As you want syllabus of Aptitude Test conducted by IISC Bangalore for admission in M.Tech Program, here I am providing following:

IISC Bangalore Aptitude Test Syllabus for M.Tech

Mathematics:
Real Analysis:- Real valued functions of a real variable: continuity and differentiability, uniform convergence, sequences and series of real numbers and function, Riemann integration, fundamental theorem of integral calculus. Topology of R, Compactness and Connectedness.
Complex Analysis:- Continuity and differentiability, analytic functions. Cauchy’s theorem, Cauchy’s integral formula. Laurent’s series,Taylor and Maclaurin expansions, singularities, theory of residues and contour integration, conformal mappings.
Linear Algebra:- Vector Space: linear independence, basis, dimension, linear transformations and matrices, Systems of linear equations, rank and nullity, characteristic values and characteristic vectors, diagonalizability, Cayley-Hamilton theorem, characteristic and minimal polynomials, Jordan canonical form.
Abstract Algebra:- Groups: subgroups. Lagrange’s theorem, normal subgroup, quotient group, permutation groups. Cayley’s theorems, homomorphisms, Sylow theorems, Rings, Ideals Fields.
Ordinary Differential Equations: – First order ODEs and their solutions, singular solutions, existence and uniqueness of initial value problems for first order ODE. General theory of homogeneous and non-homogeneous linear differential equations. Variation of parameters. Types of singular points in the phase plane of an autonomous system of two equations.

Chemistry:
Structure and Bonding :- Atomic orbitals: electronic configuration of atoms (Aufbau principle); periodic properties of elements, chemical bonding, the concept of hybridization, molecular orbitals, electronic configuration of diatomic molecules, shapes of molecules and physical properties, bond angles, bond order and bond energies, bond length intermolecular forces, hydrogen bond, kinetic theory of gases, Solutions-Coligivative properties, activity coefficients; solids-types of solids, crystal structure and packing.
Spectroscopy: Principles of electronic, vibrational, rotational and magnetic resonance spectroscopy and mass spectrometry and their application to simple structural problems in chemistry. Dipole moment and molecular structure.
Chemical Energetics and Chemical Dynamics: Law of conservation of energy, enthalpy, entropy and free energy of chemical reaction, relationship between free energy change and equilibrium. Rates of chemical reactions, theories of chemical reactions and Arrhenius equation, homogeneous and heterogeneous catalysis, Electro-chemistry, strong and weak electrolytes, Debye-Huckel-Onsager treatment, Electrochemical cells. Electrode-electrolyte interface.
s, p, d, f, Block Elements and Coordination Compounds: General characteristics of each block, Nuclear Chemistry: Noble gas compounds, Lanthanides and actinides: Co-ordination compounds, Crystal and ligand field theories, Spectral and magnetic properties, Stereochemistry and isomerism.
Nomenclature of Organic Compounds and Stereo Chemistry of Organic Compounds: Compounds containing not more than three rings and three hetroatoms principles of chirality and optical activity, optical and geometrical isomerism, methods of resolution, conformational analysis of cyclohexanes.
Common Organic Reactions and Mechanisms : Formation, stability and structure of carbonium ions, carbanions and radicals: nucleophilic and electrophilic substitution and addition reactions, mechanism of SN1 and SN2reactions, the concept of aromaticity and characteristic reactions of aromatic compounds; elimination reactions, rearrangements such as Beckmann, Hoffman, Claisen, pinacol-pinacolone and benzidine rearrangement. Routine functional group transformations and interconversion of simple functionalities.

Biological Sciences:
Acids, Bases and solutions: Chemical reactions, Energy, Enzymes: Viruses. Prokaryotes and eukaryotes, Cellular organisation and function, Cell cycle, Genetic material, Inheritance, Vitamins and hormones, Body defence mechanisms, Evolution.
Structure of biomolecules: Viruses, bacteriophages, prokaryotic and eukaryotic cells, Nutrition and growth of prokaryotic and cukaryotic cells, Enzymes and enzyme kinetics, Intermediary metabolism and its regulation, Structure and function of cell membranes, Photosynthesis, Gene structure, expression and regulation, Transduction, conjugation and transformation, Recombinant DNA methodology Mutation and gene mapping: Micro-organisms and diseases: Environmental and industrial microbiology; Antimicrobial agents and their mode of action; Bio-geochemical cycles: Plant and animal hormones and their mode of action: Pathogens and host parasite relationships. Antibody structure and function; Humoral and cellular immune responses and their regulation, Morphogenesis and differentiation. Mechanisms and evolution of Animal behaviour; Systematics; Population dynamics and Community Ecology of plants and animals. Population Genetics, Basic Statistical Analysis. Basic statistics and Mathematics. Basic Principles in Evolutionary Biology

Ecological Sciences:
M Sc. Level: Population ecology, community ecology, ecosystem ecology, animal behaviour, evolutionary biology, population and classical genetics, conservation biology, environmental science, botany, zoology and statistics.
Class XII Level: Basic mathematics, physics, chemistry, cell and molecular biology.

Management:
PART A: Analytical Ability and Management Aptitude
Logical and analytical reasoning
Understanding of descriptive material and verbal ability
Quantitative aptitude with mathematical knowledge at +2 level.

PART B: Section I: Business Administration
Development of Management Thought: Principles of Management Functions and Processes of Management as they relate to Planning, Organizing, Directing and Control of Business and Industry. Man Power Planning, Selection and Recruitment. Training and Development, Compensation of Employees, Motivation and Communication.
Production Planning and Control, Facility. Location and Plant Layout Productivity Improvement through Work Study, Production and Inventory Control, Quality, Project Planning and Control using Networks.
Organizational Funds-Sources, Financial Statement, Determination of Cost of Capital, Use of Capital Budgeting, Time Value of Money, Cost-Value, Profit Analysis, Investment Decisions. Use of Accounting for Planning and Control, Marketing of Goods and Services, Buyer Behavior. Market Segmentation, Marketing Planning. Marketing Mix, Product Life-Cycle, Pricing, Distribution, Advertising and Promotion, Marketing Control. Management Information Systems, Applications of Computers. Statistical and Quantitative Techniques for Management Decisions.

PART B: Section II: Economics
Theories of Consumer Behavior, Production Function, Cost Function, Economics of Scale and Scope, Market Structure, Pricing of Products, National Income Accounting, National Income Measurement in India, Theories of Inflation, Price Indices and Inflation Measurement in India, Economic Reforms, Monetary Policy, Industrial Policy, Small Scale Industry, Foreign Investment. Theories of Economic Growth and Industrial Development

PART B: Section III: Psychology
Concepts and Principles of Human Behaviour-Determinants of Behavior-Attention-Perception-Memory-Learning-Motivation-Emotions-Frustration and Conflict. Application of Social Psychology in Industries- Attitudes and morale- the role of Industrial Psychology, its scope andapplication- Job Analysis-Job Evaluation-Training-Leadership-Communication-Group Counselling- Problems of Mental Health in Industries.

PART B: Section IV: Social Work
Nature of Industrial Society: Social consequences of industrialization, Industrialism and Indian Society. History Philosophy and fields of Social Work. Social casework, group work and community organization. Attitude, Morale and Motivation. Leadership, Groups and individual behavior.
Personnel Management: Concept and functions. Industrial labour legislation. Labour movement in India. Labour welfare. Social research- design and methodology

PART B: Section V: Management Science
Calculus & Linear Algebra: – Limits Differentiation, Integration, Addition, Subtraction, Multiplication, and Inversion of matrices, Linear System of Equations, Rank, Determinants, Eigenvalues & Eigenvectors.
Probability Theory :- Combinatorics, Probability Laws, Conditional Probability Bayes Theorem, Univariate Discrete & Continuous Random Variables. p.m.f. p.d.f. c.d.f. & m.g.f. Standard Univariate Discrete & Continuous Distributions: Binomial, Geometric, Poisson, Negative Binomial, Hyper-Geometric, Uniform, Exponential, Gamma. Normal & Weibull.
Model construction (LP, IP, MILP), Simplex Method, Sensitivity Analysis, Economic Interpretation, Allocation Problems: The Assignment and Distribution of Resources, Inventory Problems, Forecasting problems, Replacement. Maintenance, and Reliability Problems, Dynamic Programming, Queuing Problems, Sequencing and Coordination (PERT and CPM) Problems, Routing Problems in Networks, Simulation.
Applied Statistics: – One & Two Sample Parametric and Non-Parametric tests for Location and Scale, Analysis of Variance, Simple and Multiple Correlation & Regression, Analysis of Covariance, Chi-Square tests for categorical variables.
Classification of Information Systems, Software Engineering, UML, Database Management Systems, SQL, Fundamental Data Structures: Linked Lists, Stacks, Queues, Binary Trees, Directed Graphs.

PART C: Section I: German
Methodology and Didactics: Brief Introduction guidance in the methods of foreign language education – grammar – top setting method, audio-ingual method,vermiltelnd method, direct method, communicative approach, interkutureile method Features of this method, learning situation. Teaching situation, Lerner perspective, teacher perspective.
Sprachoebrauch: Write-Schilderung texts, report , Eroterung description , essay , etc. grammar , sentence structure , etc.