JEE Main Maths Formula List 2026
Candidates must go through all the formulas 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. Standard form of Quadratic equation: $a x^2+b x+c=0$
2. General equation: $x=\frac{-b \pm \sqrt{\left(b^2-4 a c\right)}}{2 a}$
3. Sum of roots $=-\frac{b}{a}$
4. Product of roots discriminate $=b^2-4 a c$
5. $\sin ^2(x)+\cos ^2(x)=1$
6. $1+\tan ^2(x)=\sec ^2(x)$
7. $1+\cot ^2(x)=\operatorname{cosec}^2(x)$
8. Limit of a sum or difference: $\lim (f(x) \pm g(x))=\lim f(x) \pm \lim g(x)$
9. Limit of a product: $\lim (f(x) g(x))=\lim f(x) \times \lim g(x)$
10. Limit of a quotient: $\lim \left(\frac{f(x)}{g(x)}\right)=\frac{\lim f(x)}{\lim g(x)}$ if $\lim g(x) \neq 0$
11. Power Rule: $\frac{d}{d x}\left(x^n\right)=n x^{(n-1)}$
12. Sum/Difference Rule: $\frac{d}{d x}(f(x) \pm g(x))=f^{\prime}(x) \pm g^{\prime}(x)$
13. Product Rule: $\frac{d}{d x}(f(x) g(x))=f^{\prime}(x) g(x)+f(x) g^{\prime}(x)$
14. Quotient Rule: $\frac{d}{d x}\left(\frac{f(x)}{g(x)}\right)=\frac{\left[g(x) f^{\prime}(x)-f(x) g^{\prime}(x)\right]}{g^2(x)}$
15. $\int x^n d x=\frac{x^{n+1}}{n+1}+c$ where $n \neq-1$
16. $\int \frac{1}{x} d x=\log _e|x|+c$
17. $\int e^x d x=e^x+c$
18. $\int a^x d x=\frac{a^\omega}{\log _e a}+c$
19. Probability Formula
- $P(A \cup B)=P(A)+P(B)-P(A \cap B)$
- $P(A \cap B)=P(A) \times P\left(\frac{B}{A}\right)$
- $P\left(\frac{A}{B}\right)=\frac{P(A \cap B)}{P(B)}$
20. Trigonometric Limits
Some important JEE formulas for trigonometric limit are
(i) $\lim _{x \rightarrow 0} \frac{\sin x}{x}=1$
(ii) $\lim _{\mathrm{x} \rightarrow 0} \frac{\tan \mathrm{x}}{\mathrm{x}}=1$
(iii) $\lim _{\mathbf{x} \rightarrow \mathrm{a}} \frac{\sin (\mathbf{x}-\mathrm{a})}{\mathbf{x}-\mathbf{a}}=\mathbf{1}$
As $\lim _{x \rightarrow 0} \frac{\tan x}{x}=\lim _{x \rightarrow 0} \frac{\sin x}{x} \times \frac{1}{\cos x}$
$=\lim _{x \rightarrow 0} \frac{\sin x}{x} \times \lim _{x \rightarrow 0} \frac{1}{\cos x}=1 \times 1$
As $\lim _{x \rightarrow a} \frac{\sin (x-a)}{x-a}=\lim _{h \rightarrow 0} \frac{\sin ((a+h)-a)}{(a+h)-a}$
$$
\begin{aligned}
& =\lim _{h \rightarrow 0} \frac{\sin h}{h} \\
& =1
\end{aligned}
$$
(iv) $\lim _{\mathbf{x} \rightarrow \mathbf{a}} \frac{\tan (\mathbf{x}-\mathbf{a})}{\mathbf{x}-\mathbf{a}}=\mathbf{1}$
(v) $\lim _{x \rightarrow a} \frac{\sin (f(x))}{f(x)}=1$, if $\lim _{x \rightarrow a} f(x)=0$
Similarly, $\lim _{x \rightarrow a} \frac{\tan (f(x))}{f(x)}=1$, if $\lim _{x \rightarrow a} f(x)=0$
(vi) $\lim _{x \rightarrow 0} \cos x=1$
(vii) $\lim _{x \rightarrow 0} \frac{\sin ^{-1} x}{x}=1$
As $\lim _{x \rightarrow 0} \frac{\sin ^{-1} x}{x}=\lim _{y \rightarrow 0} \frac{y}{\sin y} \quad\left[\because \sin ^{-1} x=y\right]$
$$
=1
$$
(viii) $\lim _{\mathbf{x} \rightarrow 0} \frac{\tan ^{-1} \mathrm{x}}{\mathbf{x}}=\mathbf{1}$
21. Exponential Limits
(i) $\lim _{\mathrm{x} \rightarrow 0} \frac{\mathrm{a}^{\mathrm{x}}-1}{\mathrm{x}}=\log _{\mathrm{e}} \mathrm{a}$
Proof:
$$
\lim _{x \rightarrow 0} \frac{a^x-1}{x}=\lim _{x \rightarrow 0} \frac{\left(1+\frac{x(\log a)}{11}+\frac{x^2(\log a)^2}{2!}+\cdots\right)-1}{x}
$$
[using Taylor series expansion of $a^x$ ]
$$
\begin{aligned}
& =\lim _{x \rightarrow 0}\left(\frac{\log a}{1!}+\frac{x(\log a)^2}{2!}+\cdots\right) \\
& =\log _e a
\end{aligned}
$$
(ii) $\lim _{\mathrm{x} \rightarrow 0} \frac{\mathrm{e}^{\mathrm{x}}-1}{\mathrm{x}}=1$
In General, if $x \rightarrow a$, then we have
(a) $\lim _{x \rightarrow a} \frac{a^{f(x)}-1}{f(x)}=\log _e a$
(b) $\lim _{x \rightarrow a} \frac{e^{f(x)}-1}{f(x)}=\log _e e=1$
Remembering important formulas from Maths will be very useful for the students preparing for the JEE Main 2025 exam. Students should practice a few questions on each formula just to remember them easily. Also refer to JEE Main- Top 30 Most Repeated Questions & Topics
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 Syllabus and Exam Pattern so that they can refer to the JEE Main syllabus from the official website.
2. Try to identify the important and high-weightage topics and prepare according to that.
3. Create an effective study plan according to your preparation level. Divide your preparation into monthly, weekly, and daily targets and allocate more time to difficult subjects or topics.
4. Students must focus on conceptual clarity; they must understand the logic and derivations behind every formula.
5. Try to solve questions regularly. Solve previous years' JEE Main question papers and attempt mock tests and sample papers regularly.
