Formulas are Critical to JEE Main Success, Check The List Here

Remembering Formulas are key to your success in JEE Main. The Physics, Maths and Chemistry sections are loaded with formulas which are very critical to students to solve questions. So we thought of sharing some important formulas for students to ace the race in the upcoming sessions of JEE Main 2021 exam.  

The National Testing Agency (NTA) has already conducted the JEE Main 2021 February and March session. So, applicants who are waiting for their chance in the April Session must check the list of critical formulas so that they don’t miss anything on the exam day. Aspirants can treat this piece of information as a note before the upcoming JEE Main 2021 exam

JEE Main 2021: Important Formulas to Win the Race

Here, we have shared all the section-wise critical formulas for students to do well in the JEE Main 2021 exam. First check the formulas of Physics followed by Chemistry and Maths formulas.

JEE Main Physics Formulas: Work, Power and Energy-

1. Work Done by Constant Force: W = FS cos Ө, It is a scalar quantity.
2. Work done by Multiple Forces: W = W1 +W2+W3+…The total work done on the particle is given by the sum of all the individual work done by all the particles’ forces.
3. Dimensions of work: Work = [ML2T-2]
4. Kinetic Energy: As mass is a positive quantity kinetic, energy is also a positive quantity. The formula is – K = ½ mv2= p2/2m, p is the linear momentum.
5. Potential Energy: F = -dU/dx for conservative forces, UGravitational = mgh, Uspring = 1/2kx2
6. Work-Energy theorem: According to the work-energy theorem, the net work done by the net force on the body is the change in kinetic energy of the body. The formula is – W= ∆K
7. Mechanical Energy: Mechanical energy E of an object or a system is given by the sum of potential energy U and kinetic energy K. The formula is – E= U+K.
8. Power: Pav = W/t, Here t is the time taken, and W is the work done.

Simple Harmonic Motion Formulas-

1. General Equation of SHM: Displacement x =A sin(ωt + Φ). Here, Φ is the initial phase of the motion, and (ωt + Φ) is the phase of the motion.
2. Angular Frequency (ω): ω = 2π/T = 2πf, T is the time-period, f is the frequency.
3. Frequency (f): f = 1/T = ω/2π.
4. Time Period (T): T = 2π/ω.
5. Hooke’s law: Force (F) = -kx (for small elongation x), k is the spring constant.
6. Acceleration: a = -ω2x = -ω2 A sin(ωt + Φ).
7. Velocity: v = Acos(ωt+ Φ) = ±ω(A^2 −x^2)^(1/2), Φ is the initial phase of motion.
8. Potential Energy: U = ½ kx2 (as a function of x).
9. Kinetic Energy: K = ½ mω2(A2 – x2), K = ½ k(A2 – x2).
10. Total Energy: E = U+K, E= ½ mω2A2.
11. Simple Pendulum: T=2π{l/g}^(1/2), L is the length of the pendulum.
12. Physical Pendulum: T=2π{I/mgl}^(1/2), Here I= Icm + ml 2, l is the total distance between the centre of mass and point of suspension.
13. Torsional Pendulum: T=2π{I/k}^(1/2), k is the torsional constant.
14. Springs in parallel: Keq = k1+k2.
15. Springs in series: 1/keq = 1/k1 + 1/k2.

Heat and Thermodynamics Formulas-

The transfer of heat from one body to another body happens through three routes – Conduction, Convection, Radiation.

1. Conduction: In Conduction, the rate of flow of heat is given by – dQ/dt=−KA(dT/dx), K is the thermal conductivity, A is the area of cross-section, dx is the thickness, and dT is the Temperature difference.
2. Thermal resistance to conduction: R = L/KA. Here, k is the material’s conductivity, L is the plane thickness, A is the plane area.
3. Emissivity (e): Emissivity of a body is given by the ratio of Emissive power of a body at temperature T to the Emissive power of a black body at the same temperature.
4. Kirchoff’s Law: Kirchoff’s law in JEE Main 2021 exam states that the ratio of the emissive power of a body to the absorptive power for the radiation of a given wavelength will be the same for all substances at the same temperature, and it is always equal to the emissive power of a perfectly black body. The formula is – E(body)/a(body) = E (black body).
5. Nature of thermal radiations (Wien’s displacement law): λmax ∝ 1/T, λmax T = b, λmax is the peak wavelength of the blackbody radiation curve, b = 0.282 cm-K, Wein’s constant, T is the temperature.
6. Stefan- Boltzmann’s law: For a perfect blackbody: u = σ A T4. Here, σ is Stefan’s constant = 5.67 x 10-8 watt/m2K4, u /A is the energy flux. For a body that is not a perfect black body: u = e σ A T4. Here, e represents emissivity between 0 to 1 (which is equal to absorptive power).
7. Newton’s law of cooling: In Newton’s law of cooling, for a slight temperature difference between the body and its surrounding dθ/dt is given by dθ/dt = (θ – θ0). Here, θ and θ0 are the temperatures corresponding to the object and surroundings.
8. Temperature scales: F= 32 +(9/5)C, K = C + 273.16, F is the Fahrenheit scale, C is the Celsius scale, K is the Kelvin scale.
9. Ideal Gas equation: PV= nRT. Here, n is the number of moles. P represents Pressure, V represents Volume, T stands for temperature.
10. Van der Waals equation: (p + an2/V2)(V-nb) = nRT, P= Measure Pressure, a & b = correction factor to account for intermolecular forces, nb = It is the correction factor to account for molecule size, n = number of moles, T = Temperature.
11. Thermal expansion: Linear Expansion : L = Lo (1+αΔT), Area Expansion: A = Ao(1+βΔT), and Volume Expansion: V = Vo(1+yΔT).
12. Relation between α,β and y for isotropic solid: α/1= β/2 = y/3.

Chemistry Formulas For JEE Main 2021: Atomic Structure Formulas

1. Estimation of closest distance of approach of α particle: R = {4kze2}/{mv2}.
2. The radius of a nucleus: R=R0​(A)1/3cm.
3. Planck’s Quantum Theory: Energy of one photon = hv = hc/λ​.
4. Photoelectric Effect: hv=hv0​+me​v2.
5. De-Broglie wavelength: λ = h/mc = h/p.
6. Number of photons emitted by a sample of Hydrogen atom: Δn(Δn+1)​/2.
7. Heisenberg’s uncertainty principle: Δx.Δp > (h/4π) or mΔx ⋅ Δv ≥ (h/4π) or Δx . Δv ≥ h/4πm.

Quantum Numbers:

• Principal quantum number (n)=1,2,3,4…. to ∞.
• The Orbital angular momentum of electrons in an orbit  = {nh}/{2π}.
• Azimuthal quantum number (l) = 0,1, …to (n-1).
• Number of orbitals in each subshell = 2l+ 1.
• Max number of electrons in a particular subshell = 2 * (2l + 1).

Gaseous State Formulas:

1. Boyle’s law and measurement of pressure: At constant temperature – V α 1/p, P1​V1​=P2​V2​.
2. Charles law: At constant pressure, V∝T OR V1/T1​=V2​​/T2​.
3. Gay-lussac’s law: At constant volume, PαT, p1/T1​=p2​​/T2​  →temp on absolute scale.
4. Ideal gas Equation: PV = nRT, PV = wRT/m.
5. Amagat’s law of partial volume: V=V1​+V2​+V3​+…….

Mathematics Formulas For JEE Main 2021: Straight Line Formulas 

1. Distance formula: d = √[(x2-x1)2+(y2-y1)2].
2. Section Formula: x = (mx2+nx1)/(m+n), y = (my2+ny1)/(m+n).
3. Centroid: G = [(x1+x2+x3)/3, (y1+y2+y3)/3].
4. Incentre: I = {(ax1+bx2+cx3)/(a+b+c), (ay1+by2+cy3)/(a+b+c)}.
5. Excentre: I1 = {(-ax1+bx2+cx3)/(-a+b+c), (-ay1+by2+cy3)/(-a+b+c)}.

Slope Formula:

• Slope of Line joining two points (x1, y1) and (x2, y2) is m = (y1  – y2) / (x1 – x2).
• Slope of a line ax+by+c = 0 is given by = -coefficient of x/coefficient of y = -b/a.

Various forms of straight line equation:

• Point Slope form: y – y1 = m(x – x1).
• Slope intercept form: y = mx + c.
• Two point form: y-y1 = {(y2 – y1)/(x2 – x1)} * (x-x1).
• Intercept form: (x/a) + (y/b) = 1.
• Perpendicular or Normal form: xcos α  +ysin α = p.
• Parametric form: x = x1+ r cos θ, y = y1 + r sin θ.
• Symmetric form: (x–x1)/l = (y – y1)/m = (z – z1)/n.
• General form of straight line: ax + by + c = 0, x intercept = -c/a, y intercept = -c/b.

Integration Formulas:

• ∫ sinx dx = -cosx + c.
• ∫ cosx dx = sinx + c.
• ∫ sec2x dx = tanx + c.
• ∫ cosec2x dx = -cot x + c.
• ∫ secx tanx dx = sec x + c.
• ∫ cosec x cot x dx = -cosec x + c.
• ∫ cot x dx = log |sin x|+ c.
• ∫ tan x dx = −log| sinx| + c.
• ∫ sec x dx = log ∣secx+tanx∣ + c.
• ∫ cosec x dx = log ∣cosecx-cotx∣ + c.
• ∫ sin (ax+b)dx = -(1/a) cos (ax+b) + c.
• ∫ cos (ax+b) dx = (1/a) sin (ax+b) + c.
• ∫ tan (ax+b)dx = (1/a) ln sec (ax+b) + c.
• ∫ cot (ax+b)dx = (1/a) ln sin (ax+b) + c.
• ∫ sec2 (ax+b)dx = (1/a) tan (ax+b) + c.
• ∫ cosec2 (ax+b)dx = -(1/a) cot (ax+b) + c.
• ∫ sec (ax+b) tan (ax+b) dx = (1/a) sec (ax+b) + c.
• ∫ cosec (ax+b) cot (ax+b) dx = -(1/a) cosec (ax+b) + c.

Check these formulas to prepare for the JEE Main 2021 exam during the final phase. This piece of information will act as a note for students in the upcoming exams. For more information, students must stay updated on the latest events by referring to the Official Website. We will also bring forth useful information for JEE Main 2021 aspirants in the days to come. So, please stay tuned to us!