TIFR GS Syllabus 2027: Latest Subject-wise Syllabus & Topics

Subject

Topic

Biology Syllabus for JGEEBILS Exam

• Biology

• Physics

• Chemistry

• Mathematics

Subject

Topic

TIFR GS Chemistry

• Physical Chemistry

• Organic Chemistry

• Inorganic Chemistry

• Analytical Chemistry

• Electrochemistry

• Quantum Chemistry

• Biophysics

• Thermodynamics

• Spectroscopy -

• 
  

  1. Nuclear Magnetic Resonance (NMR)

  2. Fluorescence spectroscopy

  3. Infrared (IR) spectroscopy

  4. Ultraviolet (UV) spectroscopy

  5. X-ray spectroscopy

• Logic

• Statistics

• Mathematical methods

Topic

Sub-Topics

Discrete Mathematics

• Sets and relations

• Combinatorics (counting)

• Elementary probability theory

• Graph theory

• Propositional logic

• Predicate logic

Formal Languages, Automata Theory and Computability

• Formal languages.

• Automata theory.

• Computability.

Data Structures and Algorithms

• Arrays.

• Lists.

• Trees.

• Sorting.

• Searching.

• Graph algorithms.

• Complexity of problems.

• NP-completeness.

Fundamentals of Programming Languages and Compilers

• Control structures.

• Parameter-passing mechanisms.

• Recursion.

• Parsing.

• Type checking.

• Memory management.

Operating Systems and Concurrency

• Operating systems.

• Concurrency.

Switching Theory and Digital Circuits

• Switching theory.

• Digital circuits

Theory of Databases

Theory of databases

Topic

Sub-Topics

Engineering Mathematics

• Probability

• Linear algebra

• Basic optimization

• Basic analysis

• Calculus

Electrical and Computer Sciences

• Signals and systems

• Digital signal processing

Topic

Sub-Topics

Algebra

• Definitions and examples of groups.

1. Finite and infinite groups.

2. Commutative and non-commutative groups.

• Cyclic groups.

• Subgroups.

• Homomorphisms.

• Quotient groups.

• Group actions.

• Sylow theorems.

• Definitions and examples of rings and fields.

• Integers and their basic properties.

• Polynomial rings and their basic properties.

• Vector spaces.

• Matrices.

• Determinants.

• Ranks of linear transformations.

• Characteristic polynomials.

• Minimal polynomials.

• Symmetric matrices.

• Inner products.

• Positive definiteness.

Analysis

• Basic properties of real numbers.

• Basic properties of complex numbers.

• Convergence of sequences of real numbers.

• Convergence of sequences of complex numbers.

• Convergence of series of real numbers.

• Convergence of series of complex numbers.

• Continuity.

• Differentiability.

• Riemann integration of real-valued functions defined on finite or infinite intervals.

• Elementary functions:

• 
  

  1. Polynomial functions.

  2. Rational functions.

  3. Exponential functions.

  4. Logarithmic functions.

  5. Trigonometric functions.

• Sequences of functions.

• Series of functions.

• Different types of convergence of sequences and series of functions.

Geometry and Topology

• Elementary geometric properties of common shapes and figures in two-dimensional Euclidean space.

• Elementary geometric properties of common shapes and figures in three-dimensional Euclidean space.

• Triangles.

• Circles and discs.

• Spheres.

• Plane analytic geometry (coordinate geometry).

• Trigonometry.

• Definition and basic properties of metric spaces.

• Examples of subsets of Euclidean spaces of any dimension.

• Connectedness.

• Compactness.

• Convergence in metric spaces.

• Continuity of functions between metric spaces.

General Mathematics

• Pigeonhole principle (box principle).

• Mathematical induction.

• Elementary properties of divisibility.

• Elementary combinatorics:

• 
  

  1. Permutations.

  2. Combinations.

  3. Binomial coefficients.

• Elementary reasoning with graphs.

• Elementary probability theory.

Topic

Sub-Topic

Real Analysis

• Riemann integration.

• Riemann–Stieltjes integration in R

• Sequences and series of functions.

• Uniform convergence.

• Arzelà–Ascoli theorem.

• Functions of several variables.

• Continuity.

• Directional derivatives.

• Inverse function theorem.

• Implicit function theorem.

• Fixed-point theorems.

Ordinary Differential Equations (ODEs)

• Existence and uniqueness of solutions of initial-value problems for first-order ODEs.

• General theory of homogeneous linear ODEs.

• General theory of non-homogeneous linear ODEs.

• Stability of linear ODEs.

• Sturm–Liouville boundary-value problems.

• Green's functions.

Linear Algebra

• Vector spaces.

• Linear transformations.

• Algebra of matrices.

• Rank of matrices.

• Determinants of matrices.

• Linear equations.

• Eigenvalues and eigenvectors.

• Cayley–Hamilton theorem.

• Minimal polynomial.

• Algebraic multiplicity.

• Geometric multiplicity.

• Spectral theorem.

• Jordan forms.

Topology

• Topological spaces.

• Induced topology.

• Product topology.

• Separation axioms.

• Continuous maps.

• Homeomorphisms.

• Connectedness.

• Compactness.

• Baire category theorem.

Functional Analysis

• Normed linear spaces.

• Banach spaces.

• Continuous linear functionals.

• Dual spaces.

• Hahn–Banach theorem.

• Open mapping theorem.

• Closed graph theorem.

• Uniform boundedness principle.

• Weak convergence.

• Hilbert spaces.

• Riesz representation theorem for Hilbert spaces.

Subject Name

Topics

Physics

• Classical Mechanics

• Mathematics Relevant to Physics

• Electricity and Magnetism

• Quantum Mechanics

• Heat, Thermodynamics and Statistical Physics

• General Physics

• Modern Physics

• Electronics

• Experimental Physics

Topic

Sub-Topic

Quantitative Reasoning, Scientific Literacy and Technical Comprehension

• Quantitative reasoning.

• Scientific literacy.

• Technical comprehension.

• Logical reasoning, as described on the official HBCSE admissions page.

Education, Social Sciences and Cognitive Sciences

• Human cognition.

• External representations.

• Conceptual changes.

• Education policies.

• Sociology of science.

• Educational philosophies.

Biology

• Questions testing the ability to apply and reason with Biology concepts.

• Content up to CBSE Standard XII level.

Chemistry

• Questions testing the ability to apply and reason with Chemistry concepts.

• Content up to CBSE Standard XII level.

Mathematics

• Questions testing the ability to apply and reason with Mathematics concepts.

• Content up to CBSE Standard XII level.

Physics

• Questions testing the ability to apply and reason with Physics concepts.

• Content up to CBSE Standard XII level.

Critical Reasoning and Descriptive Assessment

The official examination instructions also include a descriptive section. The HBCSE page describes tasks involving:

• Briefly describing a research topic of interest related to science, mathematics, or design and technology education.

• Explaining why the proposed research is important.

• Outlining possible educational outcomes.

• Writing short essays on topics provided in the examination.

Topic

Sub-Topic

General Aptitude

• General aptitude.

• General knowledge.

• Analytical skills.

• English language skills.

Mathematical and Quantitative Skills

• Basic mathematical skills.

• Basic quantitative skills.

Wildlife and Conservation Science

• Basic Biology.

• Ecology.

• Conservation issues.

Essay

• An essay on a topic in ecology or wildlife conservation.

• The official instructions specify a word limit of 750 words.