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Sample papers for GITAM exam will cover questions from three subjects namely Physics, Chemistry and Mathematics. GITAM GAT is a computer based test (CBT) was conducted from April 16 to 30, 2017. The candidates can get GITAM GAT Sample Papers of the three sections mainly Mathematics, Physics and Chemistry. The sample papers of GITAM GAT will help the candidates to get an idea of the questions. GITAM Entrance Exam Model Papers Maths syllabus: SECTION – A: MATHEMATICS UNIT – 1 Functions, Types of functions, composition of functions, Inverse function, Properties of Inverse function, Extension of Domain, Periodic function, Transformation of graphs. Hyperbolic functions, Surds, Logarithms, Mathematical Induction. UNIT – 2: a) PARTIAL FRACTIONS: Resolving f(x)/g(x) into Partial fractions when g(x) contains: Non-repeated linear factors; g(x) contains repeated and non repeated linear factors. g(x) contains non-repeated and irreducible quadratic factors , g(x) contains repeated and non-repeated irreducible quadratic factors . (Note: Number of factors of g(x) should not exceed 4). b) EXPONENTIAL AND LOGARITHMIC SERIES: Expansion of ex for real x; log (1+x) expansion, condition on x (Note: Statements of the results and very simple problems such as finding the general term should only be given). c) Successive Differentiation: nth derivative of standard functions, libnitz theorem and its applications. d) Partial Differentiation: Partial derivative of Ist, 2nd orders and Euler’s Theorem on Homogeneous functions. UNIT – 3 QUADRATIC EQUATIONS & THEORY OF EQUATIONS: Quadratic equations in real and complex number system and their solutions. Reminder and Factor Theorems, common Roots, General Quadratic expression, Finding the range of a function, Location of roots, Solving inequalities using location of roots. THEORY OF EQUATIONS: The relation between the roots and coefficients in an equation; Solving the equation when two or more roots of it are connected by certain relations; Equations with real coefficients, imaginary roots occur in conjugate pairs and its consequences; Transformation of equations, Reciprocal equations. SECTION - A Page 2 of 6 GAT (UGTP) 2014 Syllabus - Mathematics UNIT – 4 a) BINOMIAL THEOREM AND ITS SIMPLE APPLICATIONS Binomial theorem for a positive integral index, general term and middle term, properties of Binomial coefficients and simple applications. b) SEQUENCES AND SERIES: Arithmetic and Geometric progressions, insertion of arithmetic, geometric means between two given numbers. Relation between A.M. and G.M. Sum to n terms of special series 2 3 n n n , , . Arithmetic - Geometric progression. UNIT – 5 PERMUTATIONS & COMBINATIONS: Definition of linear and circular permutations; To find the number of permutations of n dissimilar things taken ‘r’ at a time. To prove 1 1 1 r r r P P P n n r n from the first principles; To find number of Permutations of n Dissimilar things taken ‘r’ at a time when repetition of things is allowed any number of times.; To find number of circular Permutations of n Different things taken all at a time.; To find the number of Permutations of ‘n’ things taken ‘r’ at a time when some of them are alike and the rest are dissimilar; To find the number of combinations of ‘n’ dissimilar things taken ‘r’ at a time; To prove i) If r Cs n n C then n = r+s or r=s ii) 1 1 r r C r C C n n n . UNIT-6 MATRICES AND DETERMINANTS: Matrices, algebra of matrices, types of matrices, determinants and matrices of order two and three. Properties of determinants, evaluation of determinants, area of triangles using determinants. Adjoint and evaluation of inverse of a square matrix using determinants and elementary transformations, Test for consistency and solution of simultaneous linear equations in two or three variables using determinants and matrices, and rank of matrix. UNIT-7 VECTOR ALGEBRA AND 3D a) VECTOR ALGEBRA: Algebra of Vectors – angle between two non-zero vectors – Linear combination of vectors – Geometrical applications of vectors. Scalar and vector product of two, three and four vectors and their application. b) 3-D Geometry: Co-ordinates in three – dimensions – Distance between two points in the space – section formulas and their applications. DCs and DRs of line, angle between two lines. Cartesian equation of a plane in (i) SECTION - A Page 3 of 6 GAT (UGTP) 2014 Syllabus - Mathematics General form (ii) Normal Form (iii) Intercept Form (iv) Angle between two planes and angle between line and plane. Sphere – cartician equation – centre and radius. Section of sphere by plane. UNIT- 8 TRIGONOMETRY: Trigonometric ratios, Compound angles, multiple and sub-multiple angle, Transformations, Trigonometric expansions using Demovier’s Theorem. UNIT – 9 Trigonometric equations, Inverse Trigonometry and Heights and distances(only 2D problems). UNIT – 10 PROPERTIES OF TRIANGLES: Sine rule, cosine rule, Tangent rule, projection rule, Half angle formulae and area of triangle. In-circle and excircle of a Triangle. Pedal Triangle, Ex-central Triangle, Geometry relation of Ex-centres, Distance between centres of Triangle. m-n Theorem, problems and quadrilateral, regular polygon, solution of Triangle (Ambiguous cases). COMPLEX NUMBERS: Definitions, Integral Power of iota(i), Algebraic operations with complex numbers, square root of a complex number, Geometrical representation of a complex number, Modz, Arg of Z, polar term of Z, Eulors form of Z, Conjugate of Z, Properties of conjugate, solving complex equations, Demovre’s Theorem, Properties of √13, √14, √1𝑛,Geometrical applications of complex numbers. |
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