JEE Main 2027

Target 60+ in JEE Main 2027 Maths in 3 Months: The 10 Chapters That Matter Most

We studied the data from the 2024 and 2025 papers, then checked how accurate it proved in 2026: where the pattern held and where JEE shifted a little.

By Parth Khurana, Daily Spark ·

39shifts analysed (20 from 2024 + 19 from 2025)
45/55% of questions from Class 11 / Class 12
~33%of the syllabus (10 chapters) gave 600+ questions
~80%of the top 10 chapters stayed the same in 2026

PYQ Analysis: How Many Papers and Questions Were Analysed?

In total, 39 shifts were analysed: 20 shifts from 2024 and 19 shifts from 2025.

2024

Every paper had 30 questions (20 MCQs and 10 Numerical questions, of which only 5 had to be attempted).

20 × 30 = 600 questions

2025

NTA changed the pattern. Papers now have 25 questions (20 MCQs and 5 Numerical), and all five Numerical questions are compulsory.

19 × 25 = 475 questions

Where do the questions come from?

45% of questions from Class 1155% of questions from Class 12

Chapter-Wise Weightage for 2027: Top 10 Chapters (2024-25 PYQ Data)

After tagging every question by chapter, these chapters came out on top:

  1. 3D Geometry 93 questions about 2-3 in every paper
  2. Sets, Relations & Functions
  3. Sequence & Series
  4. Matrices
  5. Differential Equations
  6. Vectors
  7. Permutation & Combination
  8. Probability
  9. Binomial Theorem 49 questions
  10. Definite Integration 47 questions

The power of these 10 chapters

Across 39 shifts, these 10 chapters produced more than 600 questions, which is over 15 questions per paper on average.

The Maths syllabus has roughly 29 chapters. Ten chapters is about 33% of the syllabus, and the 15 questions they give amount to roughly 60 marks.

In other words, you can expect nearly double the marks relative to the share of the syllabus you study.

JEE Main 2026 Maths Paper Analysis: What Happened in 2026?

January 2026 (10 shifts)

  • Conic Sections moved to the top in January (22 questions, an average of 2.2 per paper). This was the biggest change of the year.
  • Sets, Relations & Functions gave 20 questions.
  • Sequence & Series gave 16 questions.
  • 3D Geometry gave 15 questions. It averaged two and a half per paper earlier and now averages one and a half. A drop, yes, but the chapter stayed important.
  • Matrices gave 15 questions, while Determinants gave only 1.
  • Trigonometric Equations gave only 2 questions, against 12-14 in the earlier data.
  • Complex Numbers gave about one question in nearly every paper.

April 2026

  • 3D Geometry was back at number 1 with 17 questions.
  • Definite Integration was earlier at 11 questions and has now reached 16.
  • Inverse Trigonometric Functions weightage fell from 8 to 6.

Conclusion: Roughly 80% of the top 10 chapters stayed the same. The biggest change was Conic Sections, which went to number 1 in January with 22 questions. Another shift was Area Under Curve, which was not in the 2024-25 top 10. Complex Numbers stayed steady at about one question per paper. JEE shifts gradually; it does not flip overnight.

High Weightage Chapters: Sure-Shot vs Swing Chapters

Sure-shot (always study)

3D GeometryMatricesDifferential EquationsSets-Relations-FunctionsVectorsSequence & Series

These appear every time, and their question count never drops close to zero.

Swing chapters

Chapters whose weightage stays borderline: sometimes 8 questions, sometimes 6, sometimes zero.

Example: Inverse Trigonometric Functions.

Keep in mind

  • Don't skip small chapters like Quadratic Equations and Area Under Curve. Binomial and Sets-Relations-Functions are also short and easy, yet they bring in solid marks.
  • Keep an eye on "periphery" chapters such as Circles (37 questions) and Limits (34 questions). Don't stop at the top 10: go in with 12 to 14 chapters prepared. That keeps your coverage safe.

The Most Important Lesson: Look at Topics Inside a Chapter

Take Matrices as an example. The chapter has 10-12 topics, but according to the last 5 years of data (2021-25):

Adjoint of a Matrix
~80%
Inverse of a Matrix
~15%

So just two topics of the chapter produced about 95% of its questions. This is why studying Matrices and Determinants as a single unit can be misleading.

63questions came from Matrices
10questions came from Determinants

100-Day (3-Month) Study Plan: How to Target 60+ in JEE Main Maths

A 60+ target in about 3 months means working in order: master the top 10 chapters first, then widen to 12-14 chapters, and finish with timed practice. Keep these five rules in mind for the next 100 days.

  1. Improve your coveragePicking only 7 of the top 10 chapters is risky. Prepare 12-14 chapters.
  2. Work on time managementIf the paper turns out long, no chapter list will save you. The only cure is more practice and timed tests.
  3. Don't panic if theory is incompleteStudy the theory of your chosen key chapters and practise from PYQs.
  4. Don't be swayed by friendsIf someone says Area Under Curve came up a lot in their shift, it doesn't mean it will in yours. Trust the data.
  5. Be ready for shift shockNTA can give a tough paper at any time. On that day, stay calm instead of panicking. That mental edge will help you solve more questions.

Important Maths Formulas

1. Algebra

Quadratic Equations

Roots of \(ax^2+bx+c=0\)
\(\displaystyle x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\)
Discriminant (D or Δ)
\(\displaystyle b^2-4ac\)
Sum and Product of Roots
\(\displaystyle \alpha+\beta=-\frac{b}{a},\quad \alpha\beta=\frac{c}{a}\)
Both roots common: \(a_1x^2+b_1x+c_1=0\) and \(a_2x^2+b_2x+c_2=0\)
\(\displaystyle \frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}\)
Exactly one common root (same two equations)
\(\displaystyle (c_1a_2-c_2a_1)^2=(a_1b_2-a_2b_1)(b_1c_2-b_2c_1)\)

Sequence and Series (AP & GP)

AP: \(n^{\text{th}}\) term
\(\displaystyle a_n=a+(n-1)d\)
AP: Sum of \(n\) terms
\(\displaystyle S_n=\frac{n}{2}\left[2a+(n-1)d\right]=\frac{n}{2}(a+l)\)
GP: \(n^{\text{th}}\) term
\(\displaystyle a_n=ar^{n-1}\)
GP: Sum of \(n\) terms (\(r\neq1\))
\(\displaystyle S_n=\frac{a(r^n-1)}{r-1}\)
GP: Sum to infinity (\(|r|<1\))
\(\displaystyle S_\infty=\frac{a}{1-r}\)

Binomial Theorem

General term \(T_{r+1}\) in expansion of \((x+a)^n\)
\(\displaystyle T_{r+1}=\binom{n}{r}x^{n-r}a^r\)
Middle term: If \(n\) is even → \(\left(\frac{n}{2}+1\right)^{\text{th}}\) term. If \(n\) is odd → \(\left(\frac{n+1}{2}\right)^{\text{th}}\) and \(\left(\frac{n+3}{2}\right)^{\text{th}}\) terms.

Complex Numbers

Modulus (\(z=x+iy\))
\(\displaystyle |z|=\sqrt{x^2+y^2}\)
Polar / Euler Form
\(\displaystyle z=r(\cos\theta+i\sin\theta)=re^{i\theta}\)
De Moivre's Theorem
\(\displaystyle (\cos\theta+i\sin\theta)^n=\cos(n\theta)+i\sin(n\theta)\)

2. Calculus

Limits, Continuity and Differentiability

Standard Limits
\(\displaystyle \lim_{x\to0}\frac{\sin x}{x}=1\)
\(\displaystyle \lim_{x\to0}\frac{e^x-1}{x}=1\)
\(\displaystyle \lim_{x\to0}\frac{\ln(1+x)}{x}=1\)
\(\displaystyle \lim_{x\to a}\frac{x^n-a^n}{x-a}=na^{n-1}\)
L'Hôpital's Rule (if a \(\frac{0}{0}\) or \(\frac{\infty}{\infty}\) form arises)
\(\displaystyle \lim_{x\to a}\frac{f(x)}{g(x)}=\lim_{x\to a}\frac{f'(x)}{g'(x)}\)

Differentiation Formulas

Power
\(\displaystyle \frac{d}{dx}(x^n)=nx^{n-1}\)
Trigonometric
\(\displaystyle \frac{d}{dx}(\sin x)=\cos x,\quad \frac{d}{dx}(\cos x)=-\sin x,\quad \frac{d}{dx}(\tan x)=\sec^2 x\)
Exponential / Log
\(\displaystyle \frac{d}{dx}(e^x)=e^x,\quad \frac{d}{dx}(\ln x)=\frac{1}{x}\)
Product Rule
\(\displaystyle (uv)'=u'v+uv'\)
Quotient Rule
\(\displaystyle \left(\frac{u}{v}\right)'=\frac{u'v-uv'}{v^2}\)

Integration Formulas

Indefinite Integrals
\(\displaystyle \int x^n\,dx=\frac{x^{n+1}}{n+1}+C\ \ (n\neq-1)\)
\(\displaystyle \int\frac{1}{x}\,dx=\ln|x|+C,\qquad \int e^x\,dx=e^x+C\)
\(\displaystyle \int\sin x\,dx=-\cos x+C,\qquad \int\cos x\,dx=\sin x+C\)
Definite Integration: King's Rule
\(\displaystyle \int_a^b f(x)\,dx=\int_a^b f(a+b-x)\,dx\)

3. Coordinate Geometry

Straight Lines

Distance Formula
\(\displaystyle d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)
Slope Form
\(\displaystyle y-y_1=m(x-x_1)\)
Perpendicular distance from point \((x_1,y_1)\) to \(Ax+By+C=0\)
\(\displaystyle d=\frac{|Ax_1+By_1+C|}{\sqrt{A^2+B^2}}\)

Circles & Conics

Circle Standard Equation
\(\displaystyle (x-h)^2+(y-k)^2=r^2\)
Parabola
\(\displaystyle y^2=4ax\quad\text{(Focus: }(a,0)\text{, Directrix: }x=-a\text{)}\)
Ellipse
\(\displaystyle \frac{x^2}{a^2}+\frac{y^2}{b^2}=1\quad\left(e=\sqrt{1-\frac{b^2}{a^2}}\right)\)
Hyperbola
\(\displaystyle \frac{x^2}{a^2}-\frac{y^2}{b^2}=1\quad\left(e=\sqrt{1+\frac{b^2}{a^2}}\right)\)

4. Vector Algebra and 3D Geometry

Vectors

Dot Product
\(\displaystyle \vec a\cdot\vec b=|\vec a||\vec b|\cos\theta=a_1b_1+a_2b_2+a_3b_3\)
Cross Product
\(\displaystyle \vec a\times\vec b=|\vec a||\vec b|\sin\theta\,\hat n\)
Scalar Triple Product
\(\displaystyle [\vec a\ \vec b\ \vec c]=\vec a\cdot(\vec b\times\vec c)\)

3D Geometry

Distance between \((x_1,y_1,z_1)\) and \((x_2,y_2,z_2)\)
\(\displaystyle d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2+(z_2-z_1)^2}\)
Equation of a Line
\(\displaystyle \frac{x-x_1}{a}=\frac{y-y_1}{b}=\frac{z-z_1}{c}\)

5. Trigonometry

Identities

Pythagorean Identities
\(\displaystyle \sin^2\theta+\cos^2\theta=1,\quad 1+\tan^2\theta=\sec^2\theta,\quad 1+\cot^2\theta=\csc^2\theta\)
Compound Angles
\(\displaystyle \sin(A\pm B)=\sin A\cos B\pm\cos A\sin B\)
\(\displaystyle \cos(A\pm B)=\cos A\cos B\mp\sin A\sin B\)
Multiple Angles
\(\displaystyle \sin2A=2\sin A\cos A=\frac{2\tan A}{1+\tan^2A}\)
\(\displaystyle \cos2A=\cos^2A-\sin^2A=2\cos^2A-1=1-2\sin^2A=\frac{1-\tan^2A}{1+\tan^2A}\)

6. Statistics and Probability

Probability & Statistics

Probability Addition Theorem
\(\displaystyle P(A\cup B)=P(A)+P(B)-P(A\cap B)\)
Conditional Probability
\(\displaystyle P(A|B)=\frac{P(A\cap B)}{P(B)},\quad P(B)\neq0\)
Bayes' Theorem
\(\displaystyle P(E_i|A)=\frac{P(E_i)\,P(A|E_i)}{\sum_j P(E_j)\,P(A|E_j)}\)
Variance (\(\sigma^2\))
\(\displaystyle \sigma^2=\frac{\sum(x_i-\bar x)^2}{n}=\frac{\sum x_i^2}{n}-(\bar x)^2\)

Calculus Shortcuts

Calculus accounts for roughly 35% to 40% of the total weightage in the JEE Mathematics paper. Mastering specialized shortcuts, standard integral patterns, and series expansions can save crucial minutes during the exam.

1. High-Value Integration Shortcuts & Results

Wallis's Formula (Definite Integrals of Trigonometric Powers)

For integrals of the form below, where \(n\) and \(m\) are non-negative integers:

\(\displaystyle I=\int_0^{\pi/2}\sin^n x\,\cos^m x\,dx\)
  • Numerator: Start from \((n-1)\) and keep subtracting 2 until you reach 1 or 2: \((n-1)(n-3)(n-5)\cdots\). Do the same for \(m\): \((m-1)(m-3)\cdots\). Multiply both products together. Note that the numerator starts at \(n-1\) and \(m-1\), not at \(n\) and \(m\).
  • Denominator: Start from \((n+m)\) and keep subtracting 2 until you reach 1 or 2: \((n+m)(n+m-2)(n+m-4)\cdots\).
  • Special Multiplier (\(k\)): If both \(n\) and \(m\) are even, multiply the entire result by \(\frac{\pi}{2}\). Otherwise, multiply by 1.
  • Example 1: \(\displaystyle\int_0^{\pi/2}\sin^4x\cos^2x\,dx=\frac{(3\cdot1)(1)}{6\cdot4\cdot2}\cdot\frac{\pi}{2}=\frac{\pi}{32}\)
  • Example 2: \(\displaystyle\int_0^{\pi/2}\sin^3x\cos^2x\,dx=\frac{(2)(1)}{5\cdot3\cdot1}=\frac{2}{15}\)

Leibniz Rule (Differentiation Under the Integral Sign)

When you need the derivative of a definite integral whose limits are functions of \(x\):

\(\displaystyle \frac{d}{dx}\left[\int_{g(x)}^{h(x)}f(t)\,dt\right]=f(h(x))\cdot h'(x)-f(g(x))\cdot g'(x)\)

JEE ApplicationFrequently used in limits involving integrals (combined with L'Hôpital's Rule) and in finding functional equations.

Standard Form Integrals to Memorize

\(\displaystyle \int\frac{dx}{x^2+a^2}=\frac{1}{a}\tan^{-1}\frac{x}{a}+C\)
\(\displaystyle \int\frac{dx}{x^2-a^2}=\frac{1}{2a}\ln\left|\frac{x-a}{x+a}\right|+C\)
\(\displaystyle \int\frac{dx}{a^2-x^2}=\frac{1}{2a}\ln\left|\frac{a+x}{a-x}\right|+C\)
\(\displaystyle \int\frac{dx}{\sqrt{a^2-x^2}}=\sin^{-1}\frac{x}{a}+C\)
\(\displaystyle \int\sqrt{a^2-x^2}\,dx=\frac{x}{2}\sqrt{a^2-x^2}+\frac{a^2}{2}\sin^{-1}\frac{x}{a}+C\)

2. Definite Integration Properties & Symmetry Hacks

King's Property Extension

King's Property
\(\displaystyle \int_a^b f(x)\,dx=\int_a^b f(a+b-x)\,dx\)
Shortcut Strategy: If the denominator looks difficult, substitute \(x\to(a+b-x)\) and add the original integral \(I\) to the new integral to simplify the numerator.

Even and Odd Functions

If \(f(-x)=-f(x)\) (Odd)
\(\displaystyle \int_{-a}^{a}f(x)\,dx=0\)
If \(f(-x)=f(x)\) (Even)
\(\displaystyle \int_{-a}^{a}f(x)\,dx=2\int_0^a f(x)\,dx\)

Periodic Property

If \(f(x)\) is periodic with period \(T\)
\(\displaystyle \int_0^{nT}f(x)\,dx=n\int_0^T f(x)\,dx\quad(n\in\mathbb Z)\)

3. Limits & Series Expansion Shortcuts

Using Maclaurin series expansions avoids cumbersome algebraic manipulation or repetitive L'Hôpital applications when solving tricky \(\frac{0}{0}\) limits as \(x\to0\):

Exponential
\(\displaystyle e^x=1+x+\frac{x^2}{2!}+\frac{x^3}{3!}+\cdots\)
Logarithmic
\(\displaystyle \ln(1+x)=x-\frac{x^2}{2}+\frac{x^3}{3}-\frac{x^4}{4}+\cdots\)
Trigonometric
\(\displaystyle \sin x=x-\frac{x^3}{3!}+\frac{x^5}{5!}-\cdots\)
\(\displaystyle \cos x=1-\frac{x^2}{2!}+\frac{x^4}{4!}-\cdots\)
\(\displaystyle \tan x=x+\frac{x^3}{3}+\frac{2x^5}{15}+\cdots\)
Binomial Approximation (\(x\ll1\))
\(\displaystyle (1+x)^n\approx1+nx\quad\text{(higher powers neglected)}\)

FAQs: JEE Main Maths 2027 Strategy

Which chapters are most important in JEE Main Maths 2027?

Based on 39 shifts from 2024 and 2025, the top 10 chapters are 3D Geometry (93 questions), Sets, Relations & Functions, Sequence & Series, Matrices, Differential Equations, Vectors, Permutation & Combination, Probability, Binomial Theorem (49 questions) and Definite Integration (47 questions).

How many questions come from the top 10 chapters?

These 10 chapters produced more than 600 questions across 39 shifts, which is over 15 questions per paper, or roughly 60 marks. They make up only about 33% of the Maths syllabus (about 29 chapters).

Did the 2024-25 pattern hold in JEE Main 2026?

Largely yes. Roughly 80% of the top 10 chapters stayed the same. The biggest change was Conic Sections, which led January 2026 with 22 questions. In April 2026, 3D Geometry returned to number 1 with 17 questions, and Area Under Curve showed up even though it was outside the earlier top 10.

What is the current JEE Main Maths paper pattern?

From 2025, the Maths section has 25 questions: 20 MCQs and 5 Numerical questions, and all five Numerical questions are compulsory. In 2024, papers had 30 questions (20 MCQs and 10 Numerical, of which only 5 had to be attempted). Around 45% of questions come from Class 11 and 55% from Class 12.

How many chapters should I prepare for JEE Main Maths?

Do not stop at the top 10. Prepare 12 to 14 chapters, including 'periphery' chapters such as Circles (37 questions) and Limits (34 questions), and do not skip short chapters like Quadratic Equations and Area Under Curve.

Can I target 60+ in JEE Main Maths in 3 months?

It is a realistic target if you plan it well, but it depends on your starting level. The top 10 chapters gave over 15 questions per paper, roughly 60 marks, so mastering them first is the most efficient route. Then widen your coverage to 12-14 chapters, practise PYQs chapter by chapter, and take timed tests. A 100-day plan is about 3 months of focused work.