NEET PCB Formula Bible & High-Yield Constants

Comprehensive high-yield summary for Physics, Chemistry, and Biology constants.

1. Physics High-Yield Equations

Stretched Wire Resistance: $R' = n^2 R$ where length becomes $n$ times and volume is conserved.
Escape Velocity: $v_e = \sqrt{2GM/R} = R\sqrt{8\pi G \rho / 3} = 11.2\text{ km/s}$ on Earth.
Variation of $g$ with Height: For any height $h$, $g_h = g\left(\frac{R}{R+h}\right)^2$. If $h = R$, $g_h = g/4$.
Terminal Velocity: $v_t = \frac{2}{9}\frac{r^2(\rho - \sigma)g}{\eta}$.

Lens Maker Formula: $\frac{1}{f} = (\mu_{\text{rel}} - 1)\left(\frac{1}{R_1} - \frac{1}{R_2}\right)$. For glass in water, $f_w = 4 f_{\text{air}}$.
YDSE Fringe Width: $\beta = \frac{\lambda D}{d}$. In medium of refractive index $\mu$, $\beta' = \beta / \mu$.
de-Broglie Wavelength of Electron: $\lambda = \frac{12.27}{\sqrt{V}}\text{ \AA} = \sqrt{\frac{150}{V}}\text{ \AA}$.
Photoelectric Equation: $K_{\max} = e V_s = h\nu - h\nu_0 = hc\left(\frac{1}{\lambda} - \frac{1}{\lambda_0}\right)$.

First-Order Kinetics: $t_{99.9\%} = 10 \, t_{1/2}$, $t_{99\%} = 2 \, t_{90\%}$, $t_{75\%} = 2 \, t_{1/2}$.
van 't Hoff Factor: $i = 1 + (n - 1)\alpha$. For $\text{BaCl}_2$, $n = 3 \implies i = 1 + 2\alpha$.
Solubility Product: For $A_x B_y \rightleftharpoons x A^{y+} + y B^{x-}$, $K_{sp} = x^x y^y S^{x+y}$. ($AB_3 \implies K_{sp} = 27 S^4$).
Standard Gibbs Energy: $\Delta G^\circ = -n F E^\circ_{\text{cell}} = -2.303 RT \log K_{eq}$.

Glomerular Filtration Rate (GFR): $125\text{ mL/min} = 180\text{ L/day}$. Urine output $\approx 1.5\text{ L/day}$ ($99\%$ reabsorbed).
Cardiac Output: $\text{Stroke Volume (70 mL)} \times \text{Heart Rate (72 bpm)} \approx 5040\text{ mL/min} \approx 5\text{ L/min}$.
$\text{CO}_2$ Blood Transport: $70\%$ as bicarbonate ($\text{HCO}_3^-$), $20-25\%$ as carbamino-hemoglobin, $7\%$ dissolved in plasma.
Mendelian Dihybrid F2 Ratios: Phenotypic $9:3:3:1$, Genotypic $1:2:1:2:4:2:1:2:1$.
Robert May Global Estimate: $7\text{ million species}$. Currently recorded: $>1.5\text{ million}$.