www.apeamcet.org EAMCET 2012 Syllabus : Engineering, Agricultural and Medical Common Entrance Test

[muthukalee]

Subject: MATHEMATICS

I. ALGEBRA: (a) Functions – Types of functions – Algebra of real valued functions (b) Mathematical induction and applications (c) Permutations and Combinations – linear and circular permutations – combinations. (d) Binomial theorem – for a positive integral index – for any rational index – applications – Binomial Coefficients. (e) Partial fractions (f) Exponential and logarithmic series (g) Quadratic expressions, equations and inequations in one variable. (h) Theory of equations – Relations between the roots and Coefficients in any equation – Transformation of equations – reciprocal equations. (i) Matrices and determinants – Types of matrices – Algebra of matrices – Properties of determinants – simultaneous linear equations in two and three variables – Consistency and inconsistency of simultaneous equations. (j) Complex numbers and their properties – De Moivre’s theorem – Applications – Expansions of trigonometric functions.

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II. TRIGONOMETRY: (a) Trigonometric functions – Graphs – periodicity (b) Trigonometric ratios of compound angles, multiple and sub-multiple angles, Transformations-sum and product rules (c) Trigonometric equations (d) Inverse trigonometric functions (e) Hyperbolic and inverse hyperbolic functions (f) Properties of Triangles (g) Heights and distances (in two-dimensional plane).

III. VECTOR ALGEBRA : (a) Algebra of vectors – angle between two non-zero vectors – linear combination of vectors – vector equation of line and plane (b) Scalar and vector product of two vectors and their applications c) Scalar and vector triple products, Scalar and vector products of four vectors.

IV. PROBABILITY : (a) Random experiments – Sample space – events – probability of an event – addition and multiplication theorems of probability – Conditional event and conditional probability - Baye’s theorem (b) Random variables – Mean and variance of a random variable – Binomial and Poisson distributions

V. COORDINATE GEOMETRY : (a) Locus, Translation of axes, rotation of axes (b) Straight line (c) Pair of straight lines (d) Circles (e) System of circles (f) Conics – Parabola – Ellipse – Hyperbola – Equations of tangent, normal, chord of contact and polar at any point of these conics, asymptotes of hyperbola. (g) Polar Coordinates (h) Coordinates in three dimensions, distance between two points in the space, section formula, centroid of a triangle and tetrahedron. (i) Direction Cosines and direction ratios of a line – angle between two lines (j) Cartesian equation of a plane in (i) general form (ii) normal form and (iii) intercept form – angle between two planes (k) Sphere – Cartesian equation – Centre and radius

VI. CALCULUS : (a) Functions – limits – Continuity (b) Differentiation – Methods of differentiation (c) Successive differentiation – Leibnitz’s theorem and its applications (d) Applications of differentiation (e) Partial differentiation including Euler’s theorem on homogeneous functions (f) Integration – methods of integration (g) Definite integrals and their applications to areas – reduction formulae (h) Numerical integration – Trapezoidal and Simpson’s rules (i) Differential equations – order and degree – Formation of differential equations – Solution of differential equation by variables seperable method – Solving homogeneous and linear differential equations of first order and first degree.

Subject – PHYSICS

I. MEASUREMENTS, UNITS AND DIMENSIONS : Introduction- units and Dimensions, Accuracy, precision of measuring instruments, Constant errors, systematic errors, environmental errors (errors due to external causes). Error due to imperfection, Random errors, Gross Errors, Absolute Errors, Mean absolute errors, Relative errors, percentage errors, Errors due to addition, subtraction, multiplication, division, powers of observed quantities, Significant figures, Fundamental and derived physical quantities / System of Units, definition of units in SI, Rules for writing units in SI, Derived units in SI, Multiple and submultiples of SI units, Dimensional formulae and dimensional equations, dimensional constants and dimensionless quantities. Principle of homogeneity of dimensions, Conversion of one system of units into another, to check correctness of an equation, to derive the relationship between different physical quantities.

II. ELEMENTS OF VECTORS : Classification of Physical quantities, geometrical representation of vectors, addition of vectors, equality of vectors, Resolution of a vector into components, null vector, unit vector in Cartesian co-ordinate system, position vector and its magnitude, Parallelogram law of addition of vectors, Derivation of expression for the magnitude and the direction of resultant vector, Special cases, Triangle law and polygon law of vectors, triangle law of addition of vectors, polygon law of addition of vectors, concept of relative velocity, application to relative motion of a boat in a river, motion of a boat across a river, shortest path, shortest time, Multiplication of vector with a scalar, product of two vectors, scalar product or dot product of two vectors, properties of scalar product, examples of scalar product, work done and energy, vector product of two vectors, properties of vector product of two vectors, examples of vector product of two vectors - torque, angular velocity and angular momentum.

III. KINEMATICS : Introduction : Motion in a straight line – displacement, speed and velocity, Uniform and non-uniform motion, average speed and instantaneous velocity, Uniformly accelerated motion, velocity-time and position-time graphs, equations for uniformly accelerated motion (graphical treatment), acceleration due to gravity, equations of motion of a freely falling body, Equations of motion of an object vertically projected upwards from the ground, Maximum height (H), Time of ascent, time of descent, velocity of the body on returning to the point of projection, Vertical projection of an object from a tower, Projectiles – oblique projection from ground, equation of trajectory, maximum height, time of ascent, time of flight, horizontal range, two angles of projection for the same range, velocity of projection at any instant, horizontal projection from the top of a tower, equation of trajectory, time of descent, range, velocity of the projectile (at any instant).

IV. DYNAMICS : Introduction- Newton’s laws of motion, applications of Newton’s laws. Objects suspended by strings, Atwood machine, blocks placed in contact with each other on frictionless horizontal surface, apparent weight in a lift, Impulse, law of conservation of linear momentum, conservation of linear momentum during collision, work, power, energy, K.E. & P.E. definition and derivation for both, Relation between KE and Linear momentum, conservative and non-conservative forces, workenergy theorem, Law of conservation of energy in case of freely falling body and vertically projected body.

V. COLLISIONS: Introduction – Elastic and inelastic collisions, Collisions in one dimension (Elastic collision only), body at rest, bodies moving in same direction and opposite directions, Co-efficient of restitution, definition, equation for height attained for freely falling body after number of rebounds on floor.

VI. CENTRE OF MASS (CM): Introduction- Centre of mass, difference between centre of mass and centre of gravity, coordinates of centre of mass, centre of mass of particles along a line, centre of mass of system of particles in a plane, center of mass of system of particles in space, motion of centre of mass (Velocity and acceleration of CM), characteristics of centre of mass, laws of motion of the centre of mass, velocity and acceleration, explosion.

VII. FRICTION : Introduction - cause of friction, advantages of friction, disadvantages of friction, methods of reducing friction, types of friction, static friction, kinetic (or) dynamic friction, rolling friction, Distinction between static and dynamic friction. Normal reaction, laws of friction, static friction, kinetic friction or Dynamic friction, Rolling friction, Angle of friction, motion of body on rough horizontal plane, motion of bodies on an inclined plane, Body at rest on the plane-Angle of repose-when the body is just ready to slide, when the body is sliding down. Motion of a body on smooth and rough inclined plane, body sliding down the plane, body sliding up the plane, pushing and pulling of a lawn roller. A lawn roller on a horizontal surface pulled by an inclined force, a roller on horizontal surface pushed by an inclined force.