JEE Advanced Important Formulas 2023-24

• Before you begin your preparations, gather your study materials. 

• As you prepare for the exam, make separate notes for the relevant formulas for each subject. 

• These useful notes aid with focusing on the concepts. 

• It aids in the management of exam time.

• It improves in calculation.

• Reduces the possibility of errors.

Differences Between Topics For JEE Advanced and JEE Main

The syllabus for these assessments varies as well. The JEE Main syllabus contains topics from grades 11 and 12 in Mathematics, Physics, and Chemistry. The JEE Advanced test will cover a few extra topics.

These are the key differences between JEE Mains and JEE Advanced that you should be aware of before beginning your preparations. 

Important Physics Formulas for JEE Advanced 2023-24

The JEE Advanced Physics section is regarded as Moderate to Difficult due to lengthy derivations and a wide range of topics. The Mechanics, Electricity and Magnetism, Thermodynamics, Optics, and Modern Physics sections of the JEE Advanced 2023-24 test cover a wide range of topics. Let us look at some crucial list of formulas for JEE Advanced 2023-24.

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 $W = \vec{F} \cdot \vec{S} = \left|\vec{F}\right| \left|\vec{S}\right| \cos \theta$,

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 Advanced 2023-24 Physics. To gain confidence and perform well in the exam, it is important to grasp their applications and practice various types of questions based on them.

Important Chemistry Formulas for JEE Advanced 2023-24

Chemistry is considered as a simple subject in comparison. Maximum marks can be obtained from this section with proper preparation. Let us look at some crucial list of formulas for JEE Advanced 2023-24.

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 Maths Formulas for JEE Advanced 2023-24

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 a crucial list of formulas for JEE Advanced 2023-24.

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 $n \neq -1$

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

• $\int e^x dx = e^x + c$

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

• $\int \sin x dx = - \cos x + c$

• $\int \cos x dx = \sin x + c$

• $\int \sec^2x dx = \tan x + c$

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

• $\int \sec x tan x dx = \sec x + c$

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

• $\int \cot x dx = \log |\sin x|+c$

• $\int \tan x dx = -\log ∣\cos x∣ + c$

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

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

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

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

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

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

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

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

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 that is difficult to remember 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 memorise 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 Advanced Exam. You can also download important formulas for JEE Advanced pdf and a separate list of all trigonometry formulas for JEE Advanced pdf are available on our Vedantu website, along with maths formulas for JEE advanced pdf.