SYLLABUS FOR GSAT-2011 ENTRANCE TEST for admission into B.C.A.
(Test Code No: 108)
(Test Code No: 108)
SECTION-A (15 bits: 15 Marks)
FUNCTIONS: Function, Equality of functions, Types of functions, Composite function, One-one and onto functions, Inverse function.
LOGARITHMS and SURDS: Definition, Fundamental Logarithmic identities, Common Logarithms Classification of Surds, Square root of a quadratic surd, Rationalisation of surds
MATHEMATICAL INDUCTION: Principle of Mathematical Induction, Application of Mathematical Induction Σ n, Σ n2 , Σ n3 x-y divides xn- yn for all positive integral.
BINOMIAL THEOREM:
Binomial Theorem for Positive Integral Index, Binomial Coefficients- middle terms, independent term of x.
SECTION-B (20 bits: 20 Marks)
PARTIAL FRACTIONS: Rational Function, Proper Fraction, Improper Fractions, Different types of Partial Fractions
MATRICES : Matrix definition, types of matricestranspose of a matrix, determinants of a square matrix, properties of determinants, system of non-homogeneous linear equations by Cramer’s rule,inverse of a matrix, singular and non-singular matrices, solution of system of linear equations by matrix inversion method .
TRIGONOMETRY: Trigonometric Rations of compound Angles, Trigonometic ratios of Multiple and Sub-Multiple Angles, Transformations, Trigonometric equations, inverse trigonometric functions, Hyperbolic functions, properties of triangles, complex numbers
SECTION-C (25 bits: 25 Marks)
VECTOR ANALYSIS : Vector addition, vector equation of a line and plane , scalar and vector product of two vectors. Scalar and vector point function – vector operator del, Gradient, divergence and curl.
GEOMETRY: Definition and equation of locus, change of axes, Elements of conics, parabola, ellipse, hyperbola and polar coordinates vectors. Three dimensional coordinates , direction cosines.
CALCULUS : Definition of limit , infinite limits. standard limits, Continuity, First principle of derivative, properties, rules for finding the Sum, product, quantitative and function of function, Functions of two or more variable partial derivatives, Euler’s theorem. Indefinite integrals, Integration by substitution, Integration by parts.
MODEL QUESTIONS
1. The angle between any two diagonals of a cube is equal to ( )
(a) Cos-1 (1/2) (b) Cos-1 (1/4) (c) Cos-1 (1/3) (d) Cos-1 (1/5)
2. The value of tan 15 0 + tan 75 0 < ( )
(a) 4 (b) 3 (c) 2 (d) None of these
3. For a function f to have inverse it should be ( )
(a) one-one (b) onto (c) both one-one and onto (d) identity
FUNCTIONS: Function, Equality of functions, Types of functions, Composite function, One-one and onto functions, Inverse function.
LOGARITHMS and SURDS: Definition, Fundamental Logarithmic identities, Common Logarithms Classification of Surds, Square root of a quadratic surd, Rationalisation of surds
MATHEMATICAL INDUCTION: Principle of Mathematical Induction, Application of Mathematical Induction Σ n, Σ n2 , Σ n3 x-y divides xn- yn for all positive integral.
BINOMIAL THEOREM:
Binomial Theorem for Positive Integral Index, Binomial Coefficients- middle terms, independent term of x.
SECTION-B (20 bits: 20 Marks)
PARTIAL FRACTIONS: Rational Function, Proper Fraction, Improper Fractions, Different types of Partial Fractions
MATRICES : Matrix definition, types of matricestranspose of a matrix, determinants of a square matrix, properties of determinants, system of non-homogeneous linear equations by Cramer’s rule,inverse of a matrix, singular and non-singular matrices, solution of system of linear equations by matrix inversion method .
TRIGONOMETRY: Trigonometric Rations of compound Angles, Trigonometic ratios of Multiple and Sub-Multiple Angles, Transformations, Trigonometric equations, inverse trigonometric functions, Hyperbolic functions, properties of triangles, complex numbers
SECTION-C (25 bits: 25 Marks)
VECTOR ANALYSIS : Vector addition, vector equation of a line and plane , scalar and vector product of two vectors. Scalar and vector point function – vector operator del, Gradient, divergence and curl.
GEOMETRY: Definition and equation of locus, change of axes, Elements of conics, parabola, ellipse, hyperbola and polar coordinates vectors. Three dimensional coordinates , direction cosines.
CALCULUS : Definition of limit , infinite limits. standard limits, Continuity, First principle of derivative, properties, rules for finding the Sum, product, quantitative and function of function, Functions of two or more variable partial derivatives, Euler’s theorem. Indefinite integrals, Integration by substitution, Integration by parts.
MODEL QUESTIONS
1. The angle between any two diagonals of a cube is equal to ( )
(a) Cos-1 (1/2) (b) Cos-1 (1/4) (c) Cos-1 (1/3) (d) Cos-1 (1/5)
2. The value of tan 15 0 + tan 75 0 < ( )
(a) 4 (b) 3 (c) 2 (d) None of these
3. For a function f to have inverse it should be ( )
(a) one-one (b) onto (c) both one-one and onto (d) identity
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