Organisation : National Institute of Science Education and Research (NISER) Bhubaneswar
Announcement : Syllabus
Entrance Test : NEST National Entrance Screening Test
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Syllabus for NEST :
Mathematics :
Algebra :
Algebra of complex numbers, addition, multiplication, conjugation, polar representation, properties of modulus and principal argument, triangle inequality, cube roots of unity, geometric interpretations. Quadratic equations with real coefficients, relations between roots and coefficients, formation of quadratic equations with given roots, symmetric functions of roots.
Related / Similar Syllabus : NEST Syllabus 2020
Arithmetic, geometric and harmonic progressions, arithmetic, geometric and harmonic means, sums of finite arithmetic and geometric progressions, infinite geometric series, sums of squares and cubes of the first n natural numbers.
Logarithms and their properties.
Permutations and combinations, Binomial theorem for positive integral index, properties of binomial coefficients. Matrices as a rectangular array of real numbers, equality of matrices, addition, multiplication by a scalar and product of matrices, transpose of a matrix, determinant of a square matrix of order up to three, inverse of a square matrix of order up to three, properties of these matrix operations, diagonal, symmetric and skewsymmetric matrices and their properties, solutions of simultaneous linear equations in two or three variables.
Addition and multiplication rules of probability, conditional probability, Bayes Theorem, independence of events, computation of probability of events using permutations and combinations.
Trigonometry :
Trigonometric functions, their periodicity and graphs, addition and subtraction formulae, formulae involving multiple and sub-multiple angles, general solution of trigonometric equations.
Relations between sides and angles of a triangle, sine rule, cosine rule, half-angle formula and the area of a triangle, inverse trigonometric functions (principal value only).
Analytical geometry :
Two dimensions – Cartesian coordinates, distance between two points, section formulae, shift of origin. Equation of a straight line in various forms, angle between two lines, distance of a point from a line. Lines through the point of intersection of two given lines, equation of the bisector of the angle between two lines, concurrency of lines. Centroid, orthocentre, incentre and circumcentre of a triangle.
Equation of a circle in various forms, equations of tangent, normal and chord.
Parametric equations of a circle, intersection of a circle with a straight line or a circle, equation of a circle through the points of intersection of two circles and those of a circle and a straight line.
Equations of a parabola, ellipse and hyperbola in standard form, their foci, directrices and eccentricity, parametric equations, equations of tangent and normal. Locus Problems.
Three dimensions – Direction cosines and direction ratios, equation of a straight line in space, equation of a plane, distance of a point from a plane.
Differential calculus :
Real valued functions of a real variable, into, onto and one-to-one functions, sum, difference, product and quotient of two functions, composite functions, absolute value, polynomial, rational, trigonometric, exponential and logarithmic functions.
Limit and continuity of a function, limit and continuity of the sum, difference, product and quotient of two functions, L’Hospital rule for evaluation of limits of functions.
Even and odd functions, inverse of a function, continuity of composite functions, intermediate value property of continuous functions. Derivative of a function, derivative of the sum, difference, product and quotient of two functions, chain rule, derivatives of polynomial, rational, trigonometric, inverse trigonometric, exponential and logarithmic functions.
Derivatives of implicit functions, derivatives up to order two, geometrical interpretation of the derivative, tangents and normals, increasing and decreasing functions, maximum and minimum values of a function, Rolle’s Theorem and Lagrange’s Mean Value Theorem.
Integral calculus :
Integration as the inverse process of differentiation, indefinite integrals of standard functions, definite integrals and their properties, Fundamental Theorem of Integral Calculus.
Integration by parts, integration by the methods of substitution and partial fractions, application of definite integrals to the determination of areas involving simple curves.
Formation of ordinary differential equations, solution of homogeneous differential equations, separation of variables method, linear first order differential equations.
Vectors :
Addition of vectors, scalar multiplication, dot and cross products, scalar triple products and their geometrical interpretations.
Physics :
General: Units and dimensions, dimensional analysis. least count, significant figures. Methods of measurement (Direct, Indirect, Null) and measurement of length, time, mass, temperature, potential difference, current and resistance.
Design of some simple experiments, such as:
i) Searle’s method to determine Young’s modulus,
ii) determination of ‘g’ by simple pendulum,
iii) speed of sound using resonance tube,
iv) coefficient of friction using angle of repose,
v) determination of focal length of a convex lens by plotting a graph between ‘u’ and ‘v’,
vi) refractive index of material of prism using the method of minimum deviation,
vii) verification of Ohm’s law,
viii) resistance of galvanometer using half deflection method,
ix) specific heat of a liquid using calorimeter,
x) I-V characteristic curve for p-n junction in forward and reverse bias.
Graphical representation and interpretation of data. Errors in the measurements and error analysis.
Mechanics: Kinematics in one and two dimensions (Cartesian coordinates only), projectiles. Uniform circular motion. Relative velocity. Newton’s laws of motion. Inertial and uniformly accelerated (linear only) frames of reference. Static and dynamic friction. Kinetic and potential energy. Linear and circular simple harmonic motion. Work and power. Conservation of linear momentum and mechanical energy.
Systems of particles. Centre of mass and its motion. Centre of gravity. Impulse. Elastic and inelastic collisions.
Law of gravitation. Centripetal acceleration and centrifugal force. Gravitational potential and field. Acceleration due to gravity. Motion of planets and satellites in circular orbits. Escape velocity.
Rigid body, moment of inertia, parallel and perpendicular axes theorems, moment of inertia of uniform bodies with simple geometrical shapes. Angular momentum, Torque. Conservation of angular momentum. Dynamics of rigid bodies with fixed axis of rotation. Rolling without slipping of rings, cylinders and spheres. Equilibrium of rigid bodies. Collision of point masses with rigid bodies. Hooke’s law and stress – strain relations. Elastic limit, plastic deformation. Young’s modulus, bulk and shear moduli.
Pressure in a fluid. Pascal’s law. Buoyancy. Surface energy and surface tension, capillary rise. Viscosity – Stoke’s and Poiseuille’s law, Terminal velocity. Qualitative understanding of turbulence. Reynolds number. Streamline flow, equation of continuity. Bernoulli’s theorem.
Sound and mechanical waves: Plane wave motion, longitudinal and transverse waves, superposition of waves. Progressive and stationary waves. Vibration of strings and air columns. Resonance (qualitative understanding). Beats. Speed of sound in gases. Doppler Effect.
Thermal physics: Thermal expansion of solids, liquids and gases. Calorimetry, latent heat. Heat conduction in one dimension. Elementary concepts of convection and radiation. Newton’s law of cooling. Ideal gas laws. Specific heats (CV and CP for monoatomic and diatomic gases). Isothermal and adiabatic processes, bulk modulus of gases. Equivalence of heat and work. First and second law of thermodynamics and its applications (only for ideal gases). Entropy. Blackbody radiation – absorptive and emissive powers. Kirchhoff’s law. Wien’s displacement law, Stefan’s law.
Electricity and magnetism: Coulomb’s law. Electric field and potential. Electrical potential energy of a system of point charges and of electrical dipoles in a uniform electrostatic field; Electric field lines. Flux of electric field. Gauss’s law and its application in simple cases, such as to find field due to infinitely long straight wire. Uniformly charged infinite plane sheet and uniformly charged thin spherical shell.
Capacitance – Calculation of capacitance with and without dielectrics. Capacitors in series and parallel. Energy stored in a capacitor. Electric current. Ohm’s law. Series and parallel arrangements of resistances and cells. Kirchhoff’s laws and simple applications; Heating effect of current. Biot-Savart’s law and Ampere’s law. Magnetic field near a current carrying straight wire, along the axis of a circular coil and inside a long straight solenoid. Force on a moving charge and on a current carrying wire in a uniform magnetic field.
Magnetic moment of a current loop. Effect of a uniform magnetic field on a current loop. Moving coil galvanometer, voltmeter, ammeter and their conversions. Electromagnetic induction – Faraday’s law, Lenz’s law. Self and mutual inductance. RC, LR and LC circuits with and A.C. Sources.
Optics: Rectilinear propagation of light. Reflection and refraction at plane and spherical surfaces, Deviation and dispersion of light by a prism. Thin lenses. Combination of mirrors and thin lenses. Magnification. Wave nature of light – Huygen’s principle, interference limited to Young’s double slit experiment. Elementary idea of diffraction – Rayleigh criterion. Elementary idea of polarization – Brewster’s law and the law of Malus. Modern physics: Atomic nucleus. Alpha, beta and gamma radiations. Law of radioactive decay. Decay constant. Half-life and mean life. Binding energy and its calculation. Fission and fusion processes. Energy calculation in these processes.
Photoelectric effect. Bohr’s theory of hydrogen like atoms. Characteristic and continuous X-rays, Moseley’s law. de Broglie wavelength of matter waves. Heisenberg’s uncertainty principle.