www.amrita.edu University : B.tech Entrance Exam Syllabus

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MATHEMATICS
a. Complex Numbers
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.
Cube roots of unity, triangle inequality.

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b. Linear Inequalities
Linear inequalities. Algebraic solutions of linear inequalities in one variable and their representation on the number line.

c. Permutations and Combinations
Fundamental principle of counting; Permutation as an arrangement and combination as selection, Meaning of P(n,r)and C(n,r).Simple applications.

d. Binomial Theorem
Binomial theorem for positive integral indices. Pascal’s triangle.
General and middle terms in binomial expansions, simple applications.
e. Sequences and Series
Arithmetic, Geometric and Harmonic progressions. Insertion of Arithmetic, Geometric and Harmonic means between two given numbers. Relation between A.M., G.M. and H.M. Special series n, n2, n3. Arithmetico-Geometric Series, Exponential and Logarithmic Series.

f. Matrices and Determinants
Determinants and matrices of order two and three, Properties of determinants. Evaluation of determinants. Addition and multiplication of matrices, adjoint and inverse of matrix. Solution of simultaneous linear equations using determinants.

g. Quadratic Equations
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;

h. Relations and Functions
Definition of a relation. Domain, codomain and range of a relation. Function as special kind of relation and their domain, codomain and range. Real valued function of a real variable. Constant, identity, polynomial, rational.
Modulus, signum and greatest integer functions. Sum. Difference, product and quotient of functions.
Types of relations: refelexive, symmetric, transitive and equivalence relations. One to one and onto functions. Composite functions, inverse of a function.
i. Trigonometry
Trigonometrical identities and equations. Inverse trigonometric functions and their properties. Properties of triangles, including centroid, incentre, circumcentre and orthocentre, solution of triangles. Heights and distances.

j. Measures of Central Tendency and Dispersion Calculation of Mean, Median and Mode of grouped and ungrouped data. Calculation of standard deviation, variance and mean deviation for grouped and ungrouped data.

k. Probability
Probability of an event, addition and multiplication theorems of probability and their applications; Conditional probability; Bayes’ theorem, Probability distribution of a random variate; Binomial and Poisson distributions
and their properties.

l. Differential Calculus
Polynomials, rational, trigonometric, logarithmic and exponential functions. Graphs of simple functions. Limits, Continuity; 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. Applications of derivatives: Maxima and Minima of functions one variable, tangents and normals, Rolle’s and Langrage’s Mean Value Theorems.

m. Integral Calculus
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. Integral as a limit of sum. Properties of definite integrals. Evaluation of definite integral; Determining areas of the regions
bounded by simple curves.

n. Differential Equations
Ordinary differential equations, their order and degree. Formation of differential equation. Solutions of differential equations by the method of separation of variables. Solution of Homogeneous and linear differential equations, and those of type d2y/dx2= f(x).

o. Two Dimensional Geometry
Review of Cartesian system of rectangular co-ordinates in a plane, distance formula, area of triangle, condition for the collinearity of three points, slope of a line, parallel and perpendicular lines, intercepts of a line on the coordinate axes.

p. The straight line and pair of 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, equation of family lines passing through the point of intersection of two lines, homogeneous equation of second degree in x and y, angle between pair of lines through the origin, combined equation of the bisectors of the angles between a pair of lines, condition for the general second degree equation to represent a pair of lines, point of intersections and angles between two lines.

q. Circles and Family of Circles
Standard form of equation of a circle, general form of the equation of a circle, its radius and centre, equation of a circle in the parametric form, equation of a circle when the end points of a diameter are given, points of intersection of a line and circle with the centre at the origin and condition for a line to be tangent, equation of a family of circles through the
intersection of two circles, condition for two intersecting circles to be orthogonal.

r. Conic Sections
Sections of cones, equations of conic sections ( parabola, ellipse and hyperbola) in standard forms, conditions for y = mx+c to be a tangent and point(s) of tangency.

s. Vector Algebra
Vector and scalars, addition of two vectors, components of a vector in two dimensions and three dimensional space, scalar and vector products, scalar and vector triple product. Application of vectors to plane geometry.

t. Three Dimensional Geometry
Distance between two points. Direction cosines of a line joining two points. Cartesian and vector equation of a line. Coplanar and skew lines. Shortest distance between two lines.Cartesian and vector equation of a
plane. Angle between (i) two lines (ii) two planes (iii) a line and a plane Distance of a point from a plane.

PHYSICS
a. UNITS AND DIMENSIONS
Units for measurement, system of units, SI, fundamental and derived units, dimensions and their applications.

b. MECHANICS
Motion in straight line, uniform and non-uniform motion, uniformly accelerated motion and its applications Scalars and Vectors, and their properties; resolution of vectors, scalar and vector products; uniform circular motion and its applications, projectile motion Newton’s Laws of motion; conservation of linear momentum and its applications, laws of
friction, Concept of work, energy and power; energy-kinetic and potential; conservation of energy; different forms of energy. Elastic collisions in one and two dimensions. Center of mass of a many particle system; center of mass of a rigid body, rotational motion and torque. Angular
momentum and its conservation. Moments of inertia, parallel and perpendicular axes theorem, moment of inertia for a thin rod, ring, disc and sphere.
Gravitation: Acceleration due to gravity and its properties. One and two dimensional motion under gravity. Universal law of gravitation, planetary motion, Kepler’s laws, artificial satellite-geostationary satellite, gravitational potential energy near the surface of earth, gravitational potential and escape velocity.

h. SOLIDS AND FLUIDS
Solids: Elastic properties, Hooke’s law, Young’s modulus, bulk modulus, modulus of rigidity.Liquids: Cohesion and adhesion; surface energy and surface tension; flow of fluids, Bernoulli’s theorem and its applications; viscosity, Stoke’s Law, terminal velocity.

(i) OSCILLATIONS AND WAVES
Periodic motion, simple harmonic motion and its equation, oscillations of a spring and simple pendulum. Wave motion, properties of waves, longitudinal and transverse waves, superposition of waves, Progressive and
standing waves. Free and forced oscillations, resonance, vibration of strings and air columns, beats, Doppler effect.
(ii) HEAT AND THERMODYNAMICS
Thermal expansion of solids, liquids and gases and their specific heats, relationship between Cp and Cv for gases, first and second laws of thermodynamics , Carnot cycle, efficiency of heat engines. Transference of heat; thermal conductivity; black body radiations, Kirchoff’s law, Wein’s Law, Stefan’s law of radiation and Newton’s law of cooling.
(iii) ELECTROSTATICS,CURRENT ELECTRICITY AND MAGNETOSTATICS
Coloumb’s law, dielectric constant, electric field, lines of force, field due to dipole , electric flux, Gauss’s theorem and its applications; electric potential, potential due to a point charge; conductors and insulators,distribution of charge on conductors; capacitance, parallel plate capacitor, combination of capacitors, energy stored in a capacitor.
Electric current : Cells-primary and secondary, grouping of cells; resistance and specific resistivity and its temperature dependence. Ohm’s law, Kirchoff’s Law. Series and parallel circuits; Wheatstone’s Bridge and potentiometer with their applications. Heating effects of current, electric power, concept of thermoelectricity-Seebeck effect and thermocouple; chemical effect of current- Faraday’s laws of electrolysis.
Magnetic effects: Oersted’s experiment, Biot Savert’s law, magnetic field due to straight wire, circular loop and solenoid, force on a moving charge in a uniform magnetic field(Lorentz force),forces and torques on a current carrying conductor in a magnetic field, force between current carrying wires, moving coil galvanometer and conversion to ammeter and voltmeter.
Magnetostatics: Bar magnet, magnetic field, lines of force, torque on a bar magnet in a magnetic field, earth’s magnetic field; para, dia and ferro magnetism, magnetic induction, magnetic susceptibility.

d. ELECTROMAGNETIC INDUCTION AND ELECTROMAGNETIC WAVES
Induced e.m.f., Faraday’s law, Lenz’s law, self and mutual inductance; alternating currents, impedance and reactance, power in ac; circuits with L C and R series combination, resonant circuits, transformer and AC generator. Electromagnetic waves and their characteristics; electromagnetic spectrum from gamma to radio waves.

e. RAY AND WAVE OPTICS
Reflection and refraction of light at plane and curved surfaces, total internal reflection; optical fiber; deviation and dispersion of light by a prism; lens formula, magnification and resolving power; microscope and telescope, Wave nature of light, interference, Young’s double experiment; thin films, Newton’s rings. Diffraction: diffraction due to a single slit; diffraction grating, polarization and applications.

f. MODERN PHYSICS
Dual nature of Radiation - De Broglie relation, photoelectric effect, Alpha particle scattering experiment, atomic masses, size of the nucleus; radioactivity, alpha, beta and gamma particles/rays. Radioactive decay law, half life and mean life of radio active nuclei; Nuclear binding energy, mass energy relationship, nuclear fission and nuclear fusion. Energy bands in solids, conductors, insulators and semiconductors, pn junction, diode, diode as a rectifier, transistor action, transistor as an amplifier.

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