JEE Important Formulas - Complete Mathematics, Physics, Chemistry

Mathematics Formulas

Essential formulas for Algebra, Calculus, Coordinate Geometry, and Trigonometry with examples and applications.

1 Algebra

Quadratic Formula

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

For quadratic equation \(ax^2 + bx + c = 0\)

Binomial Theorem

(a + b)^n = \sum_{k=0}^{n} \binom{n}{k} a^{n-k} b^k

Where \(\binom{n}{k} = \frac{n!}{k!(n-k)!}\)

Arithmetic Progression

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

Sum of first n terms, where a is first term, d is common difference

2 Trigonometry

Pythagorean Identity

\sin^2\theta + \cos^2\theta = 1

Sine Rule

\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C} = 2R

Where R is circumradius of triangle ABC

Cosine Rule

a^2 = b^2 + c^2 - 2bc\cos A

3 Calculus

Derivative Rules

\frac{d}{dx}(x^n) = nx^{n-1}

\frac{d}{dx}(\sin x) = \cos x

\frac{d}{dx}(\cos x) = -\sin x

Integration Formulas

\int x^n dx = \frac{x^{n+1}}{n+1} + C, n \neq -1

\int \frac{1}{x} dx = \ln|x| + C

\int e^x dx = e^x + C

Fundamental Theorem of Calculus

\int_a^b f(x) dx = F(b) - F(a)

Where F'(x) = f(x)

4 Coordinate Geometry

Distance Formula

d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}

Section Formula

P(x, y) = \left(\frac{mx_2 + nx_1}{m+n}, \frac{my_2 + ny_1}{m+n}\right)

Point dividing line segment in ratio m:n

Area of Triangle

\Delta = \frac{1}{2} \begin{vmatrix} x_1 & y_1 & 1 \\ x_2 & y_2 & 1 \\ x_3 & y_3 & 1 \end{vmatrix}

Mathematics Formula Tips

Memorize derivative and integration formulas for quick application
Practice applying trigonometric identities in different forms
Understand the geometric interpretation of coordinate geometry formulas
Learn to derive formulas rather than just memorizing them
Create flashcards for quick revision of important formulas

Physics Formulas

Essential formulas for Mechanics, Electrodynamics, Thermodynamics, and Modern Physics with applications.

1 Mechanics

Newton's Second Law

\[F = ma\]

Force equals mass times acceleration

Kinematic Equations

\[v = u + at\]

s = ut + \frac{1}{2}at^2

\[v^2 = u^2 + 2as\]

Work-Energy Theorem

W = \Delta KE = \frac{1}{2}mv^2 - \frac{1}{2}mu^2

Gravitational Force

F = G\frac{m_1m_2}{r^2}

Where G is gravitational constant

2 Thermodynamics

First Law of Thermodynamics

\Delta U = Q - W

Change in internal energy equals heat added minus work done

Ideal Gas Law

\[PV = nRT\]

Where R is universal gas constant

Efficiency of Heat Engine

\eta = 1 - \frac{Q_C}{Q_H}

Where Qc is heat rejected, Qh is heat absorbed

3 Electrodynamics

Coulomb's Law

F = \frac{1}{4\pi\epsilon_0} \frac{q_1q_2}{r^2}

Electrostatic force between two charges

Ohm's Law

\[V = IR\]

Voltage equals current times resistance

Magnetic Force on Moving Charge

F = q(\vec{v} \times \vec{B})

Faraday's Law

\mathcal{E} = -\frac{d\Phi_B}{dt}

Induced EMF equals negative rate of change of magnetic flux

4 Modern Physics

Photoelectric Effect

E = h\nu = \phi + \frac{1}{2}mv_{max}^2

Where φ is work function, h is Planck's constant

de Broglie Wavelength

\lambda = \frac{h}{p}

Where p is momentum, h is Planck's constant

Radioactive Decay

N = N_0 e^{-\lambda t}

Where λ is decay constant

Physics Formula Tips

Understand the physical meaning behind each formula
Pay attention to units and dimensions in calculations
Practice deriving formulas from fundamental principles
Learn vector forms of formulas for better application
Create formula sheets for each topic for quick revision

Chemistry Formulas

Essential formulas for Physical, Organic, and Inorganic Chemistry with applications and examples.

1 Physical Chemistry

Ideal Gas Equation

\[PV = nRT\]

Where R = 0.0821 L·atm·mol⁻¹·K⁻¹

Rate Law

\text{Rate} = k[A]^m[B]^n

For reaction aA + bB → products

Nernst Equation

E = E^0 - \frac{RT}{nF} \ln Q

For electrochemical cells

Gibbs Free Energy

\Delta G = \Delta H - T\Delta S

Spontaneous when ΔG < 0

2 Organic Chemistry

Degree of Unsaturation

\text{DU} = \frac{2C + 2 - H - X + N}{2}

Where C, H, X, N are number of carbon, hydrogen, halogen, nitrogen atoms

Beer-Lambert Law

A = \epsilon c l

Where A is absorbance, ε is molar absorptivity, c is concentration, l is path length

3 Inorganic Chemistry

Molarity

M = \frac{\text{moles of solute}}{\text{liters of solution}}

Molality

m = \frac{\text{moles of solute}}{\text{kg of solvent}}

Henderson-Hasselbalch Equation

\text{pH} = \text{p}K_a + \log\left(\frac{[\text{A}^-]}{[\text{HA}]}\right)

For buffer solutions

Crystal Field Stabilization Energy

\text{CFSE} = [-0.4n_t + 0.6n_e]\Delta_o

For octahedral complexes, where n_t and n_e are number of electrons in t₂g and e_g orbitals

4 Important Constants

Avogadro's Number

N_A = 6.022 \times 10^{23} \text{ mol}^{-1}

Gas Constant

R = 8.314 \text{ J·mol}^{-1}\text{·K}^{-1}

Faraday's Constant

F = 96485 \text{ C·mol}^{-1}

Chemistry Formula Tips

Memorize important constants with their units
Understand the conditions under which each formula applies
Practice unit conversions for different measurement systems
Learn to derive formulas from basic principles
Create summary sheets for each branch of chemistry

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Formula Memorization Tips

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Practice Regularly

Write formulas multiple times and solve problems using them daily.

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Understand Concepts

Learn the derivation and application rather than rote memorization.

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JEE Important Formulas 2025

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