JEE Main 2022 Syllabus Maths

Appendix -
SYLLABUS for JEE (Main)-2022

Syllabus for Paper-1 (B.E./B.Tech.)- Mathematics, Physics, and Chemistry
MATHEMATICS
UNIT 1: SETS, RELATIONS, AND combination as section, Meaning of P (n,r)
FUNCTIONS: and C (n,r), simple applications.

Sets and their representation: Union, UNIT 5: MATHEMATICAL INDUCTIONS:
intersection and complement of sets and
Principle of Mathematical Induction and
their algebraic properties; Power set;
its simple applications.
Relation, Type of relations, equivalence
relations, functions; one-one, into and onto UNIT 6: BINOMIAL THEOREM AND ITS
functions, the composition of functions. SIMPLE APPLICATIONS:
UNIT 2: COMPLEX NUMBERS AND Binomial theorem for a positive integral
QUADRATIC EQUATIONS: index, general term and middle term,
properties of Binomial coefficients, and
Complex numbers as ordered pairs of
simple applications.
reals, Representation of complex numbers
in the form a + ib and their representation UNIT 7: SEQUENCE AND SERIES:
in a plane, Argand diagram, algebra of
complex number, modulus and argument Arithmetic and Geometric progressions,
(or amplitude) of a complex number, insertion of arithmetic, geometric means
square root of a complex number, triangle between two given numbers, Relation
inequality, Quadratic equations in real and between A.M and G.M sum up to n terms
complex number system and their of special series; Sn, Sn2, Sn3.
solutions Relations between roots and co- Arithmetico-Geometric progression.
efficient, nature of roots, the formation of UNIT 8: LIMIT, CONTINUITY, AND
quadratic equations with given roots. DIFFERENTIABILITY:
Real–valued functions, algebra of
UNIT3: MATRICES AND DETERMINANTS: functions, polynomials, rational,
Matrices, algebra of matrices, type of trigonometric, logarithmic, and
matrices, determinants, and matrices of exponential functions, inverse function.
order two and three, properties of Graphs of simple functions. Limits,
determinants, evaluation of determinants, continuity, and differentiability.
area of triangles using determinants, Differentiation of the sum, difference,
Adjoint, and evaluation of inverse of a product, and quotient of two functions.
square matrix using determinants and Differentiation of trigonometric, inverse
elementary transformations, Test of trigonometric, logarithmic, exponential,
consistency and solution of simultaneous composite and implicit functions;
linear equations in two or three variables derivatives of order up to two, Rolle’s and
using determinants and matrices. Lagrange's Mean value Theorems,
Applications of derivatives: Rate of
UNIT 4: PERMUTATIONS AND change of quantities, monotonic-
COMBINATIONS: Increasing and decreasing functions,
The fundamental principle of counting, Maxima and minima of functions of one
permutation as an arrangement and variable, tangents and normal.

UNIT 9: INTEGRAL CALCULAS: lines, conditions for concurrence of three
lines, the distance of a point form a line,
Integral as an anti-derivative, Fundamental
equations of internal and external by
Integrals involving algebraic,
sectors of angles between two lines co-
trigonometric, exponential, and logarithms
ordinate of the centroid, orthocentre, and
functions. Integrations by substitution, by
circumcentre of a triangle, equation of the
parts, and by partial functions. Integration
family of lines passing through the point
using trigonometric identities.
of intersection of two lines.
Evaluation of simple integrals of the type
Circle, conic sections
𝑑𝑥 𝑑𝑥 𝑑𝑥
∫ 𝑥 2 +𝑎2 , ∫ , ∫ 2 2
𝑎 −𝑥
, A standard form of equations of a circle,
√𝑥 2 ± 𝑎2
𝑑𝑥 𝑑𝑥 𝑑𝑥 the general form of the equation of a
∫ √𝑎2 − 𝑥2 , ∫ 𝑎𝑥 2 +𝑏𝑥+𝑐 ,∫
√𝑎𝑥 2 + 𝑏𝑥+𝑐
,
circle, its radius and central, equation of a
(𝑝𝑥+𝑞)𝑑𝑥
∫ 𝑎𝑥 2 +𝑏𝑥+𝑐 , circle when the endpoints of a diameter are
given, points of intersection of a line and a
(𝑝𝑥+𝑞)𝑑𝑥
∫ √𝑎𝑥 2 + 𝑏𝑥+𝑐 ∫ √𝑎2 ± 𝑥 2 𝑑𝑥 , circle with the centre at the origin and
condition for a line to be tangent to a
∫ √𝑥 2 − 𝑎2 𝑑𝑥
circle, equation of the tangent, sections of
Integral as limit of a sum. The conics, equations of conic sections
fundamental theorem of calculus, (parabola, ellipse, and hyperbola) in
properties of definite integrals. Evaluation standard forms, condition for Y = mx +c to
of definite integrals, determining areas of be a tangent and point (s) of tangency.
the regions bounded by simple curves in
standard form. UNIT 12: THREE DIMENSIONAL
GEOMETRY
UNIT 10: DIFFRENTIAL EQUATIONS
Coordinates of a point in space, the
Ordinary differential equations, their distance between two points, section
order, and degree, the formation of formula, directions ratios, and direction
differential equations, solution of cosines, the angle between two
differential equation by the method of intersecting lines. Skew lines, the shortest
separation of variables, solution of a distance between them, and its equation.
homogeneous and linear differential Equations of a line and a plane in different
equation of the type forms, the intersection of a line and a
𝑑𝑦
plane, coplanar lines.
𝑑𝑥
+ 𝑝(𝑥)𝑦 = 𝑞(𝑥)
UNIT 13: VECTOR ALGEBRA
UNIT 11: CO-ORDINATE GEOMETRY
Vectors and scalars, the addition of
Cartesian system of rectangular vectors, components of a vector in two
coordinates in a plane, distance formula, dimensions and three-dimensional space,
sections formula, locus, and its equation, scalar and vector products, scalar and
translation of axes, the slope of a line, vector triple product.
parallel and perpendicular lines, intercepts
of a line on the co-ordinate axis. UNIT 14: STATISTICS AND PROBABILITY

Measures of discretion; calculation of
Straight line
mean, median, mode of grouped and
Various forms of equations of a line, ungrouped data calculation of standard
intersection of lines, angles between two

deviation, variance and mean deviation for UNIT 3: LAWS OF MOTION
grouped and ungrouped data.
Force and inertia, Newton’s First law of
Probability: Probability of an event, motion; Momentum, Newton’s Second
addition and multiplication theorems of Law of motion, Impulses; Newton’s Third
probability, Baye's theorem, probability Law of motion. Law of conservation of
distribution of a random variate, Bernoulli linear momentum and its applications.
trials, and binomial distribution. Equilibrium of concurrent forces.

UNIT 15: TRIGONOMETRY Static and Kinetic friction, laws of friction,
rolling friction.
Trigonometrical identities and equations,
trigonometrical functions, inverse Dynamics of uniform circular motion:
trigonometrical functions, and their centripetal force and its applications.
properties, heights, and distance.
UNIT 4: WORK, ENERGY, AND POWER
UNIT 16: MATHEMATICAL REASONING
Work done by a content force and a
Statement logical operations and, or, variable force; kinetic and potential
implies, implied by, if and only if, energies, work-energy theorem, power.
understanding of tautology, contradiction,
The potential energy of spring
converse, and contrapositive.
conservation of mechanical energy,
conservative and neoconservative forces;
Elastic and inelastic collisions in one and
PHYSICS two dimensions.
UNIT 1: PHYSICS AND MEASUREMENT UNIT5: ROTATIONAL MOTION
Physics, technology, and society, S I Centre of the mass of a two-particle
Units, fundamental and derived units, least system, Centre of the mass of a rigid body;
count, accuracy and precision of Basic concepts of rotational motion; a
measuring instruments, Errors in moment of a force; torque, angular
measurement, Dimensions of Physics momentum, conservation of angular
quantities, dimensional analysis, and its momentum and its applications; the
applications. moment of inertia, the radius of gyration.
UNIT 2: KINEMATICS Values of moments of inertia for

The frame of reference, motion in a simple geometrical objects, parallel and
straight line, Position- time graph, speed perpendicular axes theorems, and their
and velocity; Uniform and non-uniform applications. Rigid body rotation equations
motion, average speed and instantaneous of rotational motion.
velocity, uniformly accelerated motion, UNIT 6: GRAVITATION
velocity-time, position-time graph,
relations for uniformly accelerated motion, The universal law of gravitation.
Scalars and Vectors, Vector. Addition and Acceleration due to gravity and its
subtraction, zero vector, scalar and vector variation with altitude and depth. Kepler’s
products, Unit Vector, Resolution of a law of planetary motion. Gravitational
Vector. Relative Velocity, Motion in a potential energy; gravitational potential.
plane, Projectile Motion, Uniform Circular Escape velocity, Orbital velocity of a
Motion. satellite. Geo stationary satellites.