2 April 2026: Download JEE Main 2026 Session 2 Question papers
JEE Main 2026 Maths Preparation Tips: Study Plan, Time Table, Best Books, PYQs
Content Writer | Updated On - Apr 4, 2026
What's New?
Mathematics, contributing 30-35% of total questions, play a vital role in competitive advantage, with essential topics like Sets, Relations, and Functions serving as a base. A 25% reduction in the syllabus equals 35% increase in the weightage ,providing aspirants with a potential scoring advantage, conversely 15% syllabus reduction leads to a 35% decrease in weightage, requiring focused preparation.
- Focus on Calculus, Algebra, and Coordinate Geometry (40-50% weightage).
- Practice 70-80% to identify common questions, repeating patterns (15-20%), and time management weaknesses.
- Spend 50% of study time on mock tests and problem-solving.
- Use the remaining time to review formulas, concepts, and shortcuts.
- Early preparation boosts confidence and increases the chance of scoring 90%+ in Mathematics.
Important Links:
- JEE Main 2026 Physics Preparation Tips
- JEE Main 2026 Chemistry Preparation Tips
- JEE Main 2026 Study Materials
- JEE Main 2026 Important Topics
Also Check:
Table of Contents
- Study Plan for JEE Main Mathematics 2026
- Chapter Wise Weightage for JEE Main Mathematics 2026
2.1 JEE Main 2026 Mathematics Topic-wise Analysis
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4.1 Why Choose Chapter-wise Preparation?
- What topics have been deleted from the JEE Main 2026 Mathematics syllabus?
5.1 What is the 80/20 rule for JEE Mains?
5.2 How to score Good marks in JEE Main maths?
- How To prepare for JEE Main Mathematics 2026 without Coaching?
- Last Minute Preparation Tips for JEE Main Mathematics
- Recommended Books For JEE Main Mathematics 2026
- JEE Main vs JEE Advanced Mathematics Comparison
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Study Plan for JEE Main Mathematics 2026
| Week | Topics to Cover | Focus Area | Practice & Revision |
|---|---|---|---|
| Week 1-2 | Algebra: Quadratic Equations, Progressions (AP, GP, HP) | Understand formulas, derivations | Solve basic problems, Revise previous year questions |
| Week 3-4 | Calculus: Limits, Continuity, Differentiation | Focus on rules and applications | Practice problems, Work on speed and accuracy |
| Week 5-6 | Integral Calculus, Application of Derivatives | Learn integration techniques, Differentiation rules | Solve MCQs, Mock tests |
| Week 7-8 | Trigonometry, Matrices, and Determinants | Master formulas, focus on identities | Practice trigonometric equations and matrix operations |
| Week 9-10 | Vectors and 3D Geometry | Conceptual understanding, vector algebra | Solve 3D geometry problems, Practice previous years |
| Week 11-12 | Probability and Statistics | Probability laws, Mean, Median, Mode | Practice probability problems, Mock tests |
| Week 13-14 | Coordinate Geometry | Focus on straight lines, circles, conic sections | Solve application-based problems |
| Week 15-16 | Revision of all topics | Reinforce weak areas, focus on tricky questions | Full-length mock tests, Time management practice |
Chapter Wise Weightage for JEE Main Mathematics 2026
Cracking JEE Main Mathematics requires more than just practice; it demands smart preparation. Each chapter contributes uniquely to the paper, and understanding their weightage can be the key to success. By aligning your efforts with high-yield topics like Calculus, Algebra, and Coordinate Geometry, you can approach the exam with confidence and precision.
| Unit/Topic | Expected Weightage (%) | Remarks/Key Concepts |
|---|---|---|
| Matrices and Determinants | 6-8% | Properties of determinants, inverse of a matrix, solving linear equations using matrices |
| Complex Numbers | 5-7% | Argand plane, modulus, argument, polar form, roots of complex numbers |
| Binomial Theorem | 3-5% | General and middle terms, expansions, approximations |
| Permutation and Combination | 3-4% | Counting principles, arrangements, combinations, circular permutations |
| Sequence and Series | 4-6% | Arithmetic Progression (AP), Geometric Progression (GP), Harmonic Progression (HP), and special series |
| Probability | 3-5% | Conditional probability, Bayes’ theorem, random variables, and probability distributions |
| Sets, Relations, and Functions | 3-5% | Types of relations, domain, range, invertibility, and graphs of functions |
| Limits and Continuity | 3-5% | Epsilon-delta definition, algebra of limits, L'Hôpital’s rule |
| Differentiation | 5-7% | Derivatives of functions, chain rule, implicit differentiation |
| Application of Derivatives | 6-8% | Tangents, normals, maxima and minima, monotonicity, Rolle’s and Mean Value Theorems |
| Definite and Indefinite Integrals | 6-8% | Standard integrals, substitution, partial fractions, and properties of definite integrals |
| Differential Equations | 4-5% | First-order and first-degree equations, homogeneous equations, and applications |
| Straight Lines | 5-6% | Slope, intercepts, distance, angle between lines, and equations of lines |
| Circles | 4-5% | Standard equation, tangent, normal, and chord properties |
| Parabola, Ellipse, and Hyperbola | 5-7% | Standard forms, latus rectum, eccentricity, tangent properties |
| 3D Geometry | 5-6% | Direction cosines, direction ratios, plane equations, shortest distance between lines |
| Trigonometry | ~5-7% | |
| Trigonometric Ratios and Equations | 3-4% | Identities, transformations, solving trigonometric equations |
| Inverse Trigonometric Functions | 2-3% | Principal values, properties, and graphs |
| Vectors and Statistics | ~5-7% | |
| Vectors | 3-4% | Scalar and vector products, projections, and properties |
| Statistics and Mathematical Reasoning | 2-3% | Measures of dispersion, mean, variance, probability-based reasoning |
Also Check:
JEE Main 2026 Mathematics Topic-wise Analysis
IIT JEE Mains Maths Syllabus is an ideal mix of simple and troublesome topics. A few themes like trigonometry, differential analytics, circles and straight lines in coordinate geometry, changes and mixes in variable based math are in every case simple to crack. Those days are gone when Aspirants used to go through hours attempting one question. This is a time of different decision questions.
JEE Main Mathematics isn't extremely intense yet candidates neglect to exceed expectations in it as their fundamentals are not clear.
Below we have provided previous Year Topic wise Analysis
| Topic | Number of Questions (2024) | Marks (2024) | Weightage (2024) | Number of Questions (2023) | Marks (2023) | Weightage (2023) |
|---|---|---|---|---|---|---|
| Coordinate Geometry | 5 | 20 | 15.90% | 5 | 20 | 15.90% |
| Limits, Continuity, and Differentiability | 3 | 12 | 9.90% | 3 | 12 | 9.90% |
| Integral Calculus | 3 | 12 | 9.90% | 3 | 12 | 9.90% |
| Complex Numbers and Quadratic Equations | 2 | 8 | 6.60% | 2 | 8 | 6.60% |
| Matrices and Determinants | 2 | 8 | 6.60% | 2 | 8 | 6.60% |
| Statistics and Probability | 2 | 8 | 6.60% | 2 | 8 | 6.60% |
| Three Dimensional Geometry | 2 | 8 | 6.60% | 2 | 8 | 6.60% |
| Vector Algebra | 2 | 8 | 6.60% | 2 | 8 | 6.60% |
| Sets, Relations, and Functions | 1 | 4 | 3.30% | 1 | 4 | 3.30% |
| Permutation and Combination | 1 | 4 | 3.30% | 1 | 4 | 3.30% |
| Sequences and Series | 1 | 4 | 3.30% | 1 | 4 | 3.30% |
| Binomial Theorem and its Application | 1 | 4 | 3.30% | 1 | 4 | 3.30% |
| Mathematical Reasoning | 1 | 4 | 3.30% | 1 | 4 | 3.30% |
| Differential Equation | 1 | 4 | 3.30% | 1 | 4 | 3.30% |
| Statics and Dynamics | 1 | 4 | 3.30% | 1 | 4 | 3.30% |
| Differential Calculus | 1 | 4 | 3.30% | 1 | 4 | 3.30% |
JEE Main Mathematics 2026 Chapter-wise Preparation
Preparing for JEE Main, one of the most competitive exams in India, requires a structured and comprehensive strategy. A chapter-wise approach ensures systematic learning, enabling students to focus on each topic thoroughly before moving to the next. This method not only helps in covering the syllabus efficiently but also improves retention and problem-solving skills.
Why Choose Chapter-wise Preparation?
- Systematic Learning: Breaking down the syllabus chapter-by-chapter ensures clarity and organized study.
- Strong Fundamentals: Each chapter is mastered individually, building a solid conceptual foundation.
- Customizable Schedule: Prioritize chapters based on weightage and difficulty level.
- Time Management: Dedicated time slots for each chapter prevent last-minute rushes.
| Week | Topics | Focus Areas | Resources & Suggestions |
|---|---|---|---|
| Week 1 | Sets, Relations, and Functions; Complex Numbers; Quadratic Equations; Matrices and Determinants | Domain and range of functions, Venn diagramsPolar form, cube roots of unity in Complex NumbersNature of roots and discriminant in Quadratic Equations Properties of determinants and solving linear equations using matrices | YouTube Channels: Unacademy JEE: 'Functions JEE Revision' MathonGo: 'Matrices JEE Crash Course'Books: NCERT + RD SharmaPractice: Solve Previous Year Questions (JEE 2021-2024) for these topics. |
| Week 2 | Permutations and Combinations; Binomial Theorem; Sequences and Series;Mathematical Induction | P&C principles, understanding NCR and NPR formulasBasic binomial expansions, properties of coefficientsAP, GP, sum of infinite series, telescoping seriesMathematical induction for proving summation and divisibility problems | YouTube Channels:Vedantu JEE: 'P&C in 1 Shot'Physics Wallah: 'Binomial Theorem Quick Revision' Practice: Attempt topic-specific mock tests to build speed in combinatorics and summation problems. |
| Week 3 | Trigonometry; 2. Coordinate Geometry (2D); 3. Differentiation; 4. Applications of Derivatives | Trigonometric identities, transformations, heights, and distancesProperties of lines, circles, tangents, and conicsBasics of derivatives, tangent and normal equationsMaxima, minima, and increasing/decreasing functions | YouTube Channels: Infinity Learn by Sri Chaitanya: 'Conics for JEE'Career Point JEE: 'AOD Crash Course'Revision: Solve high-weightage PYQs and mock questions on Coordinate Geometry and AOD. |
| Week 4 | Integration; Applications of Integrals; Vector Algebra; 3D Geometry;. Probability and Statistics | Integration techniques: substitution, by parts, definite integralsArea under curves and solving application problems Vector operations: dot and cross products, equations of planes Bayes’ theorem, probability distributions, and statistical measures | YouTube Channels:Khan Academy: 'Definite Integrals Simplified'Etoos India JEE: 'Vector Algebra Revision' Mock Tests: Solve at least 3 full-length mock tests. Analyze errors and work on weak areas during revision sessions. |
Most Important Chapters for JEE Main Mathematics 2026
The JEE Main Mathematics syllabus is made up of around 14-15 Units. . That is the most crucial aspect, yet it requires a lot of effort. The following are the most essential JEE Main 2026 Mathematics chapters:
- Complex Numbers And Quadratic Equations
- Co-Ordinate Geometry
- Integral Calculus
- Three Dimensional Geometry
- Vector Algebra
- Statistics and Probability
- Trigonometry
- Permutations And Combinations
- Sequence And Series
Check Out more: JEE Main Important Topics and Chapters 2026
JEE Main Mathematics Previous Year Question Paper 2026
The JEE Main 2026 Mathematics section will feature a wide range of questions designed to assess the problem-solving skills and conceptual understanding of aspirants. Mathematics, accounting for 30-35% of the total questions, covers key topics such as Algebra, Calculus, Coordinate Geometry, and Trigonometry. Reviewing these papers will not only help in time management but also in strengthening the essential concepts needed for success in the highly competitive exam.
Check out the Question Paper pdf for JEE Main Mathematics 2026 Preparation
| Date | Shift | Paper and Answers | Papers and Solutions |
|---|---|---|---|
| 16 March | 1 | Click Here | Click Here |
| 2 | Click Here | Click Here | |
| 17 March | 1 | Click Here | Click Here |
| 2 | Click Here | Click Here | |
| 18 March | 1 | Click Here | Click Here |
| 2 | Click Here | Click Here |
What topics have been deleted from the JEE Main 2026 Mathematics syllabus?
The JEE main mathematics syllabus has undergone some changes to reduce the load and focus more on core concepts. Several Topics have been deleted from the mathematics sections Check out this table for detailed information.
| Topic | Deleted Content |
|---|---|
| Complex Numbers and Quadratic Equations | Square root of a complex number, Triangle inequality. |
| Sequences and Series | Sum up to n terms of special series, Arithmetic-geometric progression. |
| Statistics and Probability | Bernoulli trials, Binomial distribution. |
| Trigonometry | Heights and distances. |
| Integral Calculus | Integral as the limit of a sum. |
| Matrices and Determinants | Properties of determinants, Elementary transformations. |
What is the 80/20 rule for JEE Mains?
The 80/20 Rule for JEE Mains is a concept applied to time management and preparation strategies, based on Pareto Principle, which suggests that 80% of the results come from 20% of the efforts. In the context of JEE Mains , Preparation, this means:
- 80% of the questions can be solved by mastering 20% of the key topics: Focus on high-yield topics and concepts that are most frequently tested and have the highest weightage in the exam.
- Time allocation: Spend 80% your time revising and mastering these key topics , and the remaining 20% on other topics that are important but less likely to appear frequently
Key Aspects of 80/20 rule for JEE Mains:
| Priority Level | Subject | Key Chapters | Focus Areas | Problem Solving Approach |
|---|---|---|---|---|
| High | Mechanics | Kinematics, Laws of Motion, Work, Energy, Power, Rotational Motion, Gravitation | Understand Newton's Laws, motion equations, energy conservation, torque, and rotational dynamics. | Solve problems based on forces, work-energy principle, and rotational motion. Focus on conceptual understanding. |
| High | Electrostatics | Coulomb’s Law, Electric Fields & Potential, Capacitance, Gauss’s Law | Deep understanding of electric fields, potential, and capacitors. Apply concepts to complex problems. | Practice questions on the field due to their recurring nature in exams. Focus on understanding how to apply formulas. |
| High | Organic Chemistry | Hydrocarbons, Alcohols, Phenols, Ethers, Aldehydes, Ketones, Organic Reaction Mechanisms | Master reaction mechanisms, functional groups, and important reactions. Practice with named reactions. | Solve reaction mechanism problems and focus on identifying key steps in the reactions. |
| High | Algebra | Quadratic Equations, Progressions (AP, GP), Matrices & Determinants, Complex Numbers | Strengthen understanding of basic algebraic identities, quadratic equations, and matrix operations. | Practice solving equations, series, and simplifying expressions. Focus on pattern recognition. |
| Medium | Optics | Reflection and Refraction, Lenses, Mirrors, Wave Optics | Focus on ray diagrams, lenses, and understanding wave properties. | Solve ray diagram-based problems and focus on the refraction and reflection concepts. |
| Medium | Thermodynamics | Laws of Thermodynamics, Heat Engines, Entropy | Strong understanding of thermodynamic laws and their applications in heat engines and entropy. | Practice numerical problems based on work done, heat flow, and entropy change. |
| Medium | Modern Physics | Photoelectric Effect, Atomic Models, Nuclear Physics | Focus on understanding wave-particle duality and quantum mechanics. | Focus on solving problems on energy quantization, atomic spectra, and radioactivity. |
| Low | Chemistry (Inorganic) | Periodic Table Trends, Coordination Compounds, Chemical Bonding | Focus on periodic trends, hybridization, and properties of coordination compounds. | Solve questions on properties of elements, bonding, and reaction types. |
| Low | Surface Chemistry | Catalysis, Colloids, Adsorption | Understand adsorption, catalysts, and colloid properties. | Solve questions on types of colloids and catalyst reactions. |
How to score Good marks in JEE Main maths?
Scoring Good marks in JEE Main Mathematics requires a Strategic approach to mastering key concepts, practicing regularly and managing time effectively during the exam. A Focus Study Plan combined with smart techniques can help achieve this goal. Mathematics in JEE Main demands deep understanding, application of formulas and problem solving skills. This guide outlines essential tips and strategies for improving your performance in JEE Main Mathematics.
| Topic | Frequency in Past Papers | Explanation |
|---|---|---|
| Calculus | High | Calculus, including topics like Limits, Differentiation, and Integration, consistently carries significant weightage (around 35-45%). |
| Algebra | High | Topics like Quadratic Equations, Matrices, Determinants, and Progressions are crucial and appear regularly in the exam (around 20-30%). |
| Coordinate Geometry | Medium-High | Focus on straight lines, circles, conic sections (parabola, ellipse, hyperbola), and 3D geometry. This area is frequently tested (around 15-25%). |
| Trigonometry | Medium | Trigonometric identities, equations, and properties are important but slightly less frequent than other topics (around 10-15%). |
| Vectors and 3D Geometry | Medium | Vectors, Scalar and Vector Products, and 3D geometry (planes, lines, and angles) often appear in questions (around 10-15%). |
| Matrices and Determinants | Medium | Key topic in Algebra, focusing on properties, adjoint, inverse, rank, and determinants (around 10-15%). |
| Probability and Statistics | Medium-Low | Probability, permutations, combinations, and basic statistics have been appearing with moderate frequency (around 5-10%). |
| Complex Numbers | Medium-Low | Questions on the properties of complex numbers, their polar form, and conjugates show up occasionally (around 5-10%). |
| Differential Equations | Low | This is a relatively less frequent but important topic. It usually appears in one or two questions every 2-3 years (around 2-5%). |
| Permutation and Combination | Low | While it occasionally appears, it’s usually combined with probability or other topics (around 2-5%). |
| Linear Programming | Low | Rarely tested in its pure form; it may appear as part of optimization problems or in applications of Algebra (around 1-2%). |
How To prepare for JEE Main Mathematics 2026 without Coaching?
To Prepare for JEE Main Mathematics 2026 without Coaching requires a well structured strategy, discipline and the right resources.Mathematics is a high scoring subject in JEE,with topics like calculus, Algebra,Coordinate Geometry and Trinometry forming the backbone of the exam.
Below is a detailed preparation plan to help you ace JEE Main Mathematics effectively
| Resource Type | Resource Name | Description |
|---|---|---|
| YouTube Channels | Khan Academy | Free lessons on key concepts, theory, and problem-solving. |
| Unacademy JEE | Offers topic-wise lectures, doubt clearing, and live sessions. | |
| Vedantu JEE | Provides free lectures, quick revisions, and practice questions. | |
| Online Books | NCERT Mathematics Textbook | Fundamental textbook for JEE Main topics. |
| IIT Mathematics by M.L. Khanna | Comprehensive book for problem-solving and practice. | |
| Problems in Calculus of One Variable by I.A. Maron | Focus on Calculus, great for building conceptual clarity and problem-solving. | |
| Cengage Mathematics | A set of comprehensive books covering all major JEE Main topics with problems. | |
| Trigonometry by S.L. Loney | Essential for mastering Trigonometry. | |
| Higher Algebra by Hall and Knight | Focus on Algebra, useful for JEE Main preparation. | |
| Practice Websites | Embibe | Provides personalized practice and analysis for JEE Main. |
| Toppr | Online platform offering chapter-wise questions, mock tests, and video lessons. | |
| Mock Tests | NTA Abhyas App | Official mock tests for JEE Main, based on the real exam pattern. |
| Vedantu’s JEE Mock Tests | Free online mock tests with detailed solutions and analysis. |
Last Minute Preparation Tips for JEE Main Mathematics
- In the last few days before the exam preparation should be done as per importance of chapters. In addition, previous year JEE Main Question Paper trends should also be considered.
- Start revision with important topics like Algebra, Coordinate Geometry, 3 D Geometry and Vector.
- Be aware of what are the results of Algebraic calculations of properties of Conics in order to solve Coordinate Geometry questions.
- Learn graph and substitution to score well in the trigonometry section along with the formulas.
- Chapters which are relatively easy should be brushed up once as they can help cover up for the wrong attempted questions like Mathematical determinants.
- Prepare notes somewhere for the topics that are proven weak points while solving sample papers or mock tests. In the last moment, prepare and revise those topics thoroughly
Recommended Books For JEE Main Mathematics 2026
The mathematics section requires comprehensive preparation. The following Table represent best books for JEE Main Mathematics 2026
| Topic | Recommended Books |
|---|---|
| Calculus | I.A. Maron: Problems in Calculus of One Variable; R.D. Sharma: Integral Calculus for JEE Main & Advanced; M.L. Khanna: Problems in Calculus |
| Algebra | I.A. Maron: Higher Algebra; R.D. Sharma: Algebra for JEE Main & Advanced; S.K. Goyal: IIT Mathematics |
| Coordinate Geometry | S.L. Loney: The Elements of Coordinate Geometry; S.L. Loney: Trigonometry (combination with coordinate geometry) |
| Trigonometry | S.L. Loney: Trigonometry; I.A. Maron: Trigonometry for JEE |
| Vectors and 3D Geometry | A.D. Sharma: Mathematics for Class 12 (Vectors); S.L. Loney: Three Dimensional Geometry |
| Probability & Statistics | P.K. Sinha: JEE Main Mathematics Probability & Statistics; IIT Mathematics by M.L. Khanna (covers both topics) |
| Permutation and Combination | Arihant: Combinatorics, Permutation & Combination for JEE Main & Advanced; Cengage: Combinatorics & Probability for JEE Main |
| Matrices and Determinants | IIT Mathematics by M.L. Khanna; A.D. Sharma: Matrices & Determinants for JEE |
| Integral Calculus | I.A. Maron: Problems in Calculus of One Variable (covers integration); Cengage: Integral Calculus for JEE |
| Differential Equations | B.S. Grewal: Higher Engineering Mathematics; Arihant: Differential Equations for JEE |
JEE Main vs JEE Advanced Mathematics Comparison
There are many topics which are in JEE Main Mathematics but not in JEE Advanced Mathematics . Candidates can check the comparison between JEE Main and JEE Advanced Mathematics in the table below
| Aspect | JEE Main Mathematics | JEE Advanced Mathematics |
|---|---|---|
| Conceptual Depth | Tests understanding of basic to moderate concepts | Focuses on in-depth comprehension and creativity |
| Difficulty Level | Moderate most formula-based problems | High,often requiring multi-concept solution |
| Question Variety | MCQs and numerical questions | Includes multi-correct, integer-type, matrix -match |
| Topic Weightage | Uniform across syllabus | Higher weightage on Calculus and Algebra |
| Marking Scheme | No negative marks for numerical questions | Partial marking for multi-correct answers |
| Preparation Approach | NCERT-based with mock tests | Requires advanced problem-solving strategies |
| Exam Duration | 3 hours | Two 3-hour papers on the same day |
| Scoring Challenge | Easier for well-prepared students | Requires exceptional precision and practice |
JEE Main Mathematics Preparation Tips: Few Sample Questions
Question 1.
The locus of the point of intersection of the lines xcost+(1-cost)y=asint and xsint-(1+cost)y+asint=0 is 1) x2-y2=a2 3) y2 = ax 2)x2+y2=a2 4) x2 = ay
Answer
Rearranging the above equations, we get 1-cost/sint=a-x/y and 1+cost/sint=a+x/y multiplying the above equations ,we get x2+y2=a2
Question 2.
Lines ax+by+c=0, where 3a+2b+4c=0 & a,b,c all belong to the set of real numbers that are concurrent at the point? 1) (3,2) 3) (3,4) 2) (2,4) 4) (3/4, 1/2)
Answer.
We know that, 3a+2b+4c =0 which equals (3/4)a+(1/2)b+c=0 So, the line passes through (3/4,1/2)
Question 3.
If the area of the triangle formed by the equation 8×2-6xy+y2=0 and the line 2x+3y=a is 7 then the value of a is? 1) 14 3) 7 2) 28 4) 17
Answer.
Equation of the sides of the given triangle are y=2x, y=4x and 2x+3y=a So, vertices of the triangle are (a/8,a/4);(a/14,2a/7) and (0,0) By the determinant method, the area of the triangle formed by these coordinates comes out to be a2/112 which is equal to 7 This gives the value of a as 28.
Question 4.
If the line x=k; k= 1,2,3,…..,n meet the line y=3x+4 at the points Ak(xk,yk), k= 1,2,3…..,n then the ordinate of the centre of the mean position of points Ak, k= 1,2,3,…..,n is 1) n+1/2 3) 3(n+1)/2 2) 3n+11/2 4) None of the above
Answer.
We have yk=3k+4, the ordinate of intersection of x=k and y=3x+4 . So the ordinate of the mean position of the points Ak k= 1,2,3,…..,n is (1/n){sum of all yk’s} which comes out to be 3n+11/2
Question 5.
If the point (3,4) lies on the locus of the point of intersection of the lines xcost+ysint =a and xsint-ycost=b, the point (a,b) lies on the line 3x-4y=0 then |a+b|=? 1) 1 3) 7 2) 3 4) 12
Answer.
Squaring and adding the given equations of the lines we get x2+y2=a2+b2 as the locus of the point of intersection of these lines. Since (3,4) lies on the locus we get 9+16=a2+b2 Also (a,b) lies on 3x-4y=0 so 3a-4b=0 Solving the two equations for a and b, we get |a+b|= 7
Question 6.
Equation of the circle with centre (-4,3) touching internally and containing the circle x2+y2=1is 1) x2+y2+8x-6y+9=0 3) x2+y2-8x+6y+9=0 2)x2+y2+8x-6y+11=0 4) x2+y2-8x+6y-11=0
Answer.
Let the equation of the required circle be (x+4)2+(y-3)2=r2 If the above circle touches the circle x2+y2=1 internally, then the distance between the centres of the circles is equal to the difference of their radii 42+32=r-1 Which implies r=6 So the equation of the circle is x2+y2+8x-6y-11=0
Question 7.
If the normal chord at a point ‘t’ on the parabola y2=4axsubtends a right angle at the vertex, then the value of t is 1)4 3) 3 2)1 4) 2
Answer.
Equation of the normal at ‘t’ to the parabola y2=4ax is y= -tx+2at+at3 The joint equation of the lines joining the vertex to the points of the intersection of parabola and the normal is y2=4ax[y+tx/2at+t3] 4tx2-(2t+t3)y2+4xy=0 Since these lines are at right angles so the coefficient of x2+y2=0 So, it comes out to be 2.
Question 8.
The angle between a diagonal of a cube and one of its edges is, 1) cos-1(1/3) 3) /3 2) /4 4) /6
Answer.
Let a= a1i, b=a1j ,c=a1k. Then the vector d= a1(i+j+k) is a diagonal of the cube. The angle between one of the edges a, b or c and the diagonal d is given by, cos=a.d/|a||d| which comes out to be cos-1(1/3).
Question 9.
Volume of the tetrahedron with vertices P(-1,2,0) ; Q(2,1,-3) ; R(1,0,1) and S (3,-2,3) is 1) 1/3 3) 1/4 2) 2/3 4) ¾
Answer.
Volume of the tetrahedron is given by a scalar triple product, Volume of tetrahedron= ⅙|PQues.(PR x PS)| Here PQ, PR and PS are three vectors made from the above provided coordinates. So, the volume of the tetrahedron comes out to be ⅔ after solving the triple product.
Question 10.
If A,B,C and D are four points in space and |ABxCD+BCxAD+CAxBD|=(area of triangle ABC). Then the value of is- 1) 1 3) 3 2) 2 4) 4
Answer.
Let D be the origin of reference and DA=a, DB= b, DC= c So, |ABxCD+BCxAD+CAxBD|= |(b-a) x (-c) +(c-b) x (-a) + (a-c) x (-b)| = 2|axb+bxc+cxa| =2(2 area of ABC) Hence equals 4.
FAQ for JEE Main Mathematics Preparation 2026
Ques: Which are the toughest chapters of maths in JEE?
Ans: The toughest chapters in JEE Mathematics often depend on the difficulty level of the questions and the student's understanding. However, based on trends and student feedback, the following are considered the toughest chapters in JEE Main Mathematics.
| Chapter | Reason for Difficulty |
|---|---|
| Calculus | Involves multiple concepts such as limits, continuity, differentiation, and integration. The questions are often lengthy and require strong conceptual clarity and application. |
| Coordinate Geometry | Requires understanding of equations of lines, circles, ellipses, parabolas, and hyperbolas. The geometrical interpretation can be tricky. |
| Probability and Statistics | Involves complex theorems like Bayes' theorem, binomial distribution, and standard deviation. These topics demand both conceptual clarity and practical application. |
| Complex Numbers | Requires visualizing numbers geometrically (Argand plane) and understanding polar representation. Problems often involve advanced algebraic manipulation. |
| Vector Algebra and 3D Geometry | Understanding directions, planes, and vector equations can be challenging due to the spatial reasoning required. |
| Permutation and Combination | Tricky because of combinatorial reasoning and logical approaches required for different cases. Misinterpretation of problem statements is common. |
| Matrices and Determinants | Questions often involve lengthy calculations and require deep knowledge of properties and operations. |
| Trigonometry | Heavy reliance on formulas, identities, and equations, which can be confusing without proper practice. |
Ques. How should I prepare for JEE Mains maths?
Ans. Candidates have to solve previous years’ paper, sample papers everyday. They must also attend mock tests every week to check the preparation.
Ques. Is JEE Mains maths easy?
Ans. Mathematics in the JEE Main paper is the most difficult section out of other papers. Candidates must prepare well for Maths in JEE Main.
*The article might have information for the previous academic years, please refer the official website of the exam.
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It is a subjective question. However, ideally once in the beginning to see where you stand and then after you are done with a major portion of the syllabus. Going through JEE Main previous year paper will prepare you mentally to appear for the exam.
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a
ZT
Yes, the JEE Main question paper for all shifts is different in order to prevent the leaking of questions. However, the authorities try to maintain the difficulty level across the slots.
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a
ZT
If the question paper of one slot comes difficult than the other, NTA will follow the process of normalisation of scores. This will ensure a fair marking approach across all shifts.
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a
ZT
The competition level of JEE Main is very high. Moreover, the difficulty level of question paper ranges from moderate to tough. So, only with a good preparation will you be able to clear the exam.
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