CUET PG Important Formulas 2027: Check Subject-Wise Formula List

Topic

Formula

Quadratic Equation

$ax^2+bx+c=0$

Roots of Quadratic

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

Sum of Roots

$\alpha+\beta=-\dfrac{b}{a}$

Product of Roots

$\alpha\beta=\dfrac{c}{a}$

Binomial Theorem

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

$n$th term of AP

$a_n=a+(n-1)d$

Sum of $n$ terms of AP

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

$n$th term of GP

$a_n=ar^{n-1}$

Inverse of Matrix

$A^{-1}=\dfrac{1}{\det(A)}\operatorname{adj}(A)$

Eigenvalue Condition

$\det(A-\lambda I)=0$

Topic

Formula

Limit

$\lim_{x\to0}\dfrac{\sin x}{x}=1$

Limit

$\lim_{x\to0}\dfrac{e^x-1}{x}=1$

Derivative of $x^n$

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

Derivative of $e^x$

$\dfrac{d}{dx}(e^x)=e^x$

Derivative of $\ln x$

$\dfrac{d}{dx}(\ln x)=\dfrac{1}{x}$

Indefinite Integral

$\int x^ndx=\dfrac{x^{n+1}}{n+1}+C,\ n\ne -1$

Indefinite Integral

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

Definite Integral

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

Mean Value Theorem

$f'(c)=\dfrac{f(b)-f(a)}{b-a}$

Topic

Formula

Separable Differential Equation

$\dfrac{dy}{dx}=g(x)h(y)$

Solution of Separable DE

$\int\dfrac{1}{h(y)}dy=\int g(x)dx$

Linear Differential Equation

$\dfrac{dy}{dx}+Py=Q$

General Solution of Linear DE

$y=e^{-\int Pdx}\left(\int Q e^{\int Pdx}dx+C\right)$

Topic

Formula

Dot Product

$\vec{a}\cdot\vec{b} = |\vec{a}||\vec{b}|\cos\theta$

or in components

$\vec{a}\cdot\vec{b} = a_xb_x + a_yb_y + a_zb_z$

Cross Product

$|\vec{a}\times\vec{b}| = |\vec{a}||\vec{b}|\sin\theta$

Cross Product (components)

$\vec{a}\times\vec{b} = (a_yb_z-a_zb_y)\hat{i} + (a_zb_x-a_xb_z)\hat{j} + (a_xb_y-a_yb_x)\hat{k}$

Projection of $\vec {a} $ on $\vec {b}$

$\text{comp}_{\vec{b}}(\vec{a}) = \dfrac{\vec{a}\cdot\vec{b}}{|\vec{b}|}$

Projection vector
$\text{proj}_{\vec{b}}(\vec{a}) = \dfrac{\vec{a}\cdot\vec{b}}{|\vec{b}|^2} \vec{b}$

Topic

Formula

Probability (Addition Law)

$P(A\cup B) = P(A) + P(B) - P(A\cap B)$

Conditional Probability

$P(A\mid B) = \dfrac{P(A\cap B)}{P(B)},\ P(B)\neq 0$

Mean (Arithmetic Mean)

$\bar{x} = \dfrac{1}{n}\sum_{i=1}^{n} x_i$

Variance (Population)

$\sigma^2 = \dfrac{1}{n}\sum_{i=1}^{n}(x_i - \bar{x})^2$

Standard Deviation

$\sigma = \sqrt{\dfrac{1}{n}\sum_{i=1}^{n}(x_i - \bar{x})^2}$

Topic

Formula

Objective Function

$\text{Max/Min } Z = ax + by$

Optimal Solution

Lies at a corner point of the feasible region

Concept

Formula

Taylor Expansion

$f(x) = f(a) + (x-a)f'(a) + \dfrac{(x-a)^2}{2!}f''(a) + \cdots$

Jacobian

$J = \dfrac{\partial(x,y)}{\partial(u,v)}$

Gradient

$\nabla f$

Divergence

$\nabla\cdot\vec{A}$

Curl

$\nabla\times\vec{A}$

Theorem

Formula

Gauss Divergence Theorem

$\displaystyle \iiint (\nabla\cdot\vec{A})dV = \iint \vec{A}\cdot d\vec{S}$

Green’s Theorem

$\displaystyle \oint (Pdx + Qdy) = \iint \left(\dfrac{\partial Q}{\partial x} - \dfrac{\partial P}{\partial y}\right)dA$

Stokes’ Theorem

$\displaystyle \oint \vec{A}\cdot d\vec{l} = \iint (\nabla\times\vec{A})\cdot d\vec{S}$

Concept

Formula

First-order Linear DE

$\dfrac{dy}{dx} + Py = Q$

Second-order Linear DE (homogeneous)

$a y'' + b y' + c y = 0$

Euler’s Formula

$e^{i\theta} = \cos\theta + i\sin\theta$

Concept

Formula

Newton’s Second Law

$\vec{F} = m\vec{a}$

Centripetal Force

$F = \dfrac{mv^2}{r}$

Coriolis Force

$\vec{F_c} = -2m(\vec{\omega}\times\vec{v})$

Gravitational Force

$F = \dfrac{GMm}{r^2}$

Concept

Formula

Linear Momentum

$\vec{p} = m\vec{v}$

Angular Momentum

$\vec{L} = \vec{r}\times\vec{p}$

Kinetic Energy

$K = \dfrac{1}{2}mv^2$

Moment of Inertia

$I = \sum mr^2$

Parallel Axis Theorem

$I = I_{cm} + Md^2$

Rotational Kinetic Energy

$K = \dfrac{1}{2}I\omega^2$

Concept

Formula

Continuity Equation

$A_1 v_1 = A_2 v_2$

Bernoulli’s Equation

$P + \dfrac{1}{2}\rho v^2 + \rho g h = \text{constant}$

Concept

Formula

SHM Equation

$x = A\sin(\omega t + \phi)$

Angular Frequency (spring–mass)

$\omega = \sqrt{\dfrac{k}{m}}$

Time Period

$T = \dfrac{2\pi}{\omega}$

Damped Oscillator

$x = A e^{-bt/2}\sin(\omega t)$

Concept

Formula

Wave Equation

$\dfrac{\partial^2 y}{\partial x^2} = \dfrac{1}{v^2}\dfrac{\partial^2 y}{\partial t^2}$

Wave Speed

$v = \nu \lambda$

Group Velocity

$v_g = \dfrac{d\omega}{dk}$

Concept

Formula

Lens Formula

$\dfrac{1}{f} = \dfrac{1}{v} + \dfrac{1}{u}$

Magnification

$m = \dfrac{v}{u}$

YDSE Fringe Width

$\beta = \dfrac{\lambda D}{d}$

Rayleigh Criterion

$\theta = 1.22\dfrac{\lambda}{D}$

Bragg’s Law

$n\lambda = 2d\sin\theta$

Concept

Formula

Coulomb’s Law

$F = \dfrac{1}{4\pi\varepsilon_0}\dfrac{q_1 q_2}{r^2}$

Gauss’s Law

$\displaystyle \oint \vec{E}\cdot d\vec{S} = \dfrac{Q}{\varepsilon_0}$

Electric Potential

$V = \dfrac{1}{4\pi\varepsilon_0}\dfrac{q}{r}$

Capacitance

$C = \dfrac{Q}{V}$

Concept

Formula

Biot–Savart Law

$d\vec{B} = \dfrac{\mu_0}{4\pi}\dfrac{Id\vec{l}\times \hat{r}}{r^2}$

Lorentz Force

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

Cyclotron Frequency

$\omega = \dfrac{qB}{m}$

Impedance (LCR in series)

$Z = \sqrt{R^2 + \left(\omega L - \dfrac{1}{\omega C}\right)^2}$

Resonance Frequency

$\omega_0 = \dfrac{1}{\sqrt{LC}}$

Concept

Formula

Mean Kinetic Energy (per molecule)

$\dfrac{3}{2}kT$

RMS Speed

$v_{\text{rms}} = \sqrt{\dfrac{3kT}{m}}$

Ideal Gas Law

$PV = nRT$

First Law of Thermodynamics

$dQ = dU + dW$

Carnot Efficiency

$\eta = 1 - \dfrac{T_2}{T_1}$

Clausius–Clapeyron Equation

$\dfrac{dP}{dT} = \dfrac{L}{T(V_2 - V_1)}$

Concept

Formula

Lorentz Factor

$\gamma = \dfrac{1}{\sqrt{1 - v^2/c^2}}$

Mass–Energy Relation

$E = mc^2$

Photoelectric Effect

$h\nu = \phi + K_{\text{max}}$

Compton Shift

$\Delta\lambda = \dfrac{h}{mc}(1-\cos\theta)$

de Broglie Wavelength

$\lambda = \dfrac{h}{p}$

Uncertainty Principle

$\Delta x\Delta p \ge \dfrac{\hbar}{2}$

Particle in a 1D Box

$E_n = \dfrac{n^2 h^2}{8mL^2}$

Radioactive Decay Law

$N = N_0 e^{-\lambda t}$

Half-Life

$T_{1/2} = \dfrac{0.693}{\lambda}$

Concept

Formula

Density of States (3D)

$g(E) \propto \sqrt{E}$

Conductivity

$\sigma = nq\mu$

Drift Velocity

$v_d = \mu E$

Diode Equation

$I = I_0\left(e^{V/\eta V_T} - 1\right)$

Concept

Formula

CE Amplifier Gain

$A_v = \dfrac{V_o}{V_i}$

Barkhausen Condition

$A\beta = 1$

OPAMP (Inverting)

$A_v = -\dfrac{R_f}{R_i}$

OPAMP (Non-Inverting)

$A_v = 1 + \dfrac{R_f}{R_i}$

De Morgan’s Theorems

$(A+B)' = A'B'$ , $(AB)' = A' + B'$

Concept

Formula

Ideal Gas Equation

$PV = nRT$

van der Waals Equation

$\left(P + \dfrac{a}{V_m^{2}}\right)(V_m - b) = RT$

Compressibility Factor

$Z = \dfrac{PV_m}{RT}$

RMS Speed

$v_{\text{rms}} = \sqrt{\dfrac{3RT}{M}}$

Mean Free Path

$\lambda = \dfrac{kT}{\sqrt{2\pi}d^{2}P}$

Concept

Formula

Raoult’s Law

$P = X_A P_A^0$

Relative Lowering of Vapour Pressure

$\dfrac{\Delta P}{P^0} = X_B$

Elevation of Boiling Point

$\Delta T_b = K_b m$

Depression of Freezing Point

$\Delta T_f = K_f m$

Osmotic Pressure

$\pi = C R T$

van’t Hoff Factor

$i = \dfrac{\text{observed}}{\text{calculated}}$

Concept

Formula

pH

$\text{pH} = -\log[H^+]$

Ionic Product of Water

$K_w = 10^{-14}$

Acid Dissociation Constant

$K_a = \dfrac{[H^+][A^-]}{[HA]}$

Henderson–Hasselbalch Equation

$\text{pH} = pK_a + \log\dfrac{[\text{salt}]}{[\text{acid}]}$

Debye–Hückel Limiting Law

$\log\gamma = -0.509z^2\sqrt{I}$

Concept

Formula

First Law

$dU = \delta Q - \delta W$

Enthalpy

$H = U + PV$

Heat Capacity Relation

$C_p - C_v = R$

Gibbs Free Energy

$G = H - TS$

Spontaneity Condition

$\Delta G < 0$

Maxwell Relation (example)

$\left(\dfrac{\partial T}{\partial V}\right)_S = -\left(\dfrac{\partial P}{\partial S}\right)_V$

Clausius–Clapeyron Equation

$\ln P = -\dfrac{\Delta H_{\text{vap}}}{RT} + C$

Concept

Formula

Gibbs Phase Rule

( F=C-P+2 )

Reduced Phase Rule

( F=C-P+1 )

Concept

Formula

Rate Law

$r = k[A]^m[B]^n$

First-Order Integrated Law

$\ln\left(\dfrac{[A]_0}{[A]}\right) = kt$

Half-Life (First Order)

$t_{1/2} = \dfrac{0.693}{k}$

Arrhenius Equation

$k = A e^{-E_a/RT}$

Concept

Formula

Nernst Equation

$E = E^0 - \dfrac{0.0591}{n}\log Q$

Gibbs Free Energy

$\Delta G = -nFE$

Conductivity

$\kappa = \dfrac{l}{RA}$

Molar Conductivity

$\Lambda_m = \dfrac{\kappa}{c}$

Concept

Formula

Freundlich Isotherm

$\dfrac{x}{m} = K P^{1/n}$

Langmuir Isotherm

$\dfrac{1}{V} = \dfrac{1}{V_m} + \dfrac{1}{K V_m P}$

Concept

Formula

de Broglie Wavelength

$\lambda = \dfrac{h}{mv}$

Uncertainty Principle

$\Delta x\Delta p \ge \dfrac{\hbar}{2}$

Hydrogen-like Energy Levels

$E_n = -\dfrac{13.6,Z^2}{n^2}\ \text{eV}$

Concept

Formula

Born–Landé Equation

$U = \dfrac{N_AMz^+z^-e^2}{4\pi\varepsilon_0r_0}\left(1-\dfrac{1}{n}\right)$

Dipole Moment

$\mu = q r$

Concept

Formula

Effective Atomic Number

$\text{EAN} = Z - \text{oxidation state} + \text{ligand electrons}$

Spin-Only Magnetic Moment

$\mu = \sqrt{n(n+2)}\ \text{BM}$

Stability Constant

$K = \dfrac{[ML]}{[M][L]}$

Concept

Formula

Density of Unit Cell

$\rho = \dfrac{ZM}{a^{3}N_A}$

Bragg’s Law

$n\lambda = 2d\sin\theta$

Concept

Formula

Beer–Lambert Law

$A = \varepsilon c l$

IR Stretching Frequency

$\nu = \dfrac{1}{2\pi}\sqrt{\dfrac{k}{\mu}}$

NMR Chemical Shift

$\delta = \dfrac{\nu - \nu_0}{\nu_0}\times 10^6$

UV–Vis Transition

$\Delta E = h\nu$

Concept

Formula

SN1 Rate

$\text{Rate} = k[R-X]$

SN2 Rate

$\text{Rate} = k[R-X][Nu^-]$

E2 Rate

$\text{Rate} = k[R-X][Base]$

Optical Rotation

$[\alpha] = \dfrac{\alpha}{lc}$

Aromaticity Rule

$4n+2\ \pi\ \text{electrons}$

Concept

Formula

Radioactive Decay Law

$N = N_0 e^{-\lambda t}$

Half-Life

$t_{1/2} = \dfrac{0.693}{\lambda}$

Subject

Chapter / Unit

Important CUET PG Formulas to Revise

Mathematics

Algebra

Quadratic roots, determinants, inverse of a matrix, eigenvalue condition

Calculus

Limits, standard derivatives, standard integrals, and definite integral properties

Differential Equations

Linear DE, integrating factor, general solution

Probability & Statistics

Bayes’ theorem, mean, variance

Physics

Mechanics

Equations of motion, work–energy, and angular momentum

Oscillations & Waves

SHM equations, wave speed ( v = f\lambda )

Thermodynamics

First law, Carnot efficiency

Electricity & Magnetism

Coulomb’s law, Ohm’s law, Lorentz force

Modern Physics

Photoelectric equation, radioactive decay law

Chemistry

Physical Chemistry

Thermodynamic relations, Arrhenius equation, Nernst equation

Chemical Kinetics

Rate law, first-order reactions, half-life

Solutions

Raoult’s law, colligative properties

Organic Chemistry

pH, Henderson–Hasselbalch equation, SN1/SN2 rate laws

Inorganic Chemistry

CFSE, magnetic moment, bond order

Revision Tip

Usage

Revise twice daily in the final week

Exam Strategy

Focus

High-weightage numerical formulas only

Subject

Topic

Formula

Mathematics

Quadratic Formula

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

Derivative of a Power Function

$\frac{d}{d x}\left(x^n\right)-n x^{n-1}$

Conditional Probability

$P(A \mid B)=\frac{P(A \cap B)}{P(B)}$

Physics

First Equation of Motion

$v-u+a t$

Coulomb's Law

$F=\frac{1}{4 \pi \varepsilon_0} \frac{q_1 q_2}{r^2}$

Mass-Energy Equivalence

$E-m c^2$

Chemistry

Gibbs Free Energy Equation

$\Delta G-\Delta H-T \Delta S$

Arrhenius Equation

$k-A e^{-\frac{N}{1 N}}$

Nernst Equation

$E-E^{\circ}-\frac{0.0591}{n} \log Q$

Strategy

How to Apply It

Benefit

Understand the Concept First

Learn the derivation and practical application of each formula instead of memorising it in isolation.

Improves conceptual clarity and reduces confusion during problem-solving.

Prepare a Formula Notebook

Maintain a subject-wise notebook containing only important formulas and key identities.

Enables quick revision before mock tests and the final examination.

Use Flashcards

Write the formula on one side and its application or related concept on the other. Review them regularly.

Enhances long-term memory through active recall.

Practise Formula-Based Questions

Solve numerical and previous years' questions immediately after learning a formula.

Strengthens understanding and improves application speed.

Revise Using Spaced Repetition

Review formulas after 1 day, 3 days, 7 days, and 15 days instead of cramming.

Improves long-term retention and reduces forgetting.

Create Subject-wise Formula Sheets

Summarise the most important formulas for Mathematics, Physics, Chemistry, and other subjects on one or two pages.

Makes last-minute revision more efficient.

Take Regular Mock Tests

Attempt mock tests under timed conditions and identify formulas that are frequently forgotten.

Improves exam readiness and accuracy under pressure.

Revise Daily for 15–20 Minutes

Allocate a fixed time each day to revise formulas rather than studying them only before the exam.

Builds confidence and ensures faster recall during the examination.

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