Important formulas for JEE Main which can be helpful for the exam




When JEE Main is not far away with Class 12th Board examination in between it gets very important for the aspirants to keep themselves prepared for both. The best way to utilize the last months of preparation is by revision. Don’t start any new topic at the last moment but revise what all you have prepared so far. Keep a handy note of key formulas of all the three subjects. It will help you to get a quick view of the fundamentals right before the examination. In this article you will get Important formulas for JEE Main which can be helpful for the exam.

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Here we have sorted out the top 50 important formulas for JEE Main which can be helpful for the exam from the entire three subjects via. Physics, Chemistry, and Mathematics.

JEE Main Important Formulas for Mathematics

  1. The general form of Complex numbers x + is where x is Real part and y is an Imaginary part.
  2. Sum of nth root of unity is zero
  3. Product of nth root of unity (–1)n–1
  4. Cube roots of unity are 1, ω, ω2
  5. |z1+z2|<=|z1|+|z2|; |z1+z2|>=|z1|-|z2|; |z1-z2|>=|z1|-|z2|
  6. If three complex numbers z1, z2, z3 are collinear then,

[z1 z1 1

z2 z2 1

z3 z3 1] = 0

  1. If ΣCosα = ΣSinα = 0, ΣCos2α = ΣSin2α = 0,
  2. ΣCos2nα = ΣSin2nα = 0,
  3. ΣCos2α = ΣSin2α = 3/2
  4. ΣCos3α = 3Cos(α + β + γ),
  5. ΣSin3α = 3Sin(α + β + γ)
  6. ΣCos(2α – β – γ) = 3,
  7. ΣSin(2α – β – γ) = 0,
  8. a3 + b3 + c3 – 3abc = (a + b + c) (a + bω + cω2) (a + bω2 + cω)
  9. Standard form of Quadratic equation is ax2 + bx +c = 0 Sum of roots = -b/a, product of roots discriminate = b2 – 4ac If α, β are roots then Quadratic equation is x2 – x(α + β) + αβ = 0
  10. Number of terms in the expansion (x+a)n is n+1
  • Any three noncoplanar vectors are linearly independent

A system of vectors ā1, ā2,….ān are said to be linearly dependent if there

x1ā1+x2ā2+….+xnan=0

At least one of xi ≠0, i=1, 2, 3….nImportant Formulas

And determinant = 0

  1. Torque: The torque or vector moment or moment vector M of a force F about a point P is defined as M = r×F where r is the vector from the point P to any point A on the line of action L of F.
  2. a,b,c are coplanar then [abc]=0
  3. If i,j,k are unit vectors then [i j k] = 1
  4. If a,b,c are vectors then [a+b, b+c, c+a] = 2[abc]
  5. (1 + x)n – 1 is divisible by x and (1 + x)n – nx –1 is divisible by x2
  6. If nCr-1 nCr nCr+1 are in A.P (n–2r)2 =n + 2

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JEE Main Important Formulae for Physics

  1. The energy of electric dipole is given by U = – p.E.
  2. The energy of a magnetic dipole is U = – μ .B C.
  3. Electric Charge : Q = ± ne (e = 1.60218 × 10-29 C)

SI unit of Electric Charge is Coulomb (C)

  1. Coulomb’s Law : Electrostatic Force (F) = k[q1q2/r2]

and, in Vector Form : →F=k(q1q2)×→r/r3 where,

q1 and q2 = Charges on the Particle,

r = Separation between them,

→r = Position Vector,

k = Constant = 14πϵ0=8.98755×109Nm2C2

  1. Electric Current : The current at Time t : i=limΔt→0 ΔQ/Δt= dQ/dT

Where Δ Q and Δ T = Charges crosses an Area in time Δ T

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

  1. Average current density: →j=Δi/Δs

j=limΔs→0 Δi/Δs=di/dS , j=Δi/ΔScosθ

Where, Δ S = Small Area, Δ i = Current through the Area Δ S, P = Perpendicular to the flow of Charges, θ = Angle Between the normal to the Area and the direction of the current.

  1. Kirchhoff’s Law: Law of Conservation of Charge: I3 = I1 + I2
  2. Resistivity : ρ(T)=ρ(T0)[1+α(T−T0)]

Resistance: R (T) =R (T0) [1+α (T−T0)] where,

ρ (T) and ρ (T0) = Resistivity at Temperature T and T0 respectively,

α = Constant for given material.

  1. Lorentz Force : →F=q[→E+(→v×→B)] where,

E = Electric Field, B = Magnetic Field, q = Charge of Particle, v = Velocity of Particle.

  1. Magnetic Flux: Magnetic Flux through Area dS = ϕ=→B⋅d → S= B⋅dS Cos θ where, d→S = Perpendicular vector to the surface and has a magnitude equal to are Ds, →B = Magnetic Field at an element, θ = Angle Between →B and d→S, SI unit of Magnetic Flux is Weber (Wb).
  2. Straight line Equation of Motion (Constant Acceleration):

v=u+at

s=ut+1/2at2

2as=v2−u2

  • Gravitational Acceleration Equation of Motion:

S.No Motion In Upward Direction Motion In Downward Direction
A. v=u−gt v=u+gt
B. y=ut−1/2gt2 y=ut+1/2gt2
C. −2gy=v2−u2 2gy=v2−u2
  • Projectile Equation of Motion:

Horizontal Range (R) = u2sin2θ/ g

Time of Flight (T) = 2uSinθ/ g

Maximum Height (H) = u2sin2θ/ 2

Where, u = initial velocity, v = final velocity, a = constant acceleration, t = time, x = position of particle.

  • Universal Law of Gravitation

Gravitational force →F=G[Mm/r2]^r where,

M and m = Mass of two Objects, r = separation between the objects, ^r = unit vector joining two objects, G = universal Gravitational Constant [G=6.67×10−11N⋅m2/Kg2]

  • Work Done by Constant Force

Work Done (W) = →F⋅→S=∣→F∣ ∣→S∣ cosθ, Where, S = Displacement along a straight line, F = applied force, θ = Angle between S & F. It is a scalar quantity and the Dimension of work is [M1 L2 T-2], SI unit of Work is joule (J) and 1J=1N⋅m=Kg⋅m2/ s2

  • Kinetic Friction:

fk = µk · N

Maximum Static Friction (Limiting Friction): fmax = µs · N, where, N = Normal Force, µk = Coefficient of Kinetic Friction, µs = Coefficient of Static Friction.

  • Simple Harmonic Motion:

Force (F) = – k x and k = ω2 m

where, k = Force Constant, m = Mass of the Particle, x = Displacement and ω2 = Positive Constant.

JEE Main Important Formulae for Chemistry

  1. T(K)=T(⁰C) + 273.15
  2. Molarity (M)= No. of Moles of Solutes/ Volume of Solution in Liters

Unit: mole/ L

  1. Molality (m)= No. of Moles of Solutes/ Mass of solvent in kg
  2. Molecualr Mass= 2x vapor density
  3. Atomic number= No. of protons in the nucleus = No. of electrons in the nucleus
  4. Mass number= No. of protons + No. of neutrons
  5. C= vλ
  6. Boyle’s Law: P1V1 = P2V2 (at constant T and n)
  7. Charle’s Law: V1/ T1 = V2/ T2 (at constant P and n)
  8. Enthalpy: H = U + pV
  9. First Law of Thermodynamics: ΔU = q + W
  10. Ohm’s Law: V = RI where, R = ρ ι/a
  11. Faraday’s First Law of Electrolysis

M = Zit

M = mass of substance deposited

Z= Electrochemical Equivalent

I = current,

t= time

Z= Atomic Mass/ n x F

  1. Faraday’s Second Law of Electrolysis

M1/ M2 = E1/E2 , where E = equivalent weight

  1. Freundlich Adsorption Isotherem [x/m]-Kp (1/n); n>=1
  2. General Electronic Configuration: ns1-2

 


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