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JEE Main
Joint Entrance Examination — Main
Engineering entrance test. 90 questions (75 to attempt) in 180 minutes across Physics, Chemistry, and Mathematics.
Updated 5 Sept 2026 ·Vacancy counts change every cycle — always confirm the exact number in the latest official notification before applying.
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Source: official exam authority notification · refreshed weekly. How this works →
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Laws of MotionTwo blocks of masses 3 kg and 5 kg are connected by a light inextensible string passing over a smooth pulley. The system is released from rest. What is the acceleration of the system? (Take g = 10 m/s²)
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10 questions across the syllabus to see where you stand.
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JEE Main eligibility
Verified against the official notification. Source ↗ · last reconciled 2026-05.
- Education
- Class 12 with Physics, Mathematics, and one of Chemistry / Biology / Biotechnology / Technical Vocational subject.
- Candidates appearing in Class 12 in the same year of the exam can apply.
- For NIT/IIIT/GFTI admission, Class 12 aggregate must be 75% (65% for SC/ST) OR top 20 percentile of the qualifying board.
- Diploma-holders are eligible for JEE Advanced but cannot use JEE Main for NIT/IIIT admission.
- Attempts
- Three consecutive years from the year of Class 12 passing. NTA conducts 2 sessions per year (January + April) — students can attempt both; the better score counts.
- Nationality
- Open to Indian citizens, NRIs, OCIs, PIOs, and foreign nationals (with separate fee structure).
JEE Main cutoffs
Historical cutoffs are a guide, not a prediction. Use them to set a realistic target, not to predict next year's exact number.
JEE Advanced qualifying percentile (NTA-released)
These are the cutoffs to qualify for JEE Advanced (top ~2.5 lakh candidates). Counselling cutoffs for JoSAA are separately released per NIT and branch.
| Year | Category | Cutoff |
|---|---|---|
| 2024 | General / EWS | 93.23 percentile |
| 2024 | OBC-NCL | 79.67 percentile |
| 2024 | SC | 60.09 percentile |
| 2024 | ST | 46.69 percentile |
| 2023 | General | 90.77 percentile |
| 2023 | OBC-NCL | 73.61 percentile |
| 2023 | SC | 51.97 percentile |
| 2023 | ST | 37.23 percentile |
Source: official ↗ · verified 2026-05.
JoSAA closing ranks — CSE, popular NITs (2024 Round 6, Home State, General)
| Year | Category | Cutoff |
|---|---|---|
| 2024 | NIT Trichy CSE | Rank ~1,600 |
| 2024 | NIT Warangal CSE | Rank ~2,300 |
| 2024 | NIT Surathkal CSE | Rank ~3,200 |
| 2024 | IIIT Hyderabad CSE | Rank ~600 (UGEE separate gate) |
| 2024 | NIT Rourkela CSE | Rank ~6,500 |
Source: official ↗ · verified 2026-05.
JEE Main paper analysis — what actually got asked
Topic-by-topic weightage averaged across 2022-2024 papers. Use this to decide where to invest study hours, not where to skim. Source ↗ · verified 2026-05.
Mathematics
100/300 marks avg
Coordinate Geometry + Vectors + 3D
~24 marks(8%)Calculus (Limits, Differentiation, Integration)
~28 marks(9%)Algebra (Quadratic, Sequences, Complex Numbers, Matrices)
~28 marks(9%)Trigonometry + Probability + Statistics
~20 marks(7%)
Physics
100/300 marks avg
Mechanics (Kinematics, Laws, Work-Energy, Rotation, Gravitation)
~32 marks(11%)Electrodynamics + Optics + Modern Physics
~44 marks(15%)Thermo + Properties of Matter + Waves
~24 marks(8%)
Chemistry
100/300 marks avg
Physical Chemistry
~36 marks(12%)Organic Chemistry
~32 marks(11%)Inorganic Chemistry
~32 marks(11%)
Takeaways for prep planning
- Math + Phys + Chem are equally weighted (100 each). Most rank gain comes from levelling the weakest of the three — not from squeezing more out of the strongest.
- Calculus + Coordinate Geometry combined contribute ~50% of the Math paper — they're the highest-yield Math topics.
- Inorganic Chemistry is the cheapest section to crack: high-recall, low-derivation. Most full-marks Chemistry scorers report Inorganic as the differentiator.
JEE Main — Frequently asked questions
Is Shishya free for JEE Main preparation?
How many JEE Main practice questions does Shishya have?
Are JEE Main previous year question papers available?
How long is the JEE Main exam?
Previous year papers
100 questions across all yearsSome years hold a set of questions from that paper, not the full paper — each card shows how many.
2025
20 of 75 questions
Practise these →2024
20 of 75 questions
Practise these →2023
20 of 75 questions
Practise these →2022
20 of 75 questions
Practise these →2021
20 of 75 questions
Practise these →
Mock tests
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JEE Main — Physics Drill
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Practice by subject & topic
Full-length subject tests below — 25 questions each, real exam format, instant scoring. Want to drill a single topic? Every topic has its own 10-question test in the syllabus.
Physics
149 QsChemistry
131 QsMathematics
90 Qs
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Your rank
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Students
2
Mocks taken
4
Average score
24%
Top score
55%
What can I get from JEE Main?
Mock-score → expected rank → likely outcome. Use the mocks below to find your current band, then plan how many marks you need to climb.
Top 500 — Elite IIT contenders
99–100% · Rank 1 – 500
- •IIT Bombay — Computer Science (cut-off ~60-80 General), Electrical (~150-250)
- •IIT Delhi — Computer Science (cut-off ~90-120 General), Electrical (~200-350)
- •IIT Madras — Computer Science (cut-off ~100-150 General), Electrical (~250-400)
- •IIT Kanpur — Computer Science (cut-off ~180-280 General), Electrical (~400-600)
- •IIT Kharagpur — Computer Science (cut-off ~450-650 General)
- •IIT Roorkee — Computer Science (cut-off ~650-900 General)
Mid-tier IIT — most branches
96–99% · Rank 500 – 3,000
- •IIT Roorkee — Electrical, Mechanical, Chemical (cut-off ~1.5k-3k General)
- •IIT Kharagpur — CSE, ECE, EE (cut-off ~800-2.5k General depending on branch)
- •IIT Delhi / IIT Bombay — lower-demand branches like Engineering Physics, Textile (cut-off ~2k-3.5k)
- •IIT Kanpur — Mechanical, Civil, Aerospace (cut-off ~1.5k-3k General)
- •IIT Madras — branches like Metallurgy, Ocean Engineering (cut-off ~2k-3.5k General)
Top-tier NIT CSE / lower IIT range
92–96% · Rank 3,000 – 15,000
- •NIT Trichy / NIT Surathkal — Computer Science (cut-off ~5k-8k General)
- •IIIT Hyderabad — CSE (cut-off ~2k-5k General, top-tier placement records)
- •IIT (ISM) Dhanbad — Mining, Petroleum, Mechanical (cut-off ~8k-15k General)
- •IIT Guwahati / IIT Hyderabad — lower-demand branches like Chemical, Civil (cut-off ~8k-12k)
- •IIT BHU / IIT Roorkee — branches like Metallurgy, Ceramic Engineering (cut-off ~5k-12k)
Top NIT / IIIT — competitive branches
85–92% · Rank 15,000 – 50,000
- •NIT Trichy — CSE, ECE (cut-off ~8k-15k General), Mechanical (~15k-25k)
- •NIT Surathkal — Computer Science (cut-off ~6k-10k General), ECE (~10k-18k)
- •IIIT Hyderabad — CSE, ECE (cut-off ~2k-8k General, highly competitive)
- •NIT Warangal — CSE (cut-off ~10k-15k General), ECE (~12k-20k)
- •Definite JEE Advanced qualification — IIT non-CSE branches achievable with strong performance
Mid-tier NIT / IIIT range
75–85% · Rank 50,000 – 1,50,000
- •NIT Rourkela / NIT Jaipur — Mechanical, Civil, Chemical Engineering (cut-off ~40k-100k General)
- •NIT Calicut / NIT Surathkal — lower-demand branches like Metallurgy, Mining (cut-off ~50k-80k)
- •IIIT Allahabad — Electronics, IT branches (cut-off ~30k-70k General)
- •NIT Trichy / NIT Warangal — branches like Chemical, Civil (cut-off ~20k-60k depending on category)
- •Strong chance for JEE Advanced qualification — serious IIT contention possible with good attempt
Lower NIT / IIIT range
60–75% · Rank 1,50,000 – 4,00,000
- •NIT Nagaland / NIT Manipur — Civil, Mechanical, Electrical (cut-off ~150k-250k General)
- •IIIT Kota / IIIT Vadodara — Computer Science (cut-off ~100k-200k for some categories)
- •NIT Uttarakhand / NIT Goa — branches like ECE, EE (cut-off varies 80k-300k by category)
- •Good state colleges — top government engineering colleges in states like Maharashtra, Karnataka
- •Eligible for JEE Advanced if in top 2.5 lakh — prepare intensively for IIT attempt
Tier 3 colleges range
40–60% · Rank 4,00,000 – 8,00,000
- •State government engineering colleges — branches like Civil, Mechanical in home state
- •Private engineering colleges — Tier 2/3 institutions with AICTE approval
- •IIIT Sonepat / IIIT Una — lower-demand branches (cut-off ~200k-400k for some categories)
- •New NITs — branches like Chemical, Textile Engineering in newer campuses
- •Consider JEE Main Paper 2 for B.Arch if interested in architecture
Below qualifying threshold
0–40% · Rank 8,00,000+
AI-curated from historic cut-off patterns. Always verify with the latest official notification before making decisions.
News & timeline
See older updates →Latest news
NTA declared Session 2 results showing record participation across both sessions. The cutoff has been the highest in 8 years, indicating growing competition for engineering admissions.
The Central Seat Allocation Board announced Round 2 seat allotment results on August 12, 2026, completing the counselling process for NITs, IIITs and other participating institutions.
NTA released the provisional answer key for Session 2 on April 11, allowing candidates to challenge responses until April 13 with a fee of Rs 200 per objection.
Important dates
⚙️JEE Advanced 2026 exam
passedSun, 17 May, 2026
Conducted in 2 shifts for top 2.5 lakh JEE Main qualifiers
JEE Advanced 2026 result
passedMon, 1 Jun, 2026
CSAB Round 2 seat allotment result
passedWed, 12 Aug, 2026
Final counselling round for NIT/IIIT admissions
JEE Main 2027 notification (expected)
50 days awaySat, 31 Oct, 2026
NTA typically releases notification in late October each year
JEE Main 2027 Session 1 application start (expected)
50 days awaySat, 31 Oct, 2026
Registration typically opens same day as notification
JEE Main 2027 Session 1 application end (expected)
77 days awayFri, 27 Nov, 2026
Based on 2026 cycle pattern; typically 4-week window
⚙️JEE Main 2027 Session 1 exam (expected)
132 days awayThu, 21 Jan, 2027
Session 1 typically held late January; exact dates TBA
Syllabus
Tap any topic for its study notes + a 10-question topic test
Physics
Physics and Measurement
Units of measurements; SI units, fundamental and derived units; least count, accuracy and precision; significant figures; dimensional analysis and its applications.
Kinematics
Frame of reference; motion in a straight line; uniform and non-uniform motion; scalars and vectors; vector addition and subtraction; motion in a plane; projectile motion; uniform circular motion.
Laws of Motion
Newton's three laws of motion; conservation of linear momentum and its applications; equilibrium of concurrent forces; static and kinetic friction; dynamics of uniform circular motion: centripetal force.
Work, Energy and Power
Work done by a constant and variable force; kinetic and potential energies; work-energy theorem; power; conservative and non-conservative forces; elastic and inelastic collisions in one and two dimensions.
Rotational Motion
Centre of mass of a two-particle system, of a rigid body; basic concepts of rotational motion; moment of a force, torque, angular momentum; conservation of angular momentum; moment of inertia; parallel and perpendicular axes theorems; equations of rotational motion; rolling motion.
Gravitation
Universal law of gravitation; acceleration due to gravity and its variation with altitude and depth; Kepler's laws; gravitational potential energy; gravitational potential; escape velocity; motion of a satellite, orbital velocity, time period and energy of satellite.
Properties of Solids and Liquids
Elastic behaviour, stress-strain relationship, Hooke's law, Young's modulus, bulk modulus, modulus of rigidity; Pascal's law and its applications; viscosity; Stokes' law; terminal velocity; streamline and turbulent flow; Reynolds number; Bernoulli's principle; surface energy and surface tension; angle of contact; capillary rise; heat, temperature, thermal expansion; specific heat capacity; calorimetry; change of state, latent heat; heat transfer — conduction, convection and radiation.
Thermodynamics
Thermal equilibrium; zeroth, first and second law of thermodynamics; concept of work, heat, internal energy; reversible and irreversible processes; Carnot engine and its efficiency.
Kinetic Theory of Gases
Equation of state of a perfect gas, work done on compressing a gas; kinetic theory of gases — assumptions; concept of pressure; kinetic interpretation of temperature; rms speed; degrees of freedom; law of equipartition of energy; mean free path; Avogadro's number.
Oscillations and Waves
Periodic motion — period, frequency; SHM and its equation; phase; oscillations of a spring; energy in SHM; simple pendulum; free, forced and damped oscillations, resonance; wave motion; transverse and longitudinal waves; speed of travelling wave; principle of superposition; reflection of waves; standing waves in strings and organ pipes; beats; Doppler effect.
Electrostatics
Electric charges and their conservation; Coulomb's law; superposition principle; electric field due to a point charge, dipole; electric field lines; electric flux; Gauss's law and its applications; electric potential; potential due to a point charge and dipole; equipotential surfaces; capacitance; series and parallel combinations of capacitors; energy stored in a capacitor.
Current Electricity
Electric current; drift velocity; Ohm's law; electrical resistance; V-I characteristics; resistivity and conductivity; series and parallel combination of resistors; temperature dependence; internal resistance of a cell; Kirchhoff's laws and applications — Wheatstone bridge, metre bridge, potentiometer.
Magnetic Effects of Current and Magnetism
Biot-Savart law; Ampere's law; force on a moving charge in uniform magnetic and electric fields — Lorentz force; force on a current-carrying conductor; cyclotron; force between two parallel current-carrying conductors; torque on a current loop in magnetic field; moving coil galvanometer; bar magnet; magnetic dipole moment; earth's magnetic field; para-, dia- and ferromagnetism.
Electromagnetic Induction and Alternating Currents
Electromagnetic induction; Faraday's law; induced emf and current; Lenz's law; eddy currents; self and mutual induction; alternating currents; peak and rms value; reactance and impedance; LCR series circuit, resonance; quality factor; power in AC circuits; AC generator and transformer.
Electromagnetic Waves
Electromagnetic waves and their characteristics (qualitative); transverse nature; electromagnetic spectrum (radio, microwaves, infrared, visible, ultraviolet, X-rays, gamma rays) and their uses.
Optics
Reflection and refraction of light at plane and spherical surfaces; mirror formula; total internal reflection and its applications; refraction at spherical surfaces, lenses, thin lens formula; magnification; power of a lens; combination of thin lenses; refraction and dispersion through a prism; scattering of light; optical instruments — microscope and telescope; wave optics — Huygens' principle; interference, Young's double slit experiment; diffraction at single slit; polarisation; Brewster's law; Malus' law.
Dual Nature of Matter and Radiation
Photoelectric effect; Hertz and Lenard's observations; Einstein's photoelectric equation; particle nature of light; matter waves; de Broglie wavelength; Davisson-Germer experiment.
Atoms and Nuclei
Alpha-particle scattering experiment; Rutherford's model; Bohr's model and energy levels; hydrogen spectrum; composition and size of nucleus; mass-energy equivalence; nuclear binding energy per nucleon; mass defect; radioactivity — alpha, beta and gamma decays; half-life and mean life; nuclear fission and fusion.
Electronic Devices
Semiconductors; semiconductor diode — I-V characteristics in forward and reverse bias; diode as a rectifier; LED, photodiode, solar cell; Zener diode and its application as voltage regulator; transistor action; logic gates (OR, AND, NOT, NAND, NOR).
Experimental Skills
Familiarity with the basic approach and observations of the experiments and activities in NCERT — Vernier callipers, screw gauge, simple pendulum, Young's modulus by Searle's method, surface tension by capillary rise, viscosity, speed of sound by resonance tube, specific heat by method of mixtures, resistance using metre bridge and Ohm's law, focal length of mirror/lens, refractive index by travelling microscope, characteristics of p-n junction.
Chemistry
Some Basic Concepts in Chemistry
Matter and its nature; Dalton's atomic theory; concept of atom, molecule, element and compound; laws of chemical combination; atomic and molecular masses; mole concept; molar mass; percentage composition; empirical and molecular formulae; chemical equations and stoichiometry.
Atomic Structure
Bohr's model of hydrogen atom — its postulates, derivation of relations for energy of an electron and radii of orbits; dual nature of matter; de Broglie's relationship; Heisenberg uncertainty principle; quantum mechanical model of atom; orbitals; quantum numbers; Aufbau principle, Pauli's exclusion principle, Hund's rule; electronic configuration of elements.
Chemical Bonding and Molecular Structure
Kossel-Lewis approach to chemical bond formation; ionic bond — lattice enthalpy; covalent bond — Lewis structures; polar covalent bond; valence bond theory; hybridisation involving s, p and d orbitals; resonance; molecular orbital theory of homonuclear diatomic molecules; hydrogen bonding; VSEPR theory.
Chemical Thermodynamics
Fundamentals of thermodynamics — system and surroundings, types of system; first law of thermodynamics; concept of work, heat, internal energy and enthalpy; Hess's law; standard enthalpies of formation, combustion, neutralisation; bond dissociation enthalpy; second law of thermodynamics; entropy; Gibbs energy; spontaneity; relation between ΔG and equilibrium constant.
Solutions
Different methods for expressing concentration of solution; vapour pressure of solutions and Raoult's law; ideal and non-ideal solutions; colligative properties — relative lowering of vapour pressure, elevation of boiling point, depression of freezing point, osmotic pressure; van't Hoff factor.
Equilibrium
Equilibria involving physical processes; equilibrium in chemical processes; law of chemical equilibrium; equilibrium constants Kp and Kc; Le Chatelier's principle; ionic equilibrium — Bronsted-Lowry and Lewis acids/bases; ionisation of weak acids and bases; pH; common ion effect; buffer solutions; solubility product; hydrolysis of salts.
Redox Reactions and Electrochemistry
Electronic concepts of oxidation and reduction; redox reactions; oxidation number; balancing redox reactions; electrolytic and metallic conduction; conductance — specific, equivalent and molar; Kohlrausch's law; electrochemical cells; EMF; standard electrode potential; Nernst equation; relation between Gibbs energy change and EMF; electrochemical series; fuel cells; corrosion; batteries; Faraday's laws of electrolysis.
Chemical Kinetics
Rate of a chemical reaction; factors affecting rate of reaction; order and molecularity of a reaction; rate law and rate constant; differential and integral forms of zero and first order reactions; Arrhenius equation; activation energy; collision theory of bimolecular gaseous reactions.
Classification of Elements and Periodicity in Properties
Modern periodic law and present form of the periodic table; s, p, d, f block elements; periodic trends in properties — atomic and ionic radii, ionisation enthalpy, electron gain enthalpy, valence, oxidation states, electronegativity, chemical reactivity.
p-Block Elements (Groups 13-18)
Group 13 to 18 elements: general introduction, electronic configuration, occurrence, oxidation states, trends in physical and chemical properties; preparation, properties and uses of compounds — boron family (borax, boric acid, diborane), carbon family (allotropes, oxides of carbon, silicates), nitrogen family (NH3, HNO3, oxides of nitrogen), oxygen family (O3, H2SO4), halogens (HCl, oxoacids, interhalogens), noble gases (xenon compounds).
d- and f-Block Elements
General introduction, electronic configuration, occurrence and characteristics of transition elements; trends in metallic character, atomic and ionic sizes, ionisation enthalpy, oxidation states; coloured ions, magnetic properties, catalytic property, alloy formation; preparation and properties of K2Cr2O7 and KMnO4; lanthanoids and actinoids — electronic configurations, oxidation states, lanthanoid contraction.
Coordination Compounds
Introduction; ligands; coordination number; nomenclature; isomerism (structural and stereo); bonding — Werner's theory, valence bond theory, crystal field theory; magnetic properties; importance of coordination compounds (in qualitative analysis, biological systems, medicinal chemistry, catalysis).
Purification and Characterisation of Organic Compounds
Purification methods — crystallisation, sublimation, distillation, differential extraction and chromatography (principles only); qualitative analysis — detection of nitrogen, sulphur, phosphorus and halogens; quantitative analysis (basic principles only); calculation of empirical formulae and molecular formulae.
Some Basic Principles of Organic Chemistry
Tetravalency of carbon; shapes of simple molecules — hybridisation (s and p); classification of organic compounds based on functional groups; nomenclature (trivial and IUPAC); covalent bond fission — homolytic and heterolytic; electronic effects (inductive, electromeric, resonance, hyperconjugation); types of organic reactions.
Hydrocarbons
Classification — alkanes, alkenes, alkynes, aromatic; conformations of ethane and butane; cis-trans isomerism; methods of preparation, physical and chemical properties; mechanism of free-radical halogenation, addition reactions, electrophilic substitution in benzene; directive influence of functional groups in monosubstituted benzene.
Organic Compounds Containing Halogens
Haloalkanes and haloarenes — nomenclature, methods of preparation, physical and chemical properties; SN1 and SN2 reactions; uses and environmental effects of dichloromethane, trichloromethane, tetrachloromethane, iodoform, freons, DDT.
Organic Compounds Containing Oxygen
Alcohols, phenols and ethers — nomenclature, methods of preparation, physical and chemical properties; identification of primary, secondary and tertiary alcohols; mechanism of dehydration; acidic nature of phenols; aldehydes and ketones — nomenclature, preparation, properties, mechanism of nucleophilic addition; aldol and Cannizzaro reactions; carboxylic acids and derivatives.
Organic Compounds Containing Nitrogen
Amines — nomenclature, classification, preparation, physical and chemical properties; basicity of amines; identification of primary, secondary and tertiary amines; diazonium salts — preparation, important reactions and synthetic usefulness in aromatic compounds.
Biomolecules
General introduction and importance of biomolecules; carbohydrates — classification (mono-, di-, polysaccharides), glucose, fructose, sucrose, starch, cellulose; proteins — amino acids, peptide bond, primary and secondary structure; vitamins — classification and function; nucleic acids — DNA and RNA.
Principles Related to Practical Chemistry
Detection of extra elements (N, S, halogens) in organic compounds; detection of functional groups — hydroxyl (alcoholic, phenolic), carbonyl (aldehyde and ketone), carboxyl, amino; chemistry involved in titrimetric exercises — acid-base titrations using oxalic acid, potassium permanganate, ferrous sulphate; chemistry of qualitative analysis of cations and anions.
Mathematics
Sets, Relations and Functions
Sets and their representation; union, intersection and complement of sets and their algebraic properties; power set; relation, types of relations, equivalence relations; functions — one-to-one, into and onto; composition of functions.
Complex Numbers and Quadratic Equations
Complex numbers as ordered pairs; representation in argand plane; algebra of complex numbers; modulus and argument; triangle inequality; quadratic equations in real and complex number system; relations between roots and coefficients; nature of roots; formation of quadratic equations with given roots.
Matrices and Determinants
Matrices, algebra of matrices, types of matrices; determinants and matrices of order two and three; properties of determinants; evaluation of determinants; area of triangle using determinants; adjoint and inverse of a matrix; test of consistency and solution of simultaneous linear equations using determinants and matrices.
Permutations and Combinations
Fundamental principle of counting; permutation as an arrangement and combination as selection; meaning of P(n,r) and C(n,r); simple applications.
Binomial Theorem and its Simple Applications
Binomial theorem for a positive integral index; general term and middle term; properties of binomial coefficients and simple applications.
Sequences and Series
Arithmetic and geometric progressions; insertion of arithmetic and geometric means between two given numbers; relation between AM and GM; sum up to n terms of special series — Sn, Sn^2, Sn^3; arithmetico-geometric progression.
Limit, Continuity and Differentiability
Real-valued functions, algebra of functions, polynomial, rational, trigonometric, logarithmic and exponential functions; inverse functions; graphs of simple functions; limits, continuity and differentiability; differentiation of sum, difference, product and quotient of functions; derivatives of trigonometric, inverse trigonometric, logarithmic, exponential, composite and implicit functions; Rolle's and Lagrange's mean value theorems; applications — tangents and normals, increasing and decreasing functions, maxima and minima.
Integral Calculus
Integral as an anti-derivative; fundamental integrals involving algebraic, trigonometric, exponential and logarithmic functions; integration by substitution, by parts and by partial fractions; integration using trigonometric identities; evaluation of simple integrals; fundamental theorem of calculus; properties of definite integrals; evaluation of definite integrals; determining areas of regions bounded by simple curves.
Differential Equations
Ordinary differential equations, their order and degree; formation of differential equations; solution of differential equations by the method of separation of variables; solution of homogeneous and linear differential equations of the first order.
Coordinate Geometry
Cartesian system of rectangular coordinates in a plane; distance formula; section formula; locus and its equation; slope of a line; parallel and perpendicular lines; intercepts of a line on coordinate axes; various forms of equations of a line; distance of a point from a line; circle; conic sections — parabola, ellipse, hyperbola in standard form.
Three-Dimensional Geometry
Coordinates of a point in space; distance between two points; section formula; direction ratios and direction cosines; angle between two intersecting lines; skew lines; shortest distance between them and its equation; equations of a line and a plane in different forms; intersection of a line and a plane; coplanar lines.
Vector Algebra
Vectors and scalars; addition of vectors; components in two and three dimensions; scalar and vector products; scalar and vector triple products.
Statistics and Probability
Measures of dispersion — mean, median, mode of grouped and ungrouped data; standard deviation, variance and mean deviation for grouped and ungrouped data; probability — probability of an event, addition and multiplication theorems of probability, Baye's theorem, probability distribution of a random variate, Bernoulli trials and binomial distribution.
Trigonometry
Trigonometrical identities and equations; trigonometrical functions; inverse trigonometrical functions and their properties; heights and distances.