## BITSAT 2015 Logical Reasoning Syllabus

Logical Reasoning

The test is given to the candidates to judge their power of reasoning spread in verbal and nonverbal areas. The candidates  should  be  able  to  think  logically  so  that  they  perceive  the  data  accurately, understand  the relationships correctly, figure out the missing numbers or words, and to apply rules to new and different contexts. These  indicators  are  measured  through  performance  on  such  tasks  as  detecting  missing  links,  following directions, classifying words, establishing sequences, and completing analogies.

1. Verbal Reasoning

1.1         Analogy

Analogy means correspondence. In the questions based on analogy, a particular relationship is given and another similar relationship has to be identified from the alternatives provided.

1.2          Classification

Classification means to assort the items of a given group on the basis of  certain common quality they possess and then spot the odd option out.

1.3          Series Completion

Here series of numbers or letters are given and one is asked to either complete the series or find out the wrong part in the series.

1.4        Logical Deduction – Reading Passage

Here a brief passage is given and based on the passage the candidate is required to identify the correct or incorrect logical conclusions.

1.5       Chart Logic

Here a chart or a table is given that is partially filled in and asks to complete it in accordance with the information given either in the chart /table or in the question.

2. Nonverbal Reasoning

2.1        Pattern Perception

Here a certain pattern is given and generally a quarter is left blank. The candidate is required to identify the correct quarter from the given four alternatives.

2.2      Figure Formation and Analysis

The candidate is required to analyze and form a figure from various given parts.

2.3      Paper Cutting

It involves the analysis of a pattern that is formed when a folded piece of paper is cut into a definite design.

2.4       Figure Matrix

In this more than one set of figures is given in the form of a matrix, all of them following the same rule. The candidate is required to follow the rule and identify the missing figure.

2.5      Rule Detection

Here a particular rule is given and it is required to select from the given sets of figures, a set of figures, which obeys the rule and forms the .

## BITSAT 2015 English Proficiency Syllabus

English Proficiency

This test is designed to assess the test takers’ general proficiency in the use of English language as a   means of self-expression in real life situations and specifically to test the test takers’ knowledge of basic grammar, their vocabulary, their ability to read fast and comprehend, and also their ability to apply the elements of effective writing.

1. Grammar

1.1          Agreement, Time and Tense, Parallel construction, Relative pronouns

1.3          Voice, Transformation

1.4          Question tags, Phrasal verbs

2. Vocabulary

2.1          Synonyms, Antonyms, Odd Word, One Word, Jumbled letters, Homophones,

Spelling

2.2          Contextual meaning.

2.3          Analogy

3.1          Content/ideas

3.2          Vocabulary

3.3          Referents

3.4          Idioms/Phrases

3.5          Reconstruction (rewording)

4. Composition

4.1          Rearrangement

4.2          Paragraph Unity

## BITSAT 2015 Mathematics Syllabus

Mathematics

1. Algebra

1.1 Complex numbers, addition, multiplication, conjugation, polar representation, properties of modulus and principal argument, triangle inequality, roots of complex numbers, geometric interpretations; Fundamental theorem of algebra.

1.2 Theory of Quadratic equations, quadratic equations in real and complex number system and their solutions, relation between roots and coefficients, nature of roots, equations reducible to quadratic equations.

1.3 Arithmetic, geometric and harmonic progressions, arithmetic, geometric and harmonic means, arithmetico-geometric series, sums of finite arithmetic and geometric progressions, infinite geometric series, sums of squares and cubes of the first n natural numbers.

1.4 Logarithms and their properties.

1.5 Exponential series.

1.6 Permutations and combinations, Permutations as an arrangement and combination as selection, simple applications.

1.7 Binomial theorem for a positive integral index, properties of binomial coefficients, Pascal’s triangle.

1.8 Matrices and determinants of order two or three, properties and evaluation of determinants, addition and multiplication of matrices, adjoint and inverse of matrices, Solutions of simultaneous linear equations in two or three variables, elementary row and column operations of matrices.

1.9 Sets, Relations and Functions, algebra of sets applications, equivalence relations, mappings, one-one, into and onto mappings, composition of mappings, binary operation, inverse of function, functions of real variables like polynomial, modulus, signum and greatest integer.

1.10 Mathematical Induction

1.11 Linear Inequalities, solution of linear inequalities in one and two variables.

2. Trigonometry

2.1 Measurement of angles in radians and degrees, positive and negative angles, trigonometric ratios, functions and identities.

2.2 Solution of trigonometric equations.

2.3 Properties of triangles and solutions of triangles

2.4 Inverse trigonometric functions

2.5 Heights and distances

3. Two-dimensional Coordinate Geometry

3.1 Cartesian coordinates, distance between two points, section formulae, shift of origin.

3.2 Straight lines and pair of straight lines: Equation of straight lines in various forms, angle between two lines, distance of a point from a line, lines through the point of intersection of two given lines, equation of the bisector of the angle between two lines, concurrent lines.

3.3 Circles and family of circles :Equation of circle in various form, equation of tangent, normal & chords, parametric equations of a circle , intersection of a circle with a straight line or a circle, equation of circle through point of intersection of two circles, conditions for two intersecting circles to be orthogonal.

3.4 Conic sections : parabola, ellipse and hyperbola their eccentricity, directrices & foci, parametric forms, equations of tangent & normal, conditions for y=mx+c to be a tangent and point of tangency.

4. Three dimensional Coordinate Geometry

4.1 Co-ordinate axes and co-ordinate planes, distance between two points, section formula, direction cosines and direction ratios, equation of a straight line in space and skew lines.

4.2 Angle between two lines whose direction ratios are given, shortest distance between two lines.

4.3 Equation of a plane, distance of a point from a plane, condition for coplanarity of three lines, angles between two planes, angle between a line and a plane.

5. Differential calculus

5.1 Domain and range of a real valued function, Limits and Continuity of the sum, difference, product and quotient of two functions, Differentiability.

5.2 Derivative of different types of functions (polynomial, rational, trigonometric, inverse trigonometric, exponential, logarithmic, implicit functions), derivative of the sum, difference, product and quotient of two functions, chain rule.

5.3 Geometric interpretation of derivative, Tangents and Normals.

5.4 Increasing and decreasing functions, Maxima and minima of a function.

5.5 Rolle’s Theorem, Mean Value Theorem and Intermediate Value Theorem.

6. Integral calculus

6.1 Integration as the inverse process of differentiation, indefinite integrals of standard functions.

6.2 Methods of integration: Integration by substitution, Integration by parts, integration by partial fractions, and integration by trigonometric identities.

6.3 Definite integrals and their properties, Fundamental Theorem of Integral Calculus, applications in finding areas under simple curves.

6.4 Application of definite integrals to the determination of areas of regions bounded by simple curves.

7. Ordinary Differential Equations

7.1 Order and degree of a differential equation, formulation of a differential equation whole general solution is given, variables separable method.

7.2 Solution of homogeneous differential equations of first order and first degree

7.3 Linear first order differential equations

8. Probability

8.1 Various terminology in probability, axiomatic and other approaches of probability, addition and multiplication rules of probability.

8.2 Conditional probability, total probability and Baye’s theorem

8.3 Independent events

8.4 Discrete random variables and distributions with mean and variance.

9. Vectors

9.1 Direction ratio/cosines of vectors, addition of vectors, scalar multiplication, position vector of a point dividing a line segment in a given ratio.

9.2 Dot and cross products of two vectors, projection of a vector on a line.

9.3 Scalar triple products and their geometrical interpretations.

10. Statistics

10.1 Measures of dispersion

10.2 Measures of skewness and Central Tendency, Analysis of frequency distributions with equal means but different variances

11.Linear Programming

11.1 Various terminology and formulation of linear Programming

11.2 Solution of linear Programming using graphical method, feasible and infeasible regions, feasible and infeasible solutions, optimal feasible solutions (upto three nonitrivial constraints)