## Important Formulas for JEE Main 2023: Mathematics, Physics and Chemistry Formulas

JEE Main is one of India's most competitive entrance exams for engineering and technical programs at the best colleges. To do well on this exam, you must understand the fundamental concepts and formulas of Mathematics, Physics, and Chemistry. Knowing important formulas in depth can help you solve problems fast and accurately, which is important for scoring well in JEE Main.

Some of the important formulas for JEE Mains in Mathematics include quadratic formulas, trigonometric ratios, integration formulas, binomial theorem, and limits formulas. In Physics, important formulas include Newton's laws of motion, kinematics formulas, work and energy formulas, and electric charge and field formulas. In Chemistry, important formulas include chemical equations, stoichiometry, and gas laws.

As the JEE syllabus is so large and deep, it becomes challenging to remember all of the concepts, and formulas as you continue through your preparation. In this article, we will look at some methods for remembering JEE formulas for a long time, at least until the completion of JEE Main and Advanced.

## How can JEE Main Important Formulas Help?

Gather study materials before beginning preparations.

Make separate notes for the relevant formulas for each subject as you prepare for the exam.

These handy notes help with concentrating on the concepts.

It helps in exam time management.

It makes calculation easier.

Reduces the risk of errors.

## Important Formulas of Physics for JEE Mains 2023

The JEE Main Physics section is considered as being challenging section due to lengthy derivations and various topics. Physics section of the JEE Main 2023 exam covers various topics, including Mechanics, Electricity and Magnetism, Thermodynamics, Optics, and Modern Physics. Let us take a look at some important formulas for JEE Main 2023.

### Kinematics Formulas:

Average speed = Total distance/Total time

Average velocity = Total displacement/Total time

Acceleration = (Final velocity - Initial velocity) / Time taken

Final velocity = (Initial velocity + Acceleration) × Time taken

Displacement = (Initial velocity + Final velocity) / 2 × Time taken

### Newton's Laws of Motion:

$F = m \times a$ (Newton's Second Law of Motion)

Force of friction $= \mu \times N$ (where $\mu$ is the coefficient of friction and N is the normal force)

Weight $= m \times g$ (where g is the acceleration due to gravity)

Impulse = force $\times$ time

Law of Conservation of Momentum: Momentum before collision = Momentum after collision

### Work, Energy, and Power Formulas:

Work = force $\times$ displacement $\times$ $\cos \theta$

Kinetic Energy $= 0.5 \times m \times v^2$

Potential Energy $= m \times g \times h$

Total Mechanical Energy = Kinetic Energy + Potential Energy

Power = work done/time taken

### Electric Charge and Fields Formulas:

Electric Field = force per unit charge $= \dfrac{F}{Q}$

Coulomb's Law: $F = \dfrac{k \times (q_1 \times q_2)}{r^2}$

Electric Potential Energy $= q \times V$

Electric Potential $= \dfrac{V}{d}$

Energy of electric dipole: $U = – \rho E$

Energy of a magnetic dipole: $U = – \mu B C$

Electric Charge: $Q = \pm ne$ (where $e = 1.60218 \times 10^{-29} C$), SI unit of Electric Charge is Coulomb ©

### Coulomb’s Law:

Electrostatic Force (F) $= k\left[\dfrac{q_1q_2}{r_2}\right]$ and,

In Vector Form :

$\vec{F} = k(q_1q_2) \times \dfrac{\vec{r}}{r^3}$,

Where $q_1$ and $q_2$ are Charges on the Particle,

r = Separation between them,

$\vec {r}$ = Position Vector,

$k$ = Constant $= \dfrac{1}{4}\pi \epsilon_0 = 8.98755 \times 10^9Nm^2C^2$

### Electric Current :

The current at Time $t : i = \underset{\Delta t \to 0}{lim} \dfrac{\Delta Q}{\Delta t} = \dfrac{dQ}{dT}$

Where $\Delta Q$ and $\Delta T$ = Charges crosses an Area in time $\Delta T$

SI unit of Current is Ampere (A) and 1A = 1 C/s

### Average current density:

$\vec{j} = \dfrac{\Delta i}{\Delta s}$

$j = \underset{\Delta s \to 0}{lim}\dfrac{\Delta i}{\Delta s} = \dfrac{di}{dS}$

$j = \dfrac{\Delta i}{\Delta S \cos \theta}$

Where, $\Delta S$ = Small Area,

$\Delta i$ = Current through the Area $\Delta S$,

P = Perpendicular to the flow of Charges,

$\theta$ = Angle Between the normal to the Area and the direction of the current.

### Kirchhoff’s Law:

Law of Conservation of Charge: $I_3 = I_1 + I_2$

### Resistance:

Resistivity : $\rho (T) = \rho (T_0)\left[1 + \alpha (T − T_0)\right]$

$R (T) = R (T_0) \left[1 + \alpha (T−T_0)\right]$

Where, $\rho (T)$ and $\rho (T_0)$ are Resistivity at Temperature $T$ and $T_0$ respectively,

$\alpha$ = Constant for given material.

### Lorentz Force :

$\vec F = q\left[\vec E + (\vec v \times \vec B)\right]$

Where, E = Electric Field,

B = Magnetic Field,

q = Charge of Particle,

v = Velocity of Particle.

### Magnetic Flux:

Magnetic Flux through Area $dS = \varphi = \vec{B} \cdot d\vec{S} = B \cdot dS \cos \theta$

Where, $d\vec{S}$ = Perpendicular vector to the surface and has a magnitude equal to are Ds,

$\vec{B}$ = Magnetic Field at an element,

$\theta$ = Angle Between $\vec{B}$ and $d\vec{S}$,

SI unit of Magnetic Flux is Weber (Wb).

### Straight Line Equation of Motion (Constant Acceleration):

$v = u + at$

$s = ut + \dfrac{1}{2at^2}$

$2as = v^2 − u^2$

### Gravitational Acceleration Equation of Motion:

Motion in Upward Direction:

$v = u - gt$

$y = ut − \dfrac{1}{2gt^2}$

$−2gy = v^2 − u^2$

Motion in Downward Direction:

$v = u + gt$

$y = ut + \dfrac{1}{2gt^2}$

$2gy = v^2 − u^2$

### Projectile Equation of Motion:

Horizontal Range $(R) = \dfrac{u^2 \sin2θ}{g}$

Time of Flight $(T) = \dfrac {2u \sin \theta}{g}$

Maximum Height $(H) = \dfrac{u^2 \sin 2\theta}{2}$

Where, u = initial velocity,

v = final velocity,

a = constant acceleration,

t = time,

x = position of particle.

### Laws of Gravity

Universal Law of Gravitation:

Gravitational force $\vec{F} = G\left[\dfrac{Mm}{r^2}\right]^r$

Where, M and m = Mass of two Objects,

r = separation between the objects,

$\cap{r}$ = unit vector joining two objects,

G = Universal Gravitational Constant, $\left[G = 6.67 \times 10^{−11}Nm^2Kg^{-2}\right]$

Work Done by Constant Force:

Work Done $W = \vec{F} \cdot \vec{S} = |\vec{F}| |\vec{S}| \cos \theta$,

Where, S = Displacement along a straight line,

F = applied force,

$\theta$ = Angle between S & F.

It is a scalar quantity and the Dimension of work is $\left[M^1 L^2 T^{-2}\right]$, SI unit of Work is the joule (J) and $1J = 1N \cdot m = Kgm^2s^{-2}$

### Kinetic Friction:

$f_k = \mu_k \cdot N$

Maximum Static Friction (Limiting Friction): $f_{\text{max}} = \mu_s \cdot N$,

Where, N = Normal Force,

$\mu_k$ = Coefficient of Kinetic Friction,

$µ_s$ = Coefficient of Static Friction.

### Simple Harmonic Motion:

Force $(F) = – k x$ and $k = \omega^2 m$

Where, k = Force Constant,

m = Mass of the Particle,

x = Displacement and $\omega^2$ = Positive Constant.

### Torque:

The torque or vector moment or moment vector (M) of a force (F) about a point (P) is defined as:

$M = r \times F$

Where, r is the vector from the point P to any point A on the line of action L of F.

These are few of the key formulas for JEE Main 2023 Physics. To gain confidence and perform well in the exam, it is important to grasp their applications and practise various types of questions based on them.

## Important Formulas of Chemistry for JEE Main 2023

Chemistry is considered as a simple subject in comparison. Maximum marks can be obtained from this section with proper preparation.

Ideal Gas Law: $PV = nRT$

Kinetic Energy of Gas Molecules: $KE = \left(\dfrac{3}{2}\right)RT$

$T(K) = T^\circ C + 273.15$

Molarity: $(M) = \dfrac{\text{No. of Moles of Solutes}}{\text{Volume of Solution in Liters}}$

Unit: $\text{mole}/{L}$

Molality: $(m)= \dfrac{\text{No. of Moles of Solutes}}{\text{Mass of solvent in kg}}$

Molecular Mass $= 2 \times$ vapor density

Atomic number = No. of protons in the nucleus = No. of electrons in the nucleus

Mass number = No. of protons + No. of neutrons C $= v \lambda$

Boyle’s Law: $P_1V_1 = P_2V_2$ (at constant T and n)

Charles’s Law: $\dfrac{V_1}{T_1} = \dfrac{V_2}{T_2}$ (at constant P and n)

Avogadro's Law: $\dfrac{V}{n}$ = constant, where V is the volume and n is the number of moles.

Dalton's Law of Partial Pressures: $P(\text{total}) = P_1 + P_2 + P_3 + …$, where P(total) is the total pressure and $P_1, P_2, P_3$ etc. are the partial pressures of individual gases in the mixture.

Enthalpy: $H = U + pV$

First Law of Thermodynamics: $\Delta U = q + W$

Ohm’s Law: $V = RI$

Faraday’s Laws:

Faraday’s First Law of Electrolysis:

$M = Zit$

Z = Atomic Mass / n $\times$ F

Faraday’s Second Law of Electrolysis:

$\dfrac{M_1}{M_2} = \dfrac{E_1}{E_2}$

Freundlich Adsorption Isotherm:

$\left[\dfrac{x}{m}\right] - Kp^{\left(\dfrac{1}{n}\right)}; n \geq 1$

Henry's Law: $S = kH \times P$,

Where S is the solubility of a gas in a liquid, P is the partial pressure of the gas above the liquid, and kH is the Henry's law constant.

Nernst Equation: $E = E^\circ - \left(\dfrac{RT}{nF}\right)lnQ$,

Where E is the cell potential, $E^\circ$ is the standard cell potential, R is the gas constant, T is the temperature, n is the number of electrons transferred, F is the Faraday constant, and Q is the reaction quotient.

Henderson-Hasselbalch Equation: $pH = pKa + log\left(\dfrac{[A^{-}]}{[HA]}\right)$

Where pH is the negative logarithm of the hydrogen ion concentration, pKa is the acid dissociation constant, $[A^{-}]$ is the concentration of the conjugate base, and $[HA]$ is the concentration of the acid.

Beer-Lambert Law: $A = \epsilon bc$

Where A is the absorbance, $\epsilon$ is the molar absorptivity, b is the path length, and c is the concentration.

## Important Formulas of Mathematics for JEE Mains 2023

If you focus well in your board exams, you will breeze through your Mathematics course. Formulas are extremely important in the preparation of the mathematics portion. Below mentioned are few of the Maths Formulas for JEE Mains.

### Complex Number:

General form of Complex numbers: $x + i$, where ‘x’ is Real part and ‘i’ is an Imaginary part.

Sum of nth root of unity = zero

Product of nth root of unity $= (–1)n–1$

Cube roots of unity: $1, \omega, \omega^2$

$|z_1 + z_2| \leq |z_1|+|z_2|; |z_1 + z_2| \geq |z_1| - |z_2|; |z_1 - z_2| \geq |z_1| - |z_2|$

If three complex numbers $z_1, z_2, z_3$ are collinear then,

$\begin{vmatrix} z_1& \bar{z_1} & 1 \\ z_2 & \bar{z_2} & 1 \\ z_3 & \bar{z_3} & 1 \end{vmatrix} = 0$

If $\arg \cos\alpha = \arg \sin\alpha = 0, \arg \cos 2\alpha = \arg \sin 2\alpha = 0$,

$\arg \cos 2n\alpha = \arg \sin 2n\alpha = 0$

$\arg \cos 2\alpha = \arg \sin 2\alpha = \dfrac{3}{2}$

$\arg \cos 3\alpha = 3 \cos (\alpha + \beta + \gamma)$

$\arg \sin 3\alpha = 3\sin (\alpha + \beta + \gamma)$

$\arg \cos (2\alpha – \beta – \gamma) = 3$

$\arg \sin (2\alpha – \beta – \gamma) = 0$

$a^3 + b^3 + c^3 – 3abc = (a + b + c) (a + b\omega + c\omega^2) (a + b\omega^2 + c\omega)$

### Quadratic Equation:

Standard form of Quadratic equation: $ax^2 + bx + c = 0$

General equation: $x = \dfrac{-b \pm \sqrt{(b^2 - 4ac)}}{2a}$

Sum of roots $= -\dfrac{b}{a}$

Product of roots discriminate $= b^2 – 4ac$

If $\alpha, \beta$ are roots then Quadratic equation is $x^2 – x(\alpha + \beta) + \alpha \beta = 0$

Number of terms in the expansion: $(x+a)^n$ is $n+1$

Any three non coplanar vectors are linearly independent

A system of vectors $\bar{a_1}, \bar{a_2},….\bar{a_n}$ are said to be linearly dependent, If there exist, $x_1\bar{a_1} + x_2\bar{a_2} + …. + x_na_n=0$ at least one of $x_i \neq 0$, where $i = 1, 2, 3….n$ and determinant $= 0$

a, b, c are coplanar then $\left[abc\right]=0$

If i, j, k are unit vectors then $\left[i j k\right] = 1$

If a, b, c are vectors then $\left[a+b, b+c, c+a\right] = 2\left[abc\right]$

$(1 + x)^{n – 1}$ is divisible by $x$ and $(1 + x)^n – nx –1$ is divisible by $x^2$

If ${}^{n}C_{r} - 1, {}^{n}C_{r}, {}^{n}C_{r}+1$ are in A.P, then $(n–2r)^2 = n + 2$

### Trigonometric Identities:

$\sin^2(x) + \cos^2(x) = 1$

$1 + \tan^2(x) = \sec^2(x)$

$1 + \cot^2(x) = \text{cosec}^2(x)$

### Limits:

Limit of a constant function: $\lim c = c$

Limit of a sum or difference: $\lim (f(x) \pm g(x)) = \lim f(x) \pm \lim g(x)$

Limit of a product: $\lim (f(x)g(x)) = \lim f(x) \times \lim g(x)$

Limit of a quotient: $\lim \left(\dfrac{f(x)}{g(x)}\right) = \dfrac{\lim f(x)}{\lim g(x)}$ if $\lim g(x) \neq 0$

### Derivatives:

**Power Rule:**$\dfrac{d}{dx}(x^n) = nx^{(n-1)}$**Sum/Difference Rule:**$\dfrac{d}{dx}\left(f(x) \pm g(x)\right) = f'(x) \pm g'(x)$**Product Rule:**$\dfrac{d}{dx}\left(f(x)g(x)\right) = f'(x)g(x) + f(x)g'(x)$**Quotient Rule:**$\dfrac{d}{dx}\left(\dfrac{f(x)}{g(x)}\right) = \dfrac{\left[g(x)f'(x) - f(x)g'(x)\right]}{g^2(x)}$

### Integration:

$\int{x^n }dx = \dfrac{x^{n+1}}{n+1} + c$ where $n \neq -1$

$\int \dfrac{1}{x} dx = \log_{e}\left | x \right | + c$

$\int e^x dx = e^x + c$

$\int a^x dx = \dfrac{a^{x}}{\log_{e}a} + c$

$\int \sin x dx = - \cos x + c$

$\int \cos x dx = \sin x + c$

$\int \sec^2x dx = \tan x + c$

$\int \text{cosec}^2x dx = - \cot x + c$

$\int \sec x tan x dx = \sec x + c$

$\int \text{cosec }x \cot x dx = –{cosec }x + c$

$\int \cot x dx = \log |\sin x|+c$

$\int \tan x dx = -\log ∣\cos x∣ + c$

$\int \sec x dx = log ∣\sec x + \tan x∣ + c$

$\int \text{cosec }x dx = log ∣\text{cosec }x – \cot x∣ + c$

$\int \dfrac{1}{\sqrt{a^{2} - x^{2}}} dx = \sin^{-1} \left(\dfrac{x}{a}\right) + c$

$\int - \dfrac{1}{\sqrt{a^{2} - x^{2}}} dx = \cos^{-1} \left(\dfrac{x}{a}\right) + c$

$\int \dfrac{1}{{a^{2} + x^{2}}} dx = \dfrac{1}{a} \tan^{-1} \left(\dfrac{x}{a}\right) + c$

$\int - \dfrac{1}{{a^{2} + x^{2}}} dx = \dfrac{1}{a} \cot^{-1} \left(\dfrac{x}{a}\right) + c$

$\int \dfrac{1}{x\sqrt{x^{2} - a^{2}}} dx = \dfrac{1}{a} \sec^{-1} \left(\dfrac{x}{a}\right) + c$

$\int - \dfrac{1}{x\sqrt{x^{2} - a^{2}}} dx = \dfrac{1}{a} \text{cosec}^{-1} \left(\dfrac{x}{a}\right) + c$

## How to Remember Formulas for JEE?

Solve problems that require the use of formulas. The more you use each formula in a test, the better you'll remember it.

Revise the formulas on a daily basis. It will help you in remembering them permanently.

Each formula which are difficult to remeber on a sticky note. Paste them in locations where you will see them frequently, such as your study desk, laptop screen (desktop), textbooks and so on.

In Chemistry, use symbols and flashcards to help you remember chemical reactions and formulas.

On a single page, write out all of the formulas for a chapter. Read it on your way to class, between courses, at school, or before going to bed.

Always try to memorise the formula in a calm environment. So that it can be easily remembered.

## Conclusion

To solve problems efficiently, it is important to memorize and understand these formulas and their applications. Practicing different types of questions and problems based on these formulas will also help you acquire confidence and perform well on the JEE Main Exam. You can also download all important formulas for jee mains 2023 pdf from our Vedantu website.

## FAQs on JEE Main Important Formulas

1. How do I remember all the important formulas for JEE Main 2023?

Practice is the best way to remember formulas. Use the formulas to solve as many questions as possible, and make sure you revise them on a regular basis.

2. Are all these formulas important for JEE Main 2023?

While all of the above mentioned formulas are important, it is just as important to understand the underlying concept and their applications. Also engage in Vedantu JEE coaching sessions online on youtube, also courses are available which will also be beneficial.

3. Is it possible to pass JEE Main 2023 without memorising any formulas?

While memorising formulas is not the only factor that affects performance on JEE Main 2023, it is important to understand formulas and their applications.

4. Can I derive the formulas during the exam?

Yes, you can derive the formulas during the exam, but it can be time-consuming, and it's always better to memorise as many formulas as possible.

5. Suggest the easiest way to remember all the JEE Main important formulas?

Have you forgotten the letters a, b, c, d, or 1,2,3,4? Certainly not. Why? Because you revised and wrote them so many times as a child that you don't forget them. So, for remembering formulas, a basic method is "Revision and Practice."