• English (Objective) : This paper will have questions from English Grammar such as choosing correct spellings, completion of sentences with suitable prepositions/articles, meaning of a word, synonym, antonym, meaning of idioms and phrases, choosing/ correcting grammatical errors in a part of given sentence, filling the blanks with correct form of verb, adjectives, adverbs etc. (Essay writing, Précis witting, unseen passage, for comprehension etc.)

• Mathematics

• UNIT-I

• NUMBER SYSTEM

• Statements of the algebraic and order properties of the system of natural numbers, integers, rational numbers and real numbers and simple basic deductions from these properties.

• The statements of the following results with illustrations but without proofs:

• Rational numbers as terminating decimals or as non-terminating recurring decimals, inadequacy of rationals.

• Irrational numbers as non-terminating, non-recurring decimals.

• Representation of real numbers as points on a line, absolute value of real numbers.

• Complex numbers, representation of complex numbers, real and imaginary parts, modulus and argument of a complex number, conjugate of a complex number.

• Statements of the principle of mathematical induction in respect of natural number and simple application.

• TRIGONOMETRY

• Angles and their measure in degrees and radians. Trigonometric function of angles of arbitrary magnitudes.

• Addition formulae, sine, cosine and tangent of multiples and submultiples of angles. Periodicity and graph of sine, cosine and tangent functions.

• Trigonometrical ratio of related angles.

• Solution of simple trigonometric equations.

• Sine and cosine formulae for triangles and simple cases of solution of triangles, problems on heights and distances.

• COORDINATE GEOMETRY

• Distance formula and section formula.

• Equation of line in a plane, general equation, equation of first degree, angle between two lines, parallel and perpendicular lines, distance of point from a line, family of lines.

• Equation of a circle, general equation, equation of tangent and normal to a circle, radical axis of two circles.

• Parametric representations of a circle.

• Conic sections, equations of parabola, ellipse and hyperbola in standard form.

• COORDINATE GEOMETRY IN SPACE

• Cartesian equations of lines and planes in three dimensions, angle between two lines, between a line and a plane and also between two planes, distance of a point from a plane, shortest distance between two lines, equations of any plane passing through the intersection of two planes.

• Equation of a sphere, general equation.

• UNIT-II

• FUNCTIONS

• Examples of real functions and their graphs.

• Algebra of real functions, ex. of polynomial & rational functions.

• One-one, on to and inverse functions.

• QUADRATIC EQUATIONS AND INEQUATIONS

• Quadratic equations and their solutions, relationship between the roots and coefficients, formation of quadratic equations with given root, criteria for the nature of the roots of a quadratic equations.

• Solution of quadratic in equations with their graphical representation.

• SEQUENCES AND SERIES

• AP, GP and their sums.

• PERMUTATIONS, COMBINATIONS & THE BINOMIAL THEOREM

• Elementary study of combinations, value of P and C, simple applications.

• Binomial theorem for a positive integral index and its proof.

• Statement of the binomial theorem for an arbitrary index & its application to approximations.

• UNIT-III

• MATRICES & DETERMINANTS

• Determinants of square matrices of order not exceeding 3 and application to solutions of linear equations having a single solution. Cramer’s rule.

• Sum and differences of matrices with not more than 3 rows & 3 columns.

• Geometrical transformations (reflection, rotation, translation and enlargement) in a plane and their representation matrices, composite of reflections in two parallel lines and two intersecting lines.

• Composition of transformations and products of matrices, non- commutativity of matrix multiplication, examples of non-zero matrices such that their product is zero matrix.

• Non-singular matrices and their inverses, adjoint of a matrix.

• Consistency of systems of two or three linear equations with two or three unknowns, linear equations in matrix notations, applications of matrices in solving simultaneous equations in three variables.

• CALCULUS

• Notions of right handed and left handed limit and the limit and continuity of a function introduced through examples and illustrated graphically as well as numerically. Properties of continuous functions, continuity of polynomial, trigonometric, exponential and logarithmic functions.

• Derivative of a function at a point, Derivative as instantaneous rate of change and slope of a curve. Tangents and normals.

• Derivative of polynomial function.

• Interpretation of the sign of the derivative at a point.

• UNIT-IV

• CALCULUS

• Derivatives of quotients of functions and of rational functions.

• Rolle’s Theorem illustrated geometrically, Derivations of the Lagrange’s Mean Value Theorem and its geometrical interpretation, Relation between the sign of derivative in an integral and monotonicity.

• Determination of maximum and minimum values of a function. Graphs of polynomial functions of degree not exceeding 4.

• Graphs and derivatives of trigonometric, inverse trigonometrical, exponential and logarithmic functions. Differentiation of implicit function, logarithmic differentiation, derivatives of functions expressed in parametric forms, derivative of higher order.

• Primitives of functions and their calculations in simple cases.

• Integration by substitution and by parts.

• The definition of definite integral as the limit of a sum motivated by the determination of areas. Evaluation of definite integrals, properties of definite integrals.

• Applications to determination of area under curves in simple differential cases. Differential Equations, order and degree, formation of a differential equation, general and particular solution of a differential equation, solution of a differential equation by the method of separable variables. Homogenous equation and their solution: Solution of the linear equation of the first order with constant coefficients.

• UNIT-V

• VECTORS

• Vectors as a directed line segment, Addition of vectors, Multiplication of a vector by real number.

• Position vector of a point. Section Formula.

• Application of vectors of some geometrical results.

• Scalar and vector product of two vector.

• Scalar triple product, vector triple product.

• STATISTICS

• Population and sample.

• Measures of central tendency and dispersion.

• Point and interval estimation (of mean only).

• Scatter diagrams and Pearson’s correlation coefficient.

• Calculation of the regression coefficient and the two lines of regression by the methods of least squares.

• PROBABILITY

• Random experiments and sample space, events.

• Probability on a discrete sample space, addition theorem.

• Conditional probability, multiplication theorem

• Independent events

• Random variables (mean and variance. Calculations for simple probability distributions).

• Normal distribution.

• Mental Ability : This paper will have the topics of logical reasoning, graphical analysis, analytical reasoning, and quantitative comparisons and series formation.

Note :-
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