Basic English Grammar, Tenses, Articles and Adjectives, Prepositions, Conjunctions, Verb-Subject Agreement, Vocabulary: Idioms and Words in Context, Reading Comprehension, Sequencing of Ideas, Critical Reasoning and Verbal Deduction

Data Interpretation: Tables, Graphs and Charts, Numerical Computation and Estimation, Ratios, Percentages, Powers and Exponents, Logarithms, Permutations and Combinations, Mensuration, Geometry and Elementary Statistics, Probability

Logic: Deduction and Induction, Analogy, Numerical Relations and Reasoning

Transformation of Shapes: Translation, Rotation, Scaling, Mirroring, Assembling and Grouping, Paper Folding, Cutting and Inking, Patterns in 2 and 3 Dimensions

Limits, Continuity and Differentiability, Mean Value Theorems and Taylor Series, Maxima and Minima, Multiple Integrals

Systems of Linear Equations, Eigenvalues and Eigenvectors, Quadratic Forms and Positive Definiteness, Generalised Inverses

Sample Spaces and Axioms, Conditional Probability and Independence, Bayes' Theorem

Univariate and Multivariate Distributions, Expectation, Variance and Moments, Moment Generating and Characteristic Functions, Joint, Marginal and Conditional Distributions, Transformations of Random Variables, Order Statistics

Modes of Convergence, Law of Large Numbers, Central Limit Theorem, Chebyshev Inequality

Discrete: Bernoulli, Binomial, Poisson, Geometric, Negative Binomial, Hypergeometric, Continuous: Uniform, Normal, Exponential, Gamma, Beta, Cauchy, Lognormal, Sampling Distributions: Chi-Square, t and F

Method of Moments and Maximum Likelihood, Sufficiency, Completeness and Exponential Family, Unbiasedness, Consistency, Efficiency, Rao-Blackwell and Lehmann-Scheffe Theorems, Cramer-Rao Lower Bound, Confidence Intervals

Neyman-Pearson Lemma and Most Powerful Tests, Uniformly Most Powerful Tests, Likelihood Ratio Tests, Tests for Means, Variances and Proportions, Goodness of Fit: Chi-Square, Kolmogorov-Smirnov, Nonparametric Tests: Sign, Wilcoxon, Runs, Sequential Probability Ratio Test

Multivariate Normal Distribution, Hotelling's T² and MANOVA, Principal Component Analysis, Factor Analysis and Discriminant Analysis, Cluster Analysis Basics

Simple and Multiple Linear Regression, Least Squares Estimation and Gauss-Markov Theorem, Inference on Regression Coefficients, Polynomial Regression and Dummy Variables, Residual Analysis, Multicollinearity, Diagnostics, Logistic Regression Basics

Completely Randomised and Randomised Block Designs, Latin Square Design, Factorial Designs: 2², 2³ and 2k, Confounding and Fractional Factorials, Analysis of Covariance, Missing Plot Techniques

Markov Chains: Classification of States, Stationary Distributions, Poisson Process and Its Variants, Birth-Death Processes, Random Walk and Gambler's Ruin, Queuing Models: M/M/1, M/M/c

LP Formulation and Graphical Method, Simplex Method and Big-M/Two-Phase, Duality and Sensitivity Analysis, Transportation and Assignment Problems, Game Theory Basics