Mathematics
OBJECTIVE
- For concept Understanding.
- Idea of Presentation for getting Marks in Board Exam.
- Provide atmosphere to develop Reasoning and Critical Thinking.
- Quick ways of Memorization.
- Well maintenance of test results.
- Analysis of test marks to help reinforce the topic.
- To enhance Objectivity in Physics .
- Innovative time saving methods.
- Preparing for various Examination (JEE ,NEET and others).
- Help in Carrier Guidance.
About JEE
JEE Main (Conducted twice in a year- January & April) ) has two papers,
Paper-I (for admission to B.E./B.Tech courses and is conducted in an Computer Based Test mode.)and Paper-II.(for admission in B.Arch and B.Planning courses and will also be conducted in Computer Based test mode except for one paper, namely the 'Drawing Test' which shall be conducted in Pen and Paper mode or offline-mode.)
Candidates may opt for either or both of them.
Both papers contain multiple choice questions. Paper-I is Paper-II is
From January 2020 an additional Paper - III is being introduced for B.Planning courses separately.
JEE Main, unlike JEE Advanced, has a fixed exam structure and is not subject to change every year. Paper-1 is of three hours duration and consists of thirty multiple-choice (single-correct) questions in each of the three subjects (physics, chemistry, and maths). 4 marks are awarded for correct answers and 1 mark is deducted for incorrect answers.
New pattern consisting of 20+5 questions per subject is introduced in January 2020 with 20 multiple choice questions + 5 numerical type question. In multiple choice questions 4 marks are awarded for correct answers and no marks are deducted from numerical type questions.
JEE Main 2021 Mathematics Syllabus
All JEE Main aspirants
should view the syllabus and plan out the preparation strategy accordingly.
Detailed syllabus for Mathematics section has been provided below.
Unit 1: 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-one, into and onto
functions, the composition of functions.
Unit 2: Complex numbers and quadratic equations
Complex numbers as ordered pairs of reals, Representation of
complex numbers in the form a+ib and their representation in a plane, Argand
diagram, algebra of complex numbers, modulus and argument (or amplitude) of a complex
number, square root of a complex number, triangle inequality, Quadratic
equations in real and complex number systems and their solutions. The relation
between roots and coefficients, nature of roots, the formation of quadratic
equations with given roots.
Unit 3: 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 triangles using determinants. Adjoint and
evaluation of inverse of a square matrix using determinants and elementary
transformations, Test of consistency and solution of simultaneous linear
equations in two or three variables using determinants and matrices.
Unit 4: 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.
Unit 5: Mathematical induction Principle of Mathematical Induction and its simple applications
Unit 6: 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
Unit 7: Sequences and series
Arithmetic and Geometric progressions, Insertion of
arithmetic, Geometric means between two given numbers, Relation between A.M.
and G.M. sum upto n terms of special series: S n, S n2, Sn3 and Arithmetic –
Geometric progression
UNIT 8: Limit, continuity and differentiability
Real – valued functions, Algebra of functions,Polynomials,
Rational, Trigonometric, Logarithmic and exponential functions, Inverse
functions Graphs of simple functions Limits, continuity and differentiability,
Differentiation of the sum, difference, product and quotient of two functions
Differentiation of trigonometric, Inverse trigonometric, Logarithmic,
Exponential, Composite and implicit functions, Derivatives of order upto two,
Rolle’s and Lagrange’s Mean Value Theorems Applications of derivatives: Rate of
change of quantities, monotonic – increasing and decreasing functions,, Maxima
and minima of functions of one variable and Tangents and normals
Unit 9: 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 of the type Integral as limit
of a sum, Fundamental Theorem of Calculus, Properties of definite integrals,
Evaluation of definite integrals, determining areas of the regions bounded by
simple curves in standard form.
Unit 10: Differential equations
Ordinary differential equations, their order and degree.
Formation of differential equations,The solution of differential equations by
the method of separation of variables, solution of homogeneous and linear
differential equations of the type: dy/dx+p(x)y=q(x)
Unit 11: Co-ordinate geometry
Cartesian system of rectangular co-ordinates 10 in a plane,
Distance formula, Section formula, Locus and its equation, Translation of axes,
Slope of a line, Parallel and perpendicular lines, Intercepts of a line on the
coordinate axes.
Straight lines: Various forms of equations of a line,
intersection of lines, angles between two lines, conditions for concurrence of
three lines, distance of a point from a line, equations of internal and
external bisectors of angles between two lines, coordinates of centroid,
orthocentre and circumcentre of a triangle, equation of family of lines passing
through the point of intersection of two lines.
Circles, conic sections: Standard form of equation of a
circle, general form of the equation of a circle, its radius and centre,
equation of a circle when the end points of a diameter are given, points of
intersection of a line and a circle with the centre at the origin and condition
for a line to be tangent to a circle, equation of the tangent. Sections of
cones, equations of conic sections (parabola, ellipse and hyperbola) in
standard forms, condition for y = mx + c to be a tangent and point (s) of tangency.
Unit 12: 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, the 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.
Unit 13: Vector algebra
Vectors and scalars, Addition of vectors, Components of a
vector in two dimensions and three dimensional space, Scalar and vector
products, scalar and vector triple product.
Unit 14: Statistics and probability
Measures of Dispersion: Calculation of mean, median, mode of
grouped and ungrouped data calculation of 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.
Unit 15: Trigonometry
Trigonometric identities and equations, Trigonometrical
functions, Inverse trigonometrical functions and their properties, Heights and
Distances
Unit 16: Mathematical reasoning
Statements, logical operations and, or, implies, implied by, if and only if and Understanding of tautology, contradiction, converse and contra positive
Comments