T invariance and applications of symmetry arguments to particle reactions, parity non-conservation in weak interaction;
   10. Particle accelerators and detectors.