NTA JEE Main (Session 1 & Session 2)

JEE Main Mathematics: Chapter-Wise PYQs

Practise over 2,800+ solved JEE Main questions arranged strictly in pedagogical learning order. Build your cognitive ladder from foundational inequalities and functions to multi-concept calculus, vectors, 3D geometry, and stochastic probability. Includes complete weightage analysis, NTA rationalized syllabus alerts, and 2019–2026 shift papers.

26 Pedagogical Chapters
8 Conceptual Units
100 Marks (25 Questions / Shift)
2019–2026 NTA Shift Papers
Latest Rationalized Syllabus
Browse 26 Chapters Pedagogical Roadmap Exam Blueprint Weightage Matrix Shift Papers (2019–2026) Topper Strategy FAQs
Cognitive Curriculum Architecture

The Pedagogical Learning Progression: Why Order Matters

In JEE Mathematics, chapters cannot be studied in isolation. Each unit constructs the conceptual toolkit and algebraic muscle required by the next stage.

Phase 01 Foundations

Prerequisite Toolkit & Functions

Master Wavy Curve inequalities, modulus equations, and logarithms before exploring domain, range, injectivity, and inverse mappings.

Gateway to All Calculus & Algebra
Phase 02 Algebra

Algorithmic & Combinatorial Algebra

Progress from Quadratics and Complex Numbers to Progressions, Combinatorics (P&C), Binomial Expansions, and Matrix Determinants.

Powers Probability & Series Limits
Phase 03 Trigonometry

Analytical Trigonometry & ITF

Compound angles, transformation formulae, and Inverse Trigonometric Functions provide the primary substitution language for integrals and geometry.

Critical for Calculus Substitutions
Phase 04 Coordinate Geo

2D Analytical Geometry & Conics

Linear geometry of Straight Lines and Circles expands systematically into Parabola, Ellipse, and Hyperbola using eccentricity and focal properties.

Direct Visual Loci & Tangents
Phase 05 Differential Calc

Limits, Continuity & Derivative Applications

L'Hôpital's rule and differentiability lead into Applications of Derivatives (AOD): Monotonicity, Maxima-Minima, and Mean Value Theorems.

30% of Total JEE Maths Paper
Phase 06 Integral Calc

Accumulation, Areas & Differential Eqns

Master anti-derivatives and symmetry-based Definite Integrals (King's Rule, Leibniz theorem) before computing Areas and solving Differential Equations.

High Score Return-on-Investment
Phase 07 Spatial Geometry

Vectors & 3D Analytical Geometry

Vector dot/cross products transition seamlessly into 3D lines, skew distances, and spatial projections. Consistently the highest ROI in JEE Main.

3–4 Direct Questions Every Shift
Phase 08 Stochastic Thinking

Statistics & Axiomatic Probability

Direct variance/standard deviation computations combine with Bayes' theorem and binomial probability distributions for guaranteed scoring.

2 Guaranteed Questions Every Shift
Pattern & Structure

JEE Main Mathematics Examination Blueprint

Conducted by the National Testing Agency (NTA). 100 Marks across two distinct sections with negative marking.

Section A: Objective MCQs

20 Compulsory
  • 20 Single-Choice Questions: 4 options with exactly 1 correct answer.
  • Marking Scheme: +4 marks for correct choice, -1 mark penalty for incorrect attempts.
  • Recommended Time: 35 to 40 minutes with elimination and back-substitution techniques.
  • Syllabus Coverage: Spans full breadth across Algebra, Calculus, Coordinate, and Vectors.

Section B: Numerical Value Questions (NVQ)

Attempt 5 of 10
  • 10 Numerical Questions: Candidates choose and answer any 5 questions.
  • Marking Scheme: +4 marks for correct integer/decimal value, -1 mark penalty for wrong answers.
  • Selection Strategy: Scan all 10 before attempting; target Statistics, Matrices, or Definite Integrals.
  • Recommended Time: 15 to 20 minutes with double-checked numerical calculations.
NTA Rationalized Syllabus Alert: In recent sessions, NTA removed Mathematical Reasoning, Heights & Distances, and Mathematical Induction from the official syllabus. Additionally, standard auxiliary tangent/normal formulas in conic sections were simplified to general calculus-based approaches, and planes in 3D geometry were rationalized. While solving past 2019–2023 papers, our question player clearly tags rationalized topics so you practice with full syllabus precision.
Showing 26 of 26 chapters
Unit 1 · Foundations Class 11 · Essential Tool

01. Fundamentals of Mathematics & Inequalities

Prerequisite: None (Root Foundational Gateway)
Wavy Curve Method Modulus Equations & Inequations Logarithmic Inequations Interval Arithmetic
Key Law: |x| ≤ a ⇔ -a ≤ x ≤ a; log_a(x) > log_a(y) [a > 1]
85+ Solved PYQs Practise PYQs
Unit 1 · Foundations Avg 2 Qs / Shift

02. Sets, Relations and Functions

Prerequisite: Ch 01 (Inequalities & Modulus)
Equivalence Relations Domain & Range Extraction One-One & Onto Functions Composition & Inverses Functional Equations
Identity: f(f^{-1}(x)) = x, f(x + y) = f(x)f(y) ⇒ f(x) = a^x
145+ Solved PYQs Practise PYQs
Unit 2 · Core Algebra Avg 1–2 Qs / Shift

03. Quadratic Equations & Expressions

Prerequisite: Ch 01 (Inequalities & Real Roots)
Relation between Roots & Coeffs Location of Roots Conditions Common Roots Analysis Transformation of Equations
Key Cond: k ∈ (α, β) ⇔ a · f(k) < 0; Δ ≥ 0
120+ Solved PYQs Practise PYQs
Unit 2 · Core Algebra Avg 1–2 Qs / Shift

04. Complex Numbers & Geometry

Prerequisite: Ch 03 (Quadratic Solutions & Surds)
Modulus & Argument Equations Triangle Inequalities Cube Roots of Unity (1, ω, ω²) Circles & Lines in Argand Plane
Inequality: ||z_1| - |z_2|| ≤ |z_1 ± z_2| ≤ |z_1| + |z_2|; 1 + ω + ω² = 0
135+ Solved PYQs Practise PYQs
Unit 2 · Core Algebra Avg 2 Qs / Shift

05. Sequences and Series

Prerequisite: Ch 03 (Algebraic Progressions)
Arithmetic & Geometric Means Arithmetico-Geometric Series (AGP) Telescoping Series & Differences Σn, Σn², Σn³ Formulae
Sum Law: S_∞ = a / (1 - r) [|r| < 1]; AM ≥ GM ≥ HM
140+ Solved PYQs Practise PYQs
Unit 2 · Core Algebra Avg 1–2 Qs / Shift

06. Permutations and Combinations (P&C)

Prerequisite: Fundamental Counting Principles
Division & Distribution of Objects Rank of Word with Repetition Derangements (D_n) Multinomial Theorem Coefficients
Derange: D_n = n! [1 - 1/1! + 1/2! - ... + (-1)^n/n!]
130+ Solved PYQs Practise PYQs
Unit 2 · Core Algebra Avg 1–2 Qs / Shift

07. Binomial Theorem & Series

Prerequisite: Ch 06 (Combinations ^nC_r)
General Term T_{r+1} Greatest Numerical Term Sum of Binomial Coefficients Divisibility & Remainder Problems
Expansion: (x + y)^n = Σ ^nC_r x^{n-r} y^r; T_{r+1} = ^nC_r x^{n-r} y^r
125+ Solved PYQs Practise PYQs
Unit 2 · Core Algebra Goldmine · 2 Qs / Shift

08. Matrices and Determinants

Prerequisite: Linear Equations & Basic Algebra
Cramer's Rule & Consistency Properties of Determinants Adjoint & Inverse Properties Characteristic Eqn & Powers
Key Rule: |adj(A)| = |A|^{n-1}; A · adj(A) = |A| I_n
165+ Solved PYQs Practise PYQs
Unit 3 · Trigonometry Avg 1 Q / Shift

09. Trigonometric Functions & Equations

Prerequisite: Ch 02 (Functions & Periodicity)
Compound & Submultiple Angles Transformation Formulae Trigonometric Equations Extreme Values (a cos θ + b sin θ)
Extremum: -\sqrt{a^2+b^2} ≤ a\cos\theta + b\sin\theta ≤ \sqrt{a^2+b^2}
95+ Solved PYQs Practise PYQs
Unit 3 · Trigonometry Avg 1 Q / Shift

10. Inverse Trigonometric Functions (ITF)

Prerequisite: Ch 02 (Bijectivity) & Ch 09 (Trig)
Principal Value Branches Domain & Range Boundaries Sum/Difference Identities Equations Involving ITF
Identity: \sin^{-1}x + \cos^{-1}x = \pi/2; \tan^{-1}x + \tan^{-1}y
90+ Solved PYQs Practise PYQs
Unit 4 · Coordinate Geo Avg 1–2 Qs / Shift

11. Straight Lines & Triangle Geometry

Prerequisite: Cartesian Plane & Linear Equations
Distance & Perpendicular Forms Family of Lines (L_1 + λL_2 = 0) Angle Bisectors & Concurrency Centroid, Orthocentre & Circumcentre
Distance: d = |ax_1 + by_1 + c| / \sqrt{a^2 + b^2}
110+ Solved PYQs Practise PYQs
Unit 4 · Coordinate Geo Avg 1–2 Qs / Shift

12. Circles

Prerequisite: Ch 11 (Straight Lines & Distances)
Standard & Diametric Equations Condition of Tangency (c² = a²(1+m²)) Chord of Contact (T = 0) Orthogonal Intersection of Circles
Orthogonal: 2(g_1 g_2 + f_1 f_2) = c_1 + c_2
115+ Solved PYQs Practise PYQs
Unit 4 · Coordinate Geo Avg 1 Q / Shift

13. Parabola

Prerequisite: Ch 11 (Lines) & Ch 12 (Tangency)
Standard Forms y² = 4ax Focal Chord Properties (t_1 t_2 = -1) Parametric Coordinates (at², 2at) Tangents from Calculus & Condition
Tangent: y = mx + a/m [m ≠ 0]; yt = x + at^2
95+ Solved PYQs Practise PYQs
Unit 4 · Coordinate Geo Avg 1 Q / Shift

14. Ellipse

Prerequisite: Ch 12 (Circles) & Ch 13 (Parabola)
Standard Equation x²/a² + y²/b² = 1 Eccentricity e = √(1 - b²/a²) Focal Radii Sum SP + S'P = 2a Director Circle x² + y² = a² + b²
Tangency: c^2 = a^2 m^2 + b^2; y = mx ± \sqrt{a^2 m^2 + b^2}
90+ Solved PYQs Practise PYQs
Unit 4 · Coordinate Geo Avg 1 Q / Shift

15. Hyperbola

Prerequisite: Ch 14 (Ellipse Analytical Properties)
Standard Equation x²/a² - y²/b² = 1 Eccentricity e = √(1 + b²/a²) Rectangular Hyperbola (xy = c²) Asymptotes & Conjugate Forms
Condition: c^2 = a^2 m^2 - b^2; |S'P - SP| = 2a
80+ Solved PYQs Practise PYQs
Unit 5 · Differential Calc Avg 2 Qs / Shift

16. Limits, Continuity & Differentiability

Prerequisite: Ch 02 (Functions & Graphs) & Ch 09 (Trig)
Indeterminate Forms (0/0, ∞/∞, 1^∞) L'Hôpital's Rule & Series Expansion Continuity at a Point & Interval Differentiability Tests & Non-diff points
1^∞ Form: \lim_{x\to a} [f(x)]^{g(x)} = e^{\lim_{x\to a} g(x)[f(x) - 1]}
160+ Solved PYQs Practise PYQs
Unit 5 · Differential Calc Avg 1 Q / Shift

17. Methods of Differentiation (MOD)

Prerequisite: Ch 16 (Differentiability Definition)
Chain Rule & Product/Quotient Logarithmic Differentiation Parametric & Implicit Derivatives Higher Order Derivatives d²y/dx²
Parametric: \frac{d^2y}{dx^2} = \frac{d}{dt}\left(\frac{dy/dt}{dx/dt}\right) \cdot \frac{1}{dx/dt}
85+ Solved PYQs Practise PYQs
Unit 5 · Differential Calc Goldmine · 2–3 Qs / Shift

18. Application of Derivatives (AOD)

Prerequisite: Ch 17 (Calculating Derivatives)
Monotonicity (Increasing / Decreasing) Local & Global Maxima / Minima Rolle's & Lagrange's Mean Value (LMVT) Tangents, Normals & Optimization
LMVT: f'(c) = [f(b) - f(a)] / (b - a); f'(x) ≥ 0 ⇒ \text{Increasing}
278 Solved PYQs (2002–2026) Practise 278 PYQs
Unit 6 · Integral Calc Avg 1 Q / Shift

19. Indefinite Integration

Prerequisite: Ch 17 (Inverse of Differentiation)
Standard & Substitution Forms Integration by Parts (ILATE) Partial Fractions Decomposition Special Forms ∫ e^x [f(x) + f'(x)] dx
Key Law: \int e^x [f(x) + f'(x)] dx = e^x f(x) + C
100+ Solved PYQs Practise PYQs
Unit 6 · Integral Calc Goldmine · 2 Qs / Shift

20. Definite Integration & Properties

Prerequisite: Ch 19 (Indefinite Integrals)
King's Property ∫_a^b f(x)dx Newton-Leibniz Differentiation Rule Periodic & Even/Odd Integrals Definite Integral as Limit of a Sum
King's Rule: \int_a^b f(x) dx = \int_a^b f(a + b - x) dx
175+ Solved PYQs Practise PYQs
Unit 6 · Integral Calc Avg 1 Q / Shift

21. Area Under Curves (AUC)

Prerequisite: Ch 20 (Definite Integrals) & Conic Tracing
Area between Curves & Coordinate Axes Enclosed Area between Intersecting Curves Horizontal vs Vertical Strips Piecewise Function Boundaries
Area Law: A = \int_a^b [y_{\text{upper}} - y_{\text{lower}}] dx
110+ Solved PYQs Practise PYQs
Unit 6 · Integral Calc Goldmine · 1–2 Qs / Shift

22. Differential Equations

Prerequisite: Ch 17 (Derivatives) & Ch 19 (Integration)
Order and Degree Rules Variable Separable & Substitution Homogeneous Equations (y = vx) Linear Differential Eqn dy/dx + Py = Q
Linear D.E.: I.F. = e^{\int P dx}; y \cdot (I.F.) = \int Q \cdot (I.F.) dx + C
140+ Solved PYQs Practise PYQs
Unit 7 · Vectors & 3D Goldmine · 2 Qs / Shift

23. Vector Algebra

Prerequisite: Trigonometry & Coordinate Geometry
Dot Product & Orthogonal Projections Cross Product & Area of Triangles Scalar Triple Product [a b c] Vector Triple Product a × (b × c)
Triple Prod: \vec{a} \times (\vec{b} \times \vec{c}) = (\vec{a} \cdot \vec{c})\vec{b} - (\vec{a} \cdot \vec{b})\vec{c}
160+ Solved PYQs Practise PYQs
Unit 7 · Vectors & 3D Goldmine · 2 Qs / Shift

24. Three-Dimensional (3D) Geometry

Prerequisite: Ch 23 (Vector Cross & Dot Products)
Direction Cosines & Ratios (l, m, n) Equation of Straight Line in 3D Shortest Distance between Skew Lines Intersection of Lines & Foot of Perp
Skew Dist: d = |(\vec{a}_2 - \vec{a}_1) \cdot (\vec{b}_1 \times \vec{b}_2)| / |\vec{b}_1 \times \vec{b}_2|
170+ Solved PYQs Practise PYQs
Unit 8 · Probability & Stats Guaranteed 1 Q / Shift

25. Statistics & Measures of Dispersion

Prerequisite: Basic Arithmetic & Summation
Mean & Median of Grouped Data Variance σ² & Standard Deviation σ Shift of Origin vs Scale Transformations Combined Variance Formula
Variance: \sigma^2 = \frac{1}{N}\sum x_i^2 - (\bar{x})^2; \text{Var}(ax + b) = a^2 \text{Var}(x)
105+ Solved PYQs Practise PYQs
Unit 8 · Probability & Stats Goldmine · 1–2 Qs / Shift

26. Probability

Prerequisite: Ch 06 (P&C Counting Techniques) & Ch 02 (Sets)
Conditional Probability P(A|B) Total Probability & Bayes' Theorem Independent Events & Multiplication Binomial Probability Distribution
Bayes' Law: P(E_i|A) = \frac{P(E_i)P(A|E_i)}{\sum P(E_k)P(A|E_k)}
135+ Solved PYQs Practise PYQs
Shift Analysis

Unit-Wise Weightage & Return-on-Investment (ROI)

Based on empirical question frequency across 120+ official NTA shifts from 2019 to 2026.

Pedagogical Unit Chapters Avg Qs / Shift Weightage (% Marks) Difficulty Rating Prep Priority
Unit 7: Vectors & 3D Geometry Ch 23, 24 3 to 4 Qs 12% – 16% Moderate (Algorithmic) Highest ROI
Unit 5: Differential Calculus Ch 16, 17, 18 4 to 5 Qs 16% – 20% Moderate to Tough Essential Core
Unit 6: Integral Calculus Ch 19, 20, 21, 22 4 to 5 Qs 16% – 20% Moderate (Formula-Heavy) Highest ROI
Unit 2: Core Algebra Ch 03, 04, 05, 06, 07, 08 7 to 8 Qs 28% – 32% Easy to Moderate High Scoring
Unit 4: Coordinate Geometry Ch 11, 12, 13, 14, 15 4 to 5 Qs 16% – 20% Moderate to Lengthy Steady Anchor
Unit 8: Probability & Statistics Ch 25, 26 2 to 3 Qs 8% – 12% Easy (Stats) / Medium (Prob) Guaranteed Marks
Unit 3: Trigonometry & ITF Ch 09, 10 1 to 2 Qs 4% – 8% Moderate Tooling Core
Unit 1: Foundations & Functions Ch 01, 02 2 to 3 Qs 8% – 12% Conceptual Prerequisite Root
Shift Archive

Solved JEE Main Shift Papers (2019–2026)

Practise real full-paper shifts under timed exam conditions with step-by-step marking schemes and analytical shortcuts.

High-Percentile Execution

Strategic Rules for Scoring 99+ Percentile in Mathematics

Mathematics in JEE Main is widely considered the toughest and most time-intensive subject. Efficiency and strategic question selection determine your percentile.

Respect the 60-Minute Allocation

Do not exceed 60–65 minutes in Maths during the 3-hour exam. Allocate the first 10 minutes to grab low-hanging fruit (Statistics, Matrices, Vector projections) before diving into multi-step calculus.

Filter the 5 Golden Numerical Questions

In Section B, you have 10 questions but only need 5. Immediately reject questions requiring multi-case conic tangents or complex word formulations; pick direct formula-driven topics.

Use Special Values & Symmetries

In Section A multiple choice questions, testing small integer values (e.g. n = 1, 2 in Binomial series, or θ = 0, π/4 in Trigonometry) often eliminates 3 wrong choices in under 45 seconds.

Beware Calculation Traps & Domain Shifts

Always verify whether the domain excludes boundary values (e.g. log argument > 0, denominator ≠ 0, square root ≥ 0). Most negative marks in JEE Maths arise from extraneous algebraic roots.

Aspirant FAQs

Frequently Asked Questions

Essential guidance on pedagogical sequencing, syllabus changes, and high-efficiency prep.

Why is a pedagogical sequence crucial for preparing JEE Main Mathematics?

JEE Main Mathematics is strictly hierarchical. Advanced topics like Differential Calculus, Coordinate Geometry, and Probability depend directly on prerequisites such as Functions, Modulus, Inequalities, and Permutations & Combinations. Following a pedagogical learning progression ensures you acquire prerequisite algebraic tools before attempting multi-concept calculus or conic questions.

How many questions and marks are allocated to Mathematics in JEE Main?

JEE Main Mathematics carries 100 marks out of 300. The paper consists of 30 questions divided into Section A (20 compulsory MCQs with +4/-1 marking) and Section B (10 Numerical Value Questions where candidates must attempt any 5, also with +4/-1 marking).

Which chapters carry the highest weightage and return-on-investment (ROI) in JEE Main Maths?

The highest ROI units in JEE Main Maths are Vectors and 3D Geometry (typically 3 to 4 questions per shift), Matrices and Determinants (2 questions), Definite Integration & Area (2 to 3 questions), Sequences and Series (1 to 2 questions), and Statistics (1 predictable question per shift). Mastering these ensures 40+ marks with high certainty.

How has the NTA rationalized syllabus affected JEE Main Mathematics PYQs?

The NTA updated the JEE Main syllabus by removing Mathematical Reasoning, Heights & Distances, and Mathematical Induction, while trimming standard tangent/normal formulas in conic sections and planes in 3D geometry. When practising 2019-2023 PYQs, prioritize questions on the retained syllabus and practice general calculus methods for tangency.

What is the recommended strategy for Section B (Numerical Value Questions)?

Scan all 10 numerical questions before solving. Prioritize direct algorithmic topics with minimal arithmetic ambiguity, such as Statistics (variance computation), Matrices (determinant equations), or Definite Integrals (King's property). Avoid multi-case coordinate geometry or lengthy P&C questions unless you have confirmed the solution.

How many years of JEE Main PYQs should I solve to achieve a 99+ percentile in Mathematics?

Solving shift-wise PYQs from 2019 to 2026 (over 2,500 questions across multiple exam shifts) is the most effective preparation. Because NTA conducts exams across 10-12 shifts per year, 2019-2026 PYQs provide complete coverage of every possible question variation and trap.