JEE Main 2022 Syllabus B.Plan

Syllabus for Paper 2B (B.Planning)
MATHEMATICS
UNIT1:SETS, RELATIONS, AND FUNCTIONS: UNIT 5: MATHEMATICAL INDUCTIONS:

Sets and their representation: Union, Principle of Mathematical Induction and its
intersection and complement of sets and their simple applications.
algebraic properties; Power set; Relation,
UNIT 6: BINOMIAL THEOREM AND ITS
Type of relations, equivalence relations,
SIMPLE APPLICATIONS:
functions; one-one, into and onto functions,
the composition of functions. Binomial theorem for a positive integral
index, general term and middle term,
UNIT2: COMPLEX NUMBERS AND
properties of Binomial coefficients, and
QUADRATIC EQUATIONS:
simple applications.
Complex numbers as ordered pairs of reals,
UNIT 7: SEQUENCE AND SERIES:
Representation of complex numbers in the
form a + ib and their representation in a Arithmetic and Geometric progressions,
plane, Argand diagram, algebra of complex insertion of arithmetic, geometric means
number, modulus and argument (or between two given numbers, Relation
amplitude) of a complex number, triangle between A.M and G.M sum up to n terms of
inequality, Quadratic equations in real and special series; Sn, Sn2, Sn3. Arithmetico-
complex number system and their solutions Geometric progression.
Relations between roots and co-efficient,
nature of roots, the formation of quadratic UNIT 8: LIMIT, CONTINUITY, AND
DIFFERENTIABILITY:
equations with given roots. Real–valued functions, algebra of functions,
UNIT 3: MATRICES AND DETERMINANTS: polynomials, rational, trigonometric,
logarithmic, and exponential functions,
Matrices, algebra of matrices, type of inverse function. Graphs of simple functions.
matrices, determinants, and matrices of order Limits, continuity, and differentiability.
two and three, properties of determinants, Differentiation of the sum, difference,
evaluation of determinants, area of triangles product, and quotient of two functions.
using determinants, Adjoint, and evaluation Differentiation of trigonometric, inverse
of inverse of a square matrix using trigonometric, logarithmic, exponential,
determinants and elementary composite and implicit functions; derivatives
transformations, Test of consistency and of order up to two, Rolle’s and Lagrange's
solution of simultaneous linear equations in Mean value Theorems, Applications of
two or three variables using determinants and derivatives: Rate of change of quantities,
matrices. monotonic-Increasing and decreasing
UNIT4: PERMUTATIONS AND functions, Maxima and minima of functions
COMBINATIONS: of one variable, tangents and normal.

The fundamental principle of counting, UNIT 9: INTEGRAL CALCULAS:
permutation as an arrangement and Integral as an anti-derivative, Fundamental
combination as section, Meaning of P (n,r) Integrals involving algebraic, trigonometric,
and C (n,r), simple applications. exponential, and logarithms functions.
Integrations by substitution, by parts, and by

partial functions. Integration using A standard form of equations of a circle, the
trigonometric identities. general form of the equation of a circle, its
radius and central, equation of a circle when
Evaluation of simple integrals of the type
the endpoints of a diameter are given, points
𝑑𝑥 𝑑𝑥 𝑑𝑥 𝑑𝑥 of intersection of a line and a circle with the
∫ 𝑥 2 +𝑎2 , ∫ , ∫ 𝑎2 − 𝑥2 , ∫
√𝑎 2 − 𝑥 2
√𝑥 2 ± 𝑎2 centre at the origin and condition for a line to
𝑑𝑥 𝑑𝑥 (𝑝𝑥+𝑞)𝑑𝑥
, ∫ ,∫ , ∫ 2 , be tangent to a circle, equation of the
𝑎𝑥 2 +𝑏𝑥+𝑐 √𝑎𝑥 2 + 𝑏𝑥+𝑐 𝑎𝑥 +𝑏𝑥+𝑐
tangent, sections of conics, equations of
(𝑝𝑥+𝑞)𝑑𝑥
∫ √𝑎𝑥 2 + 𝑏𝑥+𝑐 ∫ √𝑎2 ± 𝑥 2 𝑑𝑥 , conic sections (parabola, ellipse, and
hyperbola) in standard forms, condition for
∫ √𝑥 2 − 𝑎2 𝑑𝑥
Y = mx +c to be a tangent and point (s) of
Integral as limit of a sum. The fundamental tangency.
theorem of calculus, properties of definite
UNIT12:THREE DIMENSIONAL GEOMETRY
integrals. Evaluation of definite integrals,
determining areas of the regions bounded by Coordinates of a point in space, the distance
simple curves in standard form. between two points, section formula,
directions ratios, direction cosines, the angle
UNIT 10: DIFFRENTIAL EQUATIONS
between two intersecting lines. Skew lines,
Ordinary differential equations, their order, the shortest distance between them, and its
and degree, the formation of differential equation. Equations of a line and a plane in
equations, solution of differential equation different forms, the intersection of a line and
by the method of separation of variables, a plane, coplanar lines.
solution of a homogeneous and linear
UNIT 13: VECTOR ALGEBRA
differential equation of the type
𝑑𝑦
Vectors and scalars, the addition of vectors,
𝑑𝑥
+ 𝑝(𝑥)𝑦 = 𝑞(𝑥) components of a vector in two dimensions
and three-dimensional space, scalar and
UNIT 11: CO-ORDINATE GEOMETRY
vector products, scalar and vector triple
Cartesian system of rectangular coordinates product.
10 in a plane, distance formula, sections
UNIT 14: STATISTICS AND PROBABILITY
formula, locus, and its equation, translation
of axis, slop of a line, parallel and Measures of discretion; calculation of mean,
perpendicular lines, intercept of a line on the median, mode of grouped and ungrouped
co-ordinate axes. data calculation of standard deviation,
variance and mean deviation for grouped and
Straight line
ungrouped data.
Various forms of equations of a line,
Probability: Probability of an event, addition
intersection of lines, angles between two
and multiplication theorems of probability,
lines, conditions for concurrence of three
Baye's theorem, probability distribution of a
lines, the distance of a point form a line,
random variate, Bernoulli trials, and
equations of internal and external by sectors
binomial distribution.
of angles between two lines co-ordinate of
the centroid, orthocentre, and circumcentre UNIT 15: TRIGONOMETRY
of a triangle, equation of the family of lines
Trigonometrical identities and equations,
passing through the point of intersection of
trigonometrical functions, inverse
two lines.
trigonometrical functions, and their
Circle, conic sections properties, heights, and distance.

UNIT 16: MATHEMATICAL REASONING PLANNING

Statement logical operations and, or, implies, UNIT-1 GENERAL AWARENESS
implied by, if and only if, understanding of
General knowledge questions and knowledge
tautology, contradiction, converse, and
about prominent cities, development issues,
contrapositive.
government programs, etc.

UNIT-2 SOCIAL SCIENCES
APTITUDE
The idea of nationalism, nationalism in India,
UNIT-1 Awareness of persons. Buildings, pre-modern world, 19th-century global
Materials. economy, colonialism, and colonial cities,
industrialization, resources, and development,
Objects, Texture related to Architecture and types of resources, agriculture, water, mineral
Build-envirounmentVisusalising three- resources, industries, national economy;
dimensional objects from two-dimensional Human Settlements
drawings. Visualizing. Different sides of
Power-sharing, federalism, political parties,
three-dimensional objects. Analytical
democracy, the constitution of India
Reasoning Mental Ability (Visual.
Numerical and Verbal) Economic development- economic sectors,
globalization, the concept of development,
UNIT –2 Three dimensional- perception: poverty; Population structure, social exclusion,
Understanding and appreciation of scale and and inequality, urbanization, rural
proportions of objects, building forms and development, colonial cities,
elements, colour texture harmony and
contrast Design and drawing of geometrical UNIT-3 THINKING SKILLS
or abstract shapes and patterns in pencil. Comprehension (unseen passage); map reading
Transformation of forms both 2D and 3D skills, scale, distance, direction, area, etc.;
union, subtraction rotation, development of critical reasoning; understanding of charts,
surfaces and volumes, Generation of Plan, graphs, and tables; basic concepts of statistics
elevations and 3D views of objects, Creating and quantitative reasoning.
two-dimensional and three-dimensional
compositions using given shapes and forms.