Table of Contents9 sections
Group-II includes six science subjects. CSS aspirants can select ONE subject from this group carrying 100 marks. This guide covers all science subjects with their complete syllabi.
Group-II Overview
| Code | Subject | Marks | MCQs | Best For |
|---|---|---|---|---|
| 12 | Physics | 100 | 20 | Physics BSc/MSc graduates |
| 13 | Chemistry | 100 | 20 | Chemistry BSc/MSc graduates |
| 14 | Applied Mathematics | 100 | 20 | Mathematics graduates |
| 15 | Pure Mathematics | 100 | 20 | Mathematics graduates |
| 16 | Statistics | 100 | 20 | Statistics, Math graduates |
| 17 | Geology | 100 | 20 | Geology graduates |
Note: Candidates who opt for Applied Mathematics cannot select Pure Mathematics, and vice versa.
1. Physics (100 Marks)
Physics is one of the challenging but scoring subjects for science background candidates.
Complete Syllabus
Part I: Mathematical Physics (15 marks)
Vector Analysis:
- Vector Algebra
- Gradient, divergence, curl
- Gauss's theorem
- Stokes' theorem
- Line, surface and volume integrals
- Applications to physics
Part II: Mechanics (15 marks)
Classical Mechanics:
- Inertial and non-inertial frames
- Centre of mass and reduced mass
- Conservation laws
- Scattering in lab and CM frames
- The rigid body
- Rotational and spinning motions
Lagrangian and Hamiltonian Mechanics:
- Lagrangian formulation
- Hamiltonian formulation
- Variational principle
- Hamilton's equations
- Poisson brackets
Special Theory of Relativity:
- Postulates of special relativity
- Lorentz transformation
- Time dilation
- Length contraction
- Relativistic energy and momentum
- Particle collisions
Part III: Waves and Oscillations, Optics (15 marks)
Oscillations:
- Simple harmonic motion
- Damped oscillations
- Forced oscillations
- Coupled oscillations
- Lissajous figures
Wave Motion:
- The wave equation
- Traveling waves
- Standing waves
- Beats
- Group velocity
- Phase velocity
Geometrical Optics:
- Fermat's principle
- Refraction
- Reflection at plane and curved surfaces
- Thin lenses
- Cardinal points and planes
- Thick lenses
Physical Optics:
- Interference of light
- Diffraction: Fresnel and Fraunhofer
- Polarization
- Double refraction
- Optical activity
Part IV: Electromagnetism (15 marks)
Electrostatics:
- Electric field and electric potential
- Coulomb's law
- Gauss's law
- Laplace's and Poisson's equations
- Boundary value problems
- Multipole expansions
- Dielectrics
Electrodynamics:
- Ohm's, Faraday's laws
- Maxwell's equations
- Energy in electromagnetic field
- Poynting theorem
- Electromagnetic waves
- Wave guides
Magnetostatics:
- Biot-Savart law
- Ampere's law
- Magnetic vector potential
- Magnetic dipole
- Magnetism in matter
Part V: Quantum Mechanics (15 marks)
Foundations:
- Inadequacies of classical physics
- Origins of quantum theory
- Planck's radiation law
- Bohr's atomic model
Wave Mechanics:
- Wave particle duality
- Uncertainty principle
- Schrodinger equation
- Operators and observables
- Eigenvalues and eigenfunctions
Applications:
- Particle in a box
- Step potential
- Tunneling
- Harmonic oscillator
- Hydrogen atom
Part VI: Atomic and Molecular Spectroscopy (15 marks)
Atomic Spectra:
- One and two electron spectra
- Fine structure
- Selection rules
- Spin-orbit coupling
- Pauli's exclusion principle
Molecular Spectroscopy:
- Molecular orbitals
- Rotational spectra
- Vibrational spectra
- Electronic spectra
- Raman effect
Effects in Fields:
- Zeeman effect
- Stark effect
- Hyperfine structure
Part VII: Statistical Mechanics (10 marks)
- Classical and quantum statistics
- Maxwell-Boltzmann distribution
- Bose-Einstein statistics
- Fermi-Dirac statistics
- Partition function
- Black body radiation
Recommended Books for Physics
| Book | Author |
|---|---|
| Concepts of Modern Physics | Arthur Beiser |
| Introduction to Quantum Mechanics | David J. Griffiths |
| Introduction to Electrodynamics | David J. Griffiths |
| Classical Mechanics | Herbert Goldstein |
| Optics | Eugene Hecht |
| Mathematical Methods for Physicists | George B. Arfken |
| Statistical Mechanics | K. Huang |
2. Chemistry (100 Marks)
Chemistry requires thorough understanding of both theoretical concepts and practical applications.
Complete Syllabus
Part A: Physical Chemistry (34 marks)
Thermodynamics (10 marks):
- First law: Energy, work, heat, enthalpy
- Second law: Entropy, free energy, chemical potential
- Third law of thermodynamics
- Partial molar properties
- Concept of fugacity
- Chemical equilibrium
Electrochemistry (8 marks):
- Faraday's laws of electrolysis
- Strong and weak electrolytes
- Electrical conductance
- EMF and cell potentials
- Potentiometric titrations
- Applications of EMF measurements
Reaction Kinetics (8 marks):
- Rate laws and order of reactions
- Activation energy
- Collision theory
- Transition state theory
- Homogeneous catalysis
- Enzyme kinetics
Quantum Mechanics (8 marks):
- Historical development
- Schrodinger wave equation
- Particle in a box
- Hydrogen atom
- Approximate methods
- Spectroscopy principles
Part B: Organic Chemistry (33 marks)
Fundamentals (5 marks):
- Hybridization (sp, sp2, sp3)
- Bonding in organic molecules
- Electronegativity
- Inductive and resonance effects
- Acidic and Basic strength
- Tautomerism
Stereochemistry (8 marks):
- Geometric isomerism
- Optical isomerism
- Chirality
- Configuration: R and S
- Conformational analysis
- Stereoisomeric relationships
Reaction Mechanisms (12 marks):
- Free radicals
- Carbocations and carbanions
- Addition reactions
- Elimination reactions (E1, E2)
- Substitution reactions (SN1, SN2)
- Nucleophilic substitutions
- Electrophilic substitutions
- Rearrangements
Functional Group Chemistry (8 marks):
- Hydrocarbons: alkanes, alkenes, alkynes, aromatics
- Alcohols, phenols, ethers
- Aldehydes and ketones
- Carboxylic acids
- Amines and amides
- Heterocyclic compounds
Part C: Inorganic Chemistry (33 marks)
Atomic Structure (6 marks):
- Quantum numbers
- Aufbau principle
- Hund's rule
- Pauli's exclusion principle
- Electronic configuration
- Periodic properties
Chemical Bonding (8 marks):
- Ionic bond
- Covalent bond
- Valence bond theory
- Molecular orbital theory
- Crystal field theory
- Metallic bonding
- Hydrogen bonding
Acids, Bases and Non-aqueous Solvents (6 marks):
- Arrhenius theory
- Bronsted-Lowry theory
- Lewis theory
- HSAB principle
- Non-aqueous solvents
- Solvents as acids and bases
Coordination Chemistry (8 marks):
- Werner's theory
- Types of ligands
- Nomenclature
- Isomerism
- Crystal field theory
- Applications of coordination compounds
Chemistry of Main Group Elements (5 marks):
- Occurrence and extraction
- Properties and uses
- Compounds of s-block elements
- Compounds of p-block elements
- Noble gases and their compounds
Recommended Books for Chemistry
| Book | Author |
|---|---|
| Atkin's Physical Chemistry | P.W. Atkins |
| A Textbook of Physical Chemistry | S. Glasstone |
| Organic Chemistry | Morrison & Boyd |
| Organic Chemistry | Paula Bruice |
| Inorganic Chemistry | Shriver & Atkins |
| Concise Inorganic Chemistry | J.D. Lee |
| Advanced Inorganic Chemistry | Cotton & Wilkinson |
| Modern Approach to Chemical Calculations | R.C. Mukherjee |
3. Pure Mathematics (100 Marks)
Pure Mathematics covers abstract mathematical concepts and proofs.
Complete Syllabus
Paper I (50 marks)
Modern Algebra:
- Groups: Definition, properties, subgroups
- Cyclic groups
- Lagrange's theorem
- Permutation groups
- Normal subgroups
- Quotient groups
- Homomorphisms and isomorphisms
Rings and Fields:
- Rings: Definition, types
- Integral domains
- Fields
- Polynomial rings
- Principal ideal domains
- Unique factorization domains
Vector Spaces:
- Linear dependence and independence
- Basis and dimension
- Linear transformations
- Matrix representation
- Eigenvalues and eigenvectors
- Inner product spaces
Calculus:
- Real number system
- Limits and continuity
- Differentiation
- Mean value theorems
- Taylor and Maclaurin series
- Riemann integration
- Improper integrals
Paper II (50 marks)
Complex Analysis:
- Complex numbers
- Analytic functions
- Cauchy-Riemann equations
- Complex integration
- Cauchy's theorem
- Taylor and Laurent series
- Residue theorem
- Conformal mapping
Topology:
- Metric spaces
- Open and closed sets
- Continuity in metric spaces
- Completeness
- Compactness
- Connectedness
Differential Equations:
- First order ODEs
- Higher order linear ODEs
- Series solutions
- Partial differential equations
- Fourier series
- Laplace transforms
Numerical Analysis:
- Roots of equations
- Interpolation
- Numerical differentiation
- Numerical integration
- Solution of ODEs
Recommended Books for Pure Mathematics
| Book | Author |
|---|---|
| Topics in Algebra | I.N. Herstein |
| Contemporary Abstract Algebra | Joseph A. Gallian |
| Linear Algebra | Hoffman & Kunze |
| Mathematical Analysis | Tom M. Apostol |
| Complex Variables | Churchill & Brown |
| Introduction to Topology | Bert Mendelson |
| Elementary Differential Equations | Boyce & DiPrima |
| Numerical Methods | Atkinson & Han |
4. Applied Mathematics (100 Marks)
Applied Mathematics focuses on mathematical modeling and computational methods.
Complete Syllabus
Paper I (50 marks)
Vector Analysis:
- Vector algebra
- Gradient, divergence, curl
- Line, surface, volume integrals
- Gauss, Stokes, Green's theorems
- Curvilinear coordinates
Statics:
- Composition of forces
- Equilibrium of forces
- Moments and couples
- Centre of mass
- Friction
- Virtual work
Dynamics:
- Kinematics of a particle
- Projectiles
- Simple harmonic motion
- Central forces
- Planetary motion
- Moment of inertia
- Kinetic energy
- Angular momentum
Paper II (50 marks)
Mathematical Methods:
- Fourier series
- Laplace transforms
- Z-transforms
- Special functions (Bessel, Legendre)
- Partial differential equations
- Wave equation
- Heat equation
- Laplace equation
Tensor Calculus:
- Tensor algebra
- Covariant and contravariant tensors
- Metric tensor
- Christoffel symbols
- Geodesics
Numerical Methods:
- Solution of algebraic equations
- Interpolation methods
- Numerical differentiation and integration
- Solution of ODEs
- Finite difference methods
Optimization:
- Linear programming
- Simplex method
- Duality
- Transportation problems
- Assignment problems
Recommended Books for Applied Mathematics
| Book | Author |
|---|---|
| Vector Analysis | Murray R. Spiegel |
| Classical Mechanics | H. Goldstein |
| Mathematical Methods for Physicists | Arfken & Weber |
| Applied Partial Differential Equations | Richard Haberman |
| Numerical Analysis | Richard L. Burden |
| Introduction to Linear Algebra | Gilbert Strang |
| Operations Research | Hamdy A. Taha |
5. Statistics (100 Marks)
Statistics is useful for candidates with quantitative backgrounds.
Complete Syllabus
Paper I: Probability and Distributions (50 marks)
Probability Theory:
- Axiomatic probability
- Conditional probability
- Bayes' theorem
- Mathematical expectation
- Moment generating functions
- Characteristic functions
Probability Distributions:
Discrete:
- Binomial
- Poisson
- Hypergeometric
- Geometric
- Negative binomial
Continuous:
- Normal
- Exponential
- Gamma
- Beta
- Chi-square
- t-distribution
- F-distribution
Sampling Distributions:
- Distribution of sample mean
- Central limit theorem
- Distribution of variance
- Joint distributions of X-bar and S-squared
Paper II: Statistical Inference (50 marks)
Estimation:
- Point estimation
- Properties of estimators
- Maximum likelihood estimation
- Method of moments
- Interval estimation
- Confidence intervals
Hypothesis Testing:
- Types of errors
- Power of test
- Neyman-Pearson lemma
- Likelihood ratio tests
- Tests for means and variances
- Chi-square tests
Regression and Correlation:
- Simple linear regression
- Multiple regression
- Correlation coefficient
- Partial and multiple correlation
- Analysis of variance (ANOVA)
Non-parametric Methods:
- Sign test
- Wilcoxon tests
- Mann-Whitney test
- Kruskal-Wallis test
- Chi-square goodness of fit
Sampling Techniques:
- Simple random sampling
- Stratified sampling
- Cluster sampling
- Systematic sampling
- Ratio and regression estimators
Recommended Books for Statistics
| Book | Author |
|---|---|
| Introduction to the Theory of Statistics | Mood, Graybill & Boes |
| Mathematical Statistics | John E. Freund |
| Probability and Statistics | DeGroot & Schervish |
| An Introduction to Probability and Statistics | Vijay K. Rohatgi |
| Introduction to Statistical Theory Part I & II | Sher Muhammad Chaudhry |
| Applied Regression Analysis | Draper & Smith |
| Sampling Techniques | William G. Cochran |
6. Geology (100 Marks)
Geology is suitable for candidates with earth sciences background.
Complete Syllabus
Physical Geology (25 marks)
Earth's Interior:
- Structure of Earth
- Seismic waves
- Core, mantle, crust
- Isostasy
Geomorphology:
- Weathering processes
- Erosion agents
- Rivers and valleys
- Glaciers and glaciation
- Wind action
- Marine processes
Plate Tectonics:
- Continental drift
- Sea-floor spreading
- Plate boundaries
- Mountain building
- Earthquakes and volcanoes
Mineralogy and Optical Mineralogy (20 marks)
Crystal Systems:
- Symmetry elements
- Crystal forms
- Twinning
Physical Properties:
- Color, streak, luster
- Hardness, cleavage
- Specific gravity
Optical Properties:
- Refractive index
- Birefringence
- Extinction angles
- Optical sign
Important Minerals:
- Silicates
- Carbonates
- Sulfides
- Oxides
Petrology (20 marks)
Igneous Rocks:
- Classification
- Texture and structure
- Magmatic processes
- Important rock types
Sedimentary Rocks:
- Classification
- Sedimentary structures
- Depositional environments
- Important rock types
Metamorphic Rocks:
- Types of metamorphism
- Metamorphic facies
- Important rock types
Stratigraphy and Paleontology (20 marks)
Stratigraphy:
- Principles of stratigraphy
- Stratigraphic nomenclature
- Correlation methods
- Geological time scale
Paleontology:
- Fossils and fossilization
- Important fossil groups
- Evolutionary history
- Biostratigraphy
Pakistan's Stratigraphy:
- Geological history
- Major formations
- Resource geology
Economic and Applied Geology (15 marks)
Mineral Deposits:
- Classification
- Origin of ore deposits
- Exploration methods
Pakistan's Mineral Resources:
- Metallic minerals
- Non-metallic minerals
- Coal and petroleum
Engineering Geology:
- Site investigations
- Rock mechanics
- Dam foundations
- Tunneling
Recommended Books for Geology
| Book | Author |
|---|---|
| Physical Geology | Plummer, McGeary & Carlson |
| Principles of Physical Geology | Arthur Holmes |
| Manual of Mineral Science | Klein & Hurlbut |
| Optical Mineralogy | W.D. Nesse |
| Igneous and Metamorphic Petrology | Myron G. Best |
| Sedimentology and Stratigraphy | Gary Nichols |
| Principles of Paleontology | Raup & Stanley |
| Economic Geology | Evans |
| Geology of Pakistan | Kazmi & Jan |
Subject Selection Comparison
| Subject | Difficulty | Best For | Scoring Potential |
|---|---|---|---|
| Physics | Very High | Physics MSc | Medium (technical) |
| Chemistry | High | Chemistry MSc | Medium |
| Applied Mathematics | High | Math graduates | High (if strong) |
| Pure Mathematics | Very High | Math graduates | Medium |
| Statistics | Medium-High | Stats, Math graduates | High |
| Geology | Medium | Geology graduates | Medium-High |
Most Popular Choice
Statistics is generally the most selected science subject due to:
- Relatively manageable syllabus
- Applications in research and policy
- Better scoring potential
- Useful for competitive exams in general
Preparation Tips for Science Subjects
- Master Fundamentals - Build strong conceptual foundation
- Practice Numericals - Science subjects have calculation-based questions
- Use Standard Textbooks - Don't rely on guides alone
- Draw Diagrams - Especially for Physics and Geology
- Memorize Formulas - Create formula sheets for revision
- Solve Past Papers - Understand FPSC exam patterns
- Time Management - Practice solving under exam conditions
- MCQ Preparation - 20 marks are from MCQs in each subject
Based on official FPSC CSS Syllabus for CE-2016 onwards. Always verify current syllabus from FPSC website.