High-Yield KaTeX Formula Vault
Interactive equation sheets with complete variable dictionaries and time-saving exam shortcut tricks.
Projectile Motion Max Height & Range
Trajectory coordinates and maximum ground range for flat projectile launch.
- : Initial launch velocity (m/s)
- : Angle of projection with horizontal (radians/deg)
- : Acceleration due to gravity (9.8 or 10) (m/s^2)
Parallel & Perpendicular Axis Theorems
Moment of inertia about arbitrary parallel axes and perpendicular axes for laminar sheets.
- : Moment of inertia about center-of-mass axis
- : Perpendicular distance between parallel axes (m)
- : Total mass of the rigid body (kg)
Carnot Engine Efficiency & Work Done
Maximum theoretical thermodynamic efficiency between source and sink temperatures.
- : Absolute temperature of hot reservoir (Source) (K)
- : Absolute temperature of cold reservoir (Sink) (K)
- : Net work done in cycle (J)
Gauss Law & Spherical Shell Electric Field
Electric flux through closed Gaussian surfaces and shell potential.
- : Total charge enclosed by Gaussian surface (C)
- : Permittivity of free space ($8.85 \times 10^{-12}$) (F/m)
Young Double Slit Interference Fringe Width
Spatial separation between consecutive constructive or destructive interference fringes.
- : Wavelength of monochromatic light (m or nm)
- : Distance from slits to screen (m)
- : Distance between two coherent slits (m or mm)
Nernst Equation & Standard EMF
Electrode and galvanic cell potential under non-standard concentration conditions at 298 K.
- : Standard cell potential ($E^\circ_{cathode} - E^\circ_{anode}$) (V)
- : Number of electrons transferred in balanced redox reaction
- : Reaction quotient of active aqueous ions
Arrhenius Equation for Rate Constants
Temperature dependence of chemical reaction rate and activation energy barrier.
- : Activation energy of reaction (J/mol or kJ/mol)
- : Universal gas constant ($8.314 \text{ J/mol K}$)
- : Arrhenius pre-exponential frequency factor
Definite Integrals: King’s Property
Fundamental symmetry reflection rule used in 80% of JEE Main & Advanced definite integrals.
- : Lower and upper integration limits
- : Continuous integrand function
Shortest Distance Between Skew Lines in 3D
Perpendicular minimum geometric separation between non-intersecting, non-parallel 3D lines.
- : Position vectors of points on Line 1 and Line 2
- : Direction vectors of Line 1 and Line 2
Hardy-Weinberg Genetic Equilibrium
Allele and genotype frequency conservation in diploid non-evolving populations.
- : Frequency of dominant allele (A)
- : Frequency of recessive allele (a)
- : Frequency of heterozygous individuals (Aa)
Cardiac Output & Stroke Volume
Volume of blood pumped by each ventricle per minute.
- : Stroke volume pumped per ventricular beat (approx 70 mL)
- : Heart rate in beats per minute (approx 72 bpm)