PAPER- I
ENGLISH AND GENERAL KNOWLEDGE
1. General Science 2. Idioms and Phrases 3. Events of National & International Importance 4. Fill in the blanks with suitable words/prepositions 5. Correction of sentences 6. Change of Voice 7. Current Affairs 8. Indian National Movement 9. History of India
MATHEMATICS
Algebra : Solution of quardratic equations, relationship between their roots and coefficients. Equations reducible to quadratic form. Symmetric Functions of roots. Formation of a quadratic equation with given roots. Arithmetic progression, Geometric progression and Arithmetico-Geometric series. Series of natural numbers (S n, S n2, S n3). Mathematical induction. Permutations and Combinations, Binomial theorem for any index. Complex numbers. Algebra of complex numbers. Modulus and argument of a complex number. Conjugate of a complex number. Triangle inequality representation of complex number in Geometric form, polar form & exponential form. Square Root of a complex number. Cube roots of unity. De-Moivre’s Theorem with simple applications. Vectors, their Scalar product and cross product. Scalar triple product and its applications. Trigonometry : Trigonometric ratios and their relations. Trigonometric Identities. T-ratios of allied angles. Addition and Subtraction formulae. Transformation of product into sum or difference and vice-versa. T-ratios of multiple and sub-multiple angles. Inverse trigonometric functions. Solution of trigonometric equations. Relations between sides & Trigonometrically ratios of the angles of a triangle. Solution of triangles. Heights and distances. Matrices and Determinants : Determinants of order 2 and 3, their elementary properties. Cramer’s rule. Definition of a matrix. Types of matrices. Equality of matrices. Operations on matrices. Symmetric & Skew Symmetric matrices. Singular and non-singular matrices. Minors and cofactors. Adjoint and inverse of a matrix. Application of matrices in solving simultaneous linear equations in 2 and 3 variables. Coordinate Geometry : Rectangular Cartesian co-ordinates. Distance between two points. Section formulae. Locus of a point. Equation of a straight line in various forms. Angle between two given lines. Condition for two lines to be parallel or perpendicular. Distance of a point from a line. Line through point of intersection of two given lines. Concurrency of lines. Equation of a circle in various forms. Intersection of a circle with a straight line. Equations of tangent and normal to a circle. Intersection of two circles. Parametric representation of equation of a circle. Equations of the parabola, ellipse and hyperbola in the standard forms & parametric form. Condition for y = mx + c to be a tangent and point of tangency. Calculus : Function, its domain and range. Limit, continuity and differentiability of a function. Derivative of sum, difference, product and quotient of two functions. Derivative of algebraic, trigonometric, exponential, logarithmic, hyperbolic and Inverse trigonometric functions. Chain rule. Derivative of functions expressed in implicit and parametric forms. Logarithmic differentiation. Tangents and Normals. Rate measure & error. Maximum and Minimum values of a function. Integration as the inverse process of differentiation. Integration by parts, by substitution and by partial fractions. Integration of rational and irrational functions. Definite integral and its application for the determination of area (simple cases). Trapezoidal & Simpson Rules.
PAPER-II
PHYSICS
Units and dimensions, SI Units, displacement, velocity, acceleration. Projectiles, circular motion, concepts of relative motion; Newton’s Law of motion, concepts of uniformly accelerated frames, momentum, frictional force and gravitational force, work, energy, power, conservation of momentum and energy. Universal law of gravitation, gravitational potential and fields, acceleration due to gravity. Angular momentum, torque, equilibrium of rigid bodies. Hook’s Law, Young’s modulus, shear and bulk moduli, Bernoulli’s theorem and its applications. Simple concept of amplitude, frequency and phase, longitudinal and transverse waves, harmonic and wave motions, superposition of waves, progressive and stationary waves, vibration of strings and aircolumns, resonance, beats. Velocity of sound, Echoes, Doppler effect. Thermal expansion of solids, liquids and gases. Kinetic theory of gases, specific heats, Isothermal and adiabatic process, laws of thermodynamics & their applications, Stefans law and Newton’s law of cooling, Coulombs law, electric fields and electric potentials, lines of forces. Capacitance, dielectric constant, parallel plate capacitor, capacitor in series and parallel, energy stored in capacitor, charging and discharging of capacitors. Electric current, Ohm’s law, series and parallel arrangements of resistances and cells. Kirchoffs law and its applications to network, heating effects of current. Biot-Savart’s law and its application. Force on a moving charge and on a current carrying wire in magnetic field. Magnetic moment of a current loop, effect of a uniform magnetic field on current loop, moving coil glavanometer, voltmeter, ammeter. Electromagnetic induction, Faraday’s and Lenz’s law, definitions of self and mutual-inductance. Rectilinear propagation of light. Reflection and refraction at plane and curved surface, total internal reflection and critical angles. Deviation and dispersion of light by a prism.Thin lens, combinations of mirror and lens, magnifications, microscope, telescope.
Wave nature of light, interference, diffraction and polarization, Radioactivity, alpha, beta and gamma radiations, laws of radioactivity, decay constant, half life and mean life. Photoelectric effect. Bohr’s theory of hydrogen like atoms, x-rays production and properties. Atomic nucleus, binding energy and its calculation. Fission and fusion processes. Elementary concepts of thermionic emission and work function, diode valve as a rectifier, Elementary ideas of conductor, semi-conductor and insulator, intrinsic and extrinsic semi-conductor, P-N junctions as a rectifier.
CHEMISTRY
Atomic Structure & Classification of Elements: Rutherford’s Model, spectra of hydrogen atom, Bohr’s model, quantum numbers, Pauli’s exclusion principle, Hund’s rule, Aufbau principle, electronic configuration of elements, shapes of s,p and d orbitals. Periods and groups, classification of elements with respect to s, p and d-block, periodicity in properties, namely atomic and ionic radii, ionization energy, electronegativity and oxidation states. Stoichiometry : Calculations involving common oxidation reduction, neutralization and displacement reactions, use of mole concept. Behaviour of Gases : Avogadro’s Law, equation of state and ideal gas, Vander waal’s equation, diffusion of gases, kinetic theory of gases, average, root mean square and most probable velocity and their relation with temperature, Gay Lussac’s Law. Solutions : Expressing concentration in terms of mole fraction, molality, molarity and normality, Raoult’s Law and molecular weight determination from lowering of vapour pressure. Chemical Equilibrium, Kinetics and Energetics: Law of mass action, equilibrium constants Kc, Kp and their relationships, Le-Chatelier’s principle and its applications, ionic equilibria in aqueous solutions, solubility product, common ion effect, acid-base theories (Bronsted and Lewis), hydrolysis of salts, pH, buffer solutions. Rate of reaction, order of reaction, molecularity, rate constant and half-life period of first order reaction, variations of rate constant with temperature (Arrhenius equation). Heat of formation, heat of combustion and heat of reaction, Hess’s Law, bond energy.
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