JEE Main Maths Formulas 2027 - Topic wise Important Mathematics Formulas

JEE Main 2027 Maths Important Formula PDF

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JEE Main 2027 Maths Formula List

Candidates must go through all the formulae and practice the mathematical problems. Without formulas, you cannot solve any problem, though you know how to solve it. Revising the formulas daily is very important. Here we have provided the Mathematics formulas for JEE Mains.

1. Sets, Relations and Functions

Sets

Union

$A \cup B=\{x: x \in A \text { or } x \in B\}$

Intersection:

$A \cap B=\{x: x \in A \text { and } x \in B\}$

Difference:

$A-B=\{x: x \in A, x \notin B\}$

Complement:

$A^{\prime}=U-A$

Number of elements in union:

$n(A \cup B)=n(A)+n(B)-n(A \cap B)$

Functions
Composite function:

$(f \circ g)(x)=f(g(x))$

Inverse function:

$f^{-1}(f(x))=x$

2. Complex Numbers and Quadratic Equations

Complex Numbers
1.Complex number:

$z=a+i b$

2. Modulus:

$|z|=\sqrt{a^2+b^2}$

3. Conjugate:

$\bar{z}=a-i b$

4. Product of a complex number and its conjugate:

$z \bar{z}=|z|^2$

Quadratic Equations
5. Standard form:

$a x^2+b x+c=0, \quad a \neq 0$

6. Roots:

$x=\frac{-b \pm \sqrt{b^2-4 a c}}{2 a}$

7. Discriminant:

$D=b^2-4 a c$

8. Sum of roots:

$\alpha+\beta=-\frac{b}{a}$

9. Product of roots:

$\alpha \beta=\frac{c}{a}$

3. Matrices and Determinants

Matrix
For a 2 × 2 matrix:

$A=\left[\begin{array}{ll}
a & b \\
c & d
\end{array}\right]$

Determinant:

$|A|=a d-b c$

Inverse:

$A^{-1}=\frac{1}{|A|}\left[\begin{array}{cc}
d & -b \\
-c & a
\end{array}\right]$

provided $|A| \neq 0$.

Determinants
1. If two rows or columns are identical, then:

$|A|=0$

2. Interchanging two rows or columns changes the sign of the determinant.

4. Permutations and Combinations

1. Factorial:

$n!=n(n-1)(n-2) \cdots 1$

2. Permutation:

${ }^n P_r=\frac{n!}{(n-r)!}$

3. Combination:

${ }^n C_r=\frac{n!}{r!(n-r)!}$

4. Relation:

${ }^n P_r={ }^n C_r r!$

6. Symmetry:

${ }^n C_r={ }^n C_{n-r}$

5. Sequence and Series

Arithmetic Progression
$n$th term:

$a_n=a+(n-1) d$

Sum of first $n$ terms:

$S_n=\frac{n}{2}[2 a+(n-1) d]$

Geometric Progression
$n$th term:

$a_n=a r^{n-1}$

Sum of first $n$ terms:

$S_n=a \frac{r^n-1}{r-1}, \quad r \neq 1$

Infinite GP:

$S_{\infty}=\frac{a}{1-r}, \quad|r|<1$

Standard Sums

$\begin{gathered}
\sum_{k=1}^n k=\frac{n(n+1)}{2} \\
\sum_{k=1}^n k^2=\frac{n(n+1)(2 n+1)}{6} \\
\sum_{k=1}^n k^3=\left[\frac{n(n+1)}{2}\right]^2
\end{gathered}$

6. Trigonometry

Basic Identities

$\begin{aligned}
& \sin ^2 x+\cos ^2 x=1 \\
& 1+\tan ^2 x=\sec ^2 x \\
& 1+\cot ^2 x=\csc ^2 x
\end{aligned}$

Compound Angles

$\begin{gathered}
\sin (A+B)=\sin A \cos B+\cos A \sin B \\
\sin (A-B)=\sin A \cos B-\cos A \sin B \\
\cos (A+B)=\cos A \cos B-\sin A \sin B \\
\cos (A-B)=\cos A \cos B+\sin A \sin B \\
\tan (A+B)=\frac{\tan A+\tan B}{1-\tan A \tan B}
\end{gathered}$

Double Angle

$\begin{gathered}
\sin 2 x=2 \sin x \cos x \\
\cos 2 x=\cos ^2 x-\sin ^2 x \\
\cos 2 x=1-2 \sin ^2 x=2 \cos ^2 x-1 \\
\tan 2 x=\frac{2 \tan x}{1-\tan ^2 x}
\end{gathered}$

7. Integral Calculus

Basic Integrals

$\begin{gathered}
\int x^n d x=\frac{x^{n+1}}{n+1}+C, \quad n \neq-1 \\
\int \frac{1}{x} d x=\ln |x|+C \\
\int e^x d x=e^x+C \\
\int a^x d x=\frac{a^x}{\ln a}+C, \quad a>0, a \neq 1 \\
\int \sin x d x=-\cos x+C \\
\int \cos x d x=\sin x+C \\
\int \sec ^2 x d x=\tan x+C \\
\int \csc ^2 x d x=-\cot x+C
\end{gathered}$

8. Coordinate Geometry

Straight Line
Slope:

$m=\frac{y_2-y_1}{x_2-x_1}$

Point-slope form:

$y-y_1=m\left(x-x_1\right)$

Slope-intercept form:

$y=m x+c$

Two-point form:

$\frac{y-y_1}{y_2-y_1}=\frac{x-x_1}{x_2-x_1}$

Distance of point $\left(x_1, y_1\right)$ from line $a x+b y+c=0$ :

$d=\frac{\left|a x_1+b y_1+c\right|}{\sqrt{a^2+b^2}}$

9. Three-Dimensional Geometry

Distance between two points:

$d=\sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2+\left(z_2-z_1\right)^2}$

Section formula:

$\left(\frac{m x_2+n x_1}{m+n}, \frac{m y_2+n y_1}{m+n}, \frac{m z_2+n z_1}{m+n}\right)$

Direction cosines:

$l^2+m^2+n^2=1$

10. Vector Algebra

Magnitude:

$|\vec{a}|=\sqrt{a_1^2+a_2^2+a_3^2}$

Dot product:

$\vec{a} \cdot \vec{b}=|\vec{a}||\vec{b}| \cos \theta$

Cross product:

$|\vec{a} \times \vec{b}|=|\vec{a}||\vec{b}| \sin \theta$

Projection of $\vec{a}$ on $\vec{b}$ :

$\frac{\vec{a} \cdot \vec{b}}{|\vec{b}|}$

Remembering important formulas from Maths will be very useful for the students preparing for the JEE Main exam. Students should practice a few questions on each formula just to remember them easily.

Preparation tips for JEE Mains

Given below are some tips to help you prepare for JEE Main and score good marks in the exam:

1. First, students need to understand the JEE Main 2027 syllabus and JEE Main exam pattern so that they can get familiar with the exam.

2. Know the chapter-wise weightage of JEE Main 2027 and plan your preparation accordingly.

3. Develop a smart study plan according to your current level of preparation. Set monthly, weekly, and daily goals for your preparation and devote more time to tougher subjects or topics.

4. Students must be careful about the conceptual clarity; they must know the logic and derivation of each and every formula.

5. Try to solve questions on a regular basis. Solve JEE Main previous years’ question papers and take mock tests and JEE Main 2027 sample papers on a regular basis

Tips to Learn Maths Formulas for JEE Main 2027

Students find it difficult to learn formulas for JEE Main, but with the right approach, they can remember them. Given below are some points to remember:

1. Students must try to understand why a formula works and how chemical reactions occur, and their mechanism.

2. Then break down formulas into chapters or topics.

3. To learn these formulas easily, try to make a formula notebook.

4. Sometimes students must try to make mnemonics and short tricks, as it helps in quick revision.

5. Try to solve as many questions and revise

6. Try to use diagrams and flowcharts.

Along with the Math formulas, also revise the JEE Main 2027 Physics Formulas and JEE Main 2027 Chemistry Formulas