Important Formulas for JEE Exam

The Joint Entrance Examination (JEE) is one of the most challenging exams in India for students aspiring to enter top engineering colleges like IITs and NITs. Preparing for JEE requires a solid understanding of concepts and, more importantly, being familiar with essential formulas. Knowing the right formulas saves time during the exam and boosts accuracy. Here’s a detailed guide on the most important formulas for JEE, covering Physics, Chemistry, and Mathematics.

Mathematics Formulas for JEE

Mathematics is a scoring subject, provided you remember the formulas well. Here's a list of crucial formulas for different topics:

1. Algebra

Roots of a quadratic equation: For ax^2 + bx + c = 0, the roots are given by:

x = (-b ± √(b² - 4ac)) / 2a

Sum of roots: α + β = -b/a

Product of roots: αβ = c/a

General expansion of (a + b)ⁿ:

(a + b)ⁿ = Σ(nCk aⁿ⁻ᵏ bᵏ)

• Quadratic Equations:
• Binomial Theorem:

2. Trigonometry

sin²θ + cos²θ = 1

1 + tan²θ = sec²θ

1 + cot²θ = csc²θ

sin(A ± B) = sinA cosB ± cosA sinB

cos(A ± B) = cosA cosB ∓ sinA sinB

sin 2θ = 2 sinθ cosθ

cos 2θ = cos²θ - sin²θ

• Basic identities:
• Sum and Difference of Angles:
• Double Angle Formulas:

3. Coordinate Geometry

• Equation of a line: y = mx + c
• Distance between two points: d = √((x₂ - x₁)² + (y₂ - y₁)²)
• Midpoint of a line segment: ((x₁ + x₂) / 2, (y₁ + y₂) / 2)

4. Calculus

f'(xⁿ) = nxⁿ⁻¹

f'(sin x) = cos x

f'(cos x) = -sin x

∫ xⁿ dx = (xⁿ⁺¹)/(n+1) + C

∫ sin x dx = -cos x + C

∫ cos x dx = sin x + C

• Derivative of standard functions:
• Integration of standard functions:

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Physics Formulas for JEE

Physics requires a deep understanding of concepts, but having formulas on hand is vital to solving problems quickly.

1. Mechanics

v = u + at

s = ut + ½at²

v² = u² + 2as

• Newton's Second Law: F = ma
• Kinematic Equations of Motion:

2. Electrostatics

• Coulomb’s Law: F = ke (q₁q₂ / r²)
• Electric Potential: V = ke (q / r)

3. Thermodynamics

• First Law of Thermodynamics: ΔU = Q - W
• Ideal Gas Equation: PV = nRT

4. Optics

• Lens Formula: 1/f = 1/v - 1/u
• Magnification: m = -v/u

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Chemistry Formulas for JEE

Chemistry is divided into Physical, Organic, and Inorganic Chemistry. Let's focus on some of the critical formulas from Physical Chemistry:

1. Mole Concept

• Number of moles: Number of moles = Given mass / Molar mass
• Avogadro’s Law: V ∝ n (at constant T and P)

2. Chemical Kinetics

• Rate of reaction: Rate = k[A]^m[B]^n
• Arrhenius Equation: k = A e^(-Ea/RT)

3. Thermodynamics in Chemistry

• Gibbs Free Energy: ΔG = ΔH - TΔS

4. Equilibrium

• Equilibrium Constant (Kc): Kc = ([C]^c [D]^d) / ([A]^a [B]^b)

Tips for Memorizing Formulas

• Understand the Concept: Don’t just memorize blindly—understand how and why a formula works.
• Practice Regularly: Use these formulas in different problems to solidify your understanding.
• Create Flashcards: Write the formulas on cards and review them daily.
• Solve Previous Year Papers: JEE past papers often contain problems that rely on key formulas.

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Conclusion

The JEE exam is a competitive test that demands a strong command of formulas from Physics, Chemistry, and Mathematics. This list highlights the most important ones that frequently appear in the exam. Regular practice and revision will help you retain these formulas, giving you a significant advantage when you sit for the exam. Remember, consistency and dedication are key to mastering these formulas and excelling in JEE. Good luck!