JEE Main 2021 Math Paper Analysis: Most Asked Topics

The Joint Entrance Examination Main, or JEE Main, the premiere examination for engineering admissions in the country, includes two papers. Paper 1 is for admission to undergraduate (UG) engineering programmes in prestigious institutes like the National Institutes of Technology, or NITs; Indian Institutes of Information Technology (IIITs) and Centrally funded Technical Institutions (CFTIs) etc. It is also an eligibility test to participate in JEE Advanced, the gateway to UG engineering programmes at the Indian Institutes of Technology, or IITs. Paper 2 is for admission to B.Arch and B. Planning courses.

As you are aware, lakhs of candidates participate in JEE Main and only a very small percentage of them are able to get admission in top engineering colleges. Despite taking coaching classes, test series and foundation courses, a huge chunk of candidates are not able to qualify JEE Main. This shows that hard work alone is not sufficient to qualify the competitive exam with good scores. Along with hard work you should make the right strategy that is also smart; analyze previous years’ papers and list out important and most asked concepts and chapters.

Careers360’s expert team analyzed the papers of JEE Main 2021, which was held in 4 sessions in 26 shifts. An analysis of 780 questions from the Mathematics section is given below along with the chapters and number of questions.

Chapter And Number Of Questions

An analysis of the above table shows that the first three chapters, i.e, Coordinate Geometry; Limit, Continuity And Differentiability and Integral Calculus are so important that together they contribute 246 questions out of 780 questions. This means that around 30% of questions in JEE Main 2021 were asked from these three chapters. It is in this context that strategy and analysis become very important. To obtain good marks,

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The students must align their study in line with the importance of the topics. A smart student will observe that no questions were asked from the chapter, Mathematical Induction. So, the students need to give only minimal focus on this chapter.

Given below is a list of the top 10 concepts of Mathematics from where maximum questions were asked in the JEE Main 2021. After this table a brief description of the concepts is given. If you don’t have enough time and want to study important concepts then these 10 concepts become most important.

Ten Important Concepts Of JEE Main 2021 Mathematics

Students can also see that 125 questions out of the 780 questions were asked from these concepts. Now let us understand the basics of these concepts in brief.

Linear Differential Equations include a variable, derivative of that variable, and other functions. Basic concepts related to Differential Calculus and Integral Calculus have some prerequisites. The general form of a linear differential equation is . Here, y is a variable; P, Q can be a function of x or constant. This is the most important topic from where maximum questions were asked in JEE Main 2021. Therefore, understanding the concept becomes very important. Some basic steps you should follow to solve this equation is given below:

Step 1: Rearrange the equation and get the general form

Step 2: Calculate the Integrating Factor (I.F) using the formula

Step 3: You can calculate the solution using the given equation

Application Of Permutation

There are two concepts, Permutation and Combination. The combination is used to select items from a list of items but permutation is selecting the items from the list and arranging them. The simplest example is, let there are n different items and we want to select r items without repeating the items then we use the combination formula, and if after selecting r items we want to arrange then we use the permutation formula .

There are so many applications of permutations in every branch of mathematics as well as other fields of science like in computer science, permutations are used for sorting algorithms; in biology, permutations are used for describing RNA sequence. Let me discuss some cases.

If there are n distinct objects and repetition is not allowed, then number of permutations of choosing r objects at a time are and If repetition is allowed then number of permutations are .

If n distinct objects are in a circle for example n distinct pearls in a garland, then the number of ways to rearrange pearls are (n-1)!

Algebra Of Statements is related to the NCERT chapter Mathematical Reasoning. It includes concepts related to the Negation of Statements, concepts related to Connectives OR, AND, etc. Questions from this chapter are low-hanging fruits, you just need to have a basic understanding of the algebra of statements, and that requires practice to get a hold on the concepts.

Dispersion (Variance And standard Deviation) is related to the NCERT chapter statistics. Standard Deviation and Variance are measures of the spread of data from the mean. We can get an idea of how the data are distributed. There are some formulas you just need to understand and remember which can help you during exams to solve problems very efficiently. Variance and standard deviation are interrelated to each other as .

General Term Of Binomial Expansion is a concept related to the NCERT chapter Binomial Theorem. Binomial theorem for any positive integer n is given by .

Since the general term is defined as (r + 1)th term in this expansion and denoted by therefore general term can be written as . There is another concept of the middle term which can be recommended to study.

Cramer’s Law is related to the NCERT chapter, Three-dimensional Geometry which helps in solving a system of equations that are equal to the unknowns. This is an important formula that uses Matrices and Determinant concepts to solve equations and becomes most efficient when a unique solution exists. After practicing you can command the concepts as given below:

Step 1: write the system of equations in the general format AX = B

Here A, B, and X are matric

Step 2: calculate the D = |A|

if D is non zero then equations have a unique solution.

If D is zero then there might be infinitely many solutions or No solutions.

Area Bounded By Two Curves is related to the NCERT chapter Application of Integration. Basics of Integral Calculus and Curves are required for solving problems. The area bounded by two curves is an application of Integration. If f(x) is greater than g(x) then the area between these two curves from x = a to x = b is calculated by the given formula

Piecewise Definite Integration:

There are some functions that have different expressions according to their definition and are known as piecewise functions. For solving these types of questions you should have basic knowledge of Function, Continuity, and Definite Integration Calculus. Let's take an example to understand it.

A piecewise function is defined as

We want to integrate it from x = -1 to x = 3

According to the definition function is when x is -1 to 1 and function is when x is 1 to 3. We can integrate according to the given limit

Multiplication Of Two Matrices requires prerequisite of Matrices i.e concepts related to the Order of Matrices, Number of Columns and Rows in a Matrix. Multiplication of two matrices is defined only when the number of columns in the first matrix is equal to the number of rows in the second matrix. Let's take an example to get it in detail.

A is a 2x3 matrix and B is also a 3x2 matrix. You can observe the number of columns in A Martic i.e 3 is equal to the number of rows in matrix B i.e 3, therefore, multiplication of A and B, that is, AB exists.

Family Of Planes is enumerated in NCERT chapter Three Dimensional Geometry. Concepts related to Vector Algebra and Direction Cosine are prerequisites for this topic. The general equation of a plane in the cartesian coordinate system is given by lx+my+nz = d. Here l,m,n are directional cosines and d is constant. The general form of plane in vector form can be written as here vector n is perpendicular to the plane and d is constant.

If you want more information and detailed explanations of important topics of Mathematics then you can visit JEE Main Exam's High Scoring Chapters and Topics and can freely download the E-Book for your reference.

After going through the analysis you will become familiar with the importance of strategy and analysis. Use your knowledge base, strategy, and concepts to obtain maximum marks with less effort and succeed in these premiere exams like JEE Main and JEE Advanced..