The IIT-JEE, the most challenging amongst national level engineering entrance examinations, remains on the top of the priority list of several lakhs of students every year. The brand value of the IITs attracts more and more students every year, but the challenge posed by the IIT-JEE ensures that only the best of the aspirants get into the IITs. Students require thorough understanding of the fundamental concepts, reasoning skills, ability to comprehend the presented situation and exceptional problem-solving skills to come on top in this highly demanding entrance examination.

The pattern of the IIT-JEE has been changing over the years. Hence an aspiring student requires a step-by-step study plan to master the fundamentals and to get adequate practice in the various types of questions that have appeared in the IIT-JEE over the last several years. Irrespective of the branch of engineering study the student chooses later, it is important to have a sound conceptual grounding in Mathematics, Physics and Chemistry. A lack of proper understanding of these subjects limits the capacity of students to solve complex problems thereby lessening his/her chances of making it to the topnotch institutes which provide quality training.

We at https://www.IITianAcademy.com serves as a source of learning that goes beyond the school curriculum of Class XI and Class XII and is intended to form the backbone of the preparation of an aspiring student. Content has been designed by Ex-IITian with the objective of guiding an aspirant to his/her goal in a clearly defined step-by-step approach.

**• Master the Concepts and Concept Strands!**

This covers all the concepts in the latest IIT-JEE syllabus by segregating them into appropriate units. The theories are explained in detail and are illustrated using solved examples detailing the different applications of the concepts.

**• Let us First Solve the Examples-Concept.**

At the end of the theory content in each unit, a good number of "Solved Examples" are provided and they are designed to give the aspirant a comprehensive exposure to the application of the concepts at the problem-solving level.

**• Do Your Exercise-Daily!**

Over hundreds of unsolved problems are presented for practice at the end of every chapter. Hints and solutions for the same are also provided. These problems are designed to sharpen the aspirant's problem-solving skills in a step-by-step manner.

**• Must go through Reference Books like S. L. Loney, Hall & Knight and Thomas and Finney.
• Remember, Practice Makes You Perfect!
• Do remeber to Ask your doubt from experts at https://www.IITianAcademy.com**

We recommend you work out ALL the problems on your own - both solved and unsolved - to enhance the effectiveness of your preparation.

A distinct feature of this site is that unlike most other reference books in the market, this is not authored by an individual. It is put together by a team of highly qualified faculty members that includes IITians, PhDs etc from some of the best institutes in India and abroad. This team of academic experts has vast experience in teaching the fundamentals and their application and in developing high quality study material for IIT-JEE https://www.IITianAcademy.com, the number 1 Online coaching institute for IIT and Medical Entrace Exams. The essence of the combined knowledge of such an experienced team is what is presented in this self-preparatory series. While the contents of these books have been organized keeping in mind the specific requirements of IIT-JEE, we are sure that you will find these useful in your preparation for various other engineering entrance exams also.

Marks: 120

**Overall Analysis of Question Paper IIT JEE Main**

The most prestigious Entrance Exam of Engineering, JEE Main 2019 in Computer based mode has been conducted on 10th April 2019 (Wednesday) from 9.30 am to 12.30 pm across the nation.

Number of questions in the paper was **90 (30 Questions each in Physics, Chemistry and Maths )** and total marks was 360 with **1/4th** negative marks for each wrong answer.

**UNITWISE DISTRIBUTION TABLE OF MATHEMATICS**

** **

Topic | Questions |
%age Portion |
Very Easy |
Easy |
Average |
Difficult |
|||||

Calculus | 10 |
33.33% |
0 |
1 |
7 |
2 |
|||||

Vector , 3D | 3 |
10% |
0 |
0 |
2 |
1 |
|||||

Algebra | 11 |
36.66% |
1 |
1 |
6 |
3 |
|||||

Trigonometry | 2 |
6.66% |
0 |
0 |
1 |
1 |
|||||

Co-ordinate geometry | 4 |
13.33% |
0 |
1 |
3 |
0 |
|||||

Total | 30 |
100% |
1 |
3 |
19 |
7 |

**We wish you the very best! **

- 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 system and their solutions.
- The relation between roots and coefficients, nature of roots, the formation of quadratic equations with given roots.

- Matrices: Algebra of matrices, types of matrices, and matrices of order two and three
- Determinants: Properties of determinants, evaluation of determinants, the 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.

- 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 up to 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, tangents, and normals.

- 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
- Integral as limit of a sum.
- Evaluation of simple integrals:
- Fundamental Theorem of Calculus.
- Properties of definite integrals, evaluation of definite integrals,
- determining areas of the regions bounded by simple curves in standard form.

- Cartesian system of rectangular co-ordinates in a plane, distance formula, section formula, locus and its equation, translation of axes, the 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**Pair Of Straight lines**: Equations of internal and external bisectors of angles between**two lines**, coordinates of centroid, orthocentr, 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 endpoints 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****hyperbola**in standard forms, condition for y = mx + c to be a tangent and point (s) of tangency.

- Coordinates of a point in space, the distance between two points.
- Section formula, direction ratios and direction cosines, the 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, the intersection of a line and a plane, coplanar lines.

- 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.