Essential Formulas for Excelling in JEE Main 2024: Physics, Chemistry and Mathematics

Trigonometry Formulas

sin²x+cos²x=1

tanx=sinx/cosx

secx=1/cosx

cotx=cosx/sinx

cosecx=1/sinx

Algebra Formulas

(a+b)²=a²+2ab+b²

(a−b)²=a²−2ab+b²

a²−b²=(a+b)(a−b)

(a+b)³=a³+3a²b+3ab²+b³

(a−b)³=a³−3a²b+3ab²−b³

Calculus Formulas

d/dx(a)=0

d/dx(ax)=a

d/dx(xⁿ)=nxⁿ⁻¹

d/dx(sinx)=cosx

d/dx(cosx)=−sinx

d/dx(tanx)=sec²x

d/dx(cotx)=−cosec²x

Probability Formulas

P(A∪B)=P(A)+P(B)−P(A∩B)

P(A∩B)=P(A)×P(B/A)

P(A/B)=P(A∩B)/P(B)

Geometry Formulas

Area of a Triangle = (1/2)× base × height

Perimeter of a Square = 4 × side

Perimeter of a Rectangle = 2 × (length + breadth)

Area of a Circle = πr²

Circumference of a Circle = 2πr

Integration Formulas

∫dx=x+c

∫xⁿdx=(x⁽ⁿ⁺¹⁾)/(n+1) + C

∫e^xdx=e^x+C

∫sinxdx=−cosx+C

∫cosxdx=sinx+C

Straight Line Formulas

m=(y₂−y₁)/(x₂−x₁)

Intercept form of a straight line: x/a + y/b = 1

Slope-intercept form of a straight line: y=mx+c

Two-point form of a straight line: (y−y₁)/(y₂−y₁)=(x−x₁)/(x₂−x₁)

Distance Formula

√[(x₂−x₁)²+(y₂−y₁)²]

Equation of Parabola

y²=4ax

Vertex form of a parabola: y−k=a(x−h)², where (h, k) is the vertex of parabola.

Standard form of a parabola: (x−h)²=4a(y−k)

Focus-Directrix Form of Parabola

(x−h)²=4a(y−k), where the focus of the parabola is (h,k+14a) and the directrix of the parabola is y = k − 1/4a

Latus Rectum Form of Parabola

y = mx + a/m

Kinematics Formulas

v=u+at  where 'v' is the final velocity and 'u' is the initial velocity.

s=ut+(1/2)at² where 's' is the displacement.

v²=u²+2as

Work, Energy, and Power Formulas

W=Fdcosθ where θ is the angle between the F and d.

K.E.=1/2mv²

P=W/t

Gravitation Formulas

F=G(m₁m₂)/r²

g=GM/r²

T²=(4π²r³)/GM

Laws of Motion Formulas

F=ma

F=μN where μ is the coefficient of friction

Fg=mg

Heat Transfer Formulas

Q=mcΔT

where 'Q' is the amount of heat transferred, 'm' is the mass of the object, 'c' is the specific heat capacity, and 'ΔT' is the temperature change.

Q=ml where 'l' is the latent heat of vaporization

Thermodynamic Processes Formulas

PV=nRT

Q=ΔU+W

Laws of Thermodynamics

ΔS=QT

ΔU=Q−W

Atomic Structure Formulas

E=−13.6/n² where 'n' is the principal quantum number

λ=h/p where 'λ' is the wavelength, 'h' is Planck's constant, and 'p' is the momentum.

E=hc/λ where 'c' is the speed of light

Electrochemistry Formulas

E⁰cell = E⁰(cathode) - E⁰(anode)

Nernst equation: Ecell = E⁰cell – [RT/nF] ln Q

Ideal Gas Law

PV=nRT

Boyle's Law

P₁V₁=P₂V₂

Charles's Law

V₁/T₁=V₂/T₂

Gay-Lussac's Law

P₁T₁=P₂T₂

Avogadro's Law

V₁/n₁=V₂/n₂

Graham's Law of Diffusion

Rate₁/Rate₂ = √M₂/√M₁

Van der Waals Equation

(P+a(n/V)²)(V−nb)=nRT