JEE Main Maths Formulas 2027 - Topic wise Important Mathematics Formulas

JEE Main Maths Formula List 2027

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. 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

$
\begin{aligned}
& -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)}
\end{aligned}
$

20. Trigonometric Limits

Some important JEE formulas for trigonometric limit are
(i) $\lim _{x \rightarrow 0} \frac{\sin x}{x}=1$
(ii) $\lim _{x \rightarrow 0} \frac{\tan x}{x}=1$
(iii) $\lim _{x \rightarrow a} \frac{\sin (x-a)}{x-a}=1$

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{gathered}
=\lim _{h \rightarrow 0} \frac{\sin h}{h} \\
=1
\end{gathered}
$

(iv) $\lim _{x \rightarrow a} \frac{\tan (x-a)}{x-a}=1$
(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

$
\begin{gathered}
\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
\end{gathered}
$

(viii) $\lim _{x \rightarrow 0} \frac{\tan ^{-1} x}{x}=1$

21. Exponential Limits

(i) $\lim _{x \rightarrow 0} \frac{e^x-1}{x}=1$

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 2027 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