15 Marks • Maximum Scoring Return

General Aptitude — Complete Revision Notes

Numerical Ability, Verbal Reasoning & Spatial Logic Shortcuts • Curated by Akshat

1. Speed, Distance & Time

Average Speed (Equal Distances): If a distance $D$ is covered at speed $S_1$ and return at speed $S_2$, average speed is the harmonic mean: $S_{avg} = \frac{2S_1 S_2}{S_1 + S_2}$.
Relative Speed: Opposite directions (approaching): $S_{rel} = S_1 + S_2$; Same direction: $S_{rel} = |S_1 - S_2|$.
Trains Crossing:
- Crossing stationary pole/man: Time $t = \frac{L_{train}}{S_{train}}$.
- Crossing platform/bridge of length $L_p$: Time $t = \frac{L_{train} + L_p}{S_{train}}$.

If A completes work in $X$ days and B in $Y$ days, working together they take $T = \frac{XY}{X+Y}$ days.
Efficiency is inversely proportional to time taken: $\frac{\text{Efficiency}_A}{\text{Efficiency}_B} = \frac{\text{Time}_B}{\text{Time}_A}$.
Man-Day Equivalence Formula: $\frac{M_1 D_1 H_1}{W_1} = \frac{M_2 D_2 H_2}{W_2}$.

Permutation ($^n P_r$): Arranging $r$ objects out of $n$ when order matters: $^n P_r = \frac{n!}{(n-r)!}$.
Combination ($^n C_r$): Selecting $r$ objects out of $n$ when order does not matter: $^n C_r = \frac{n!}{r!(n-r)!}$.
Handshake Formula: Number of handshakes among $n$ people: $\frac{n(n-1)}{2} = \binom{n}{2}$.

Reflection: Mirror image flips left and right, top and bottom remain invariant.
Paper Folding & Punching: Work in reverse order of folds, applying successive mirror reflections across each fold line.
2D to 3D Cube Folding: Opposite faces of an unfolded cross pattern can never share an edge or vertex in the assembled cube!

Linear Algebra, Calculus, Euler-Cauchy ODEs, Complex Variables, Probability & Statistics

LTI Convolution, CTFT, DTFT, Laplace ROC, Z-Transform, Nyquist Sampling

Thevenin, Norton, Max Power, Transient Step Response, AC Resonance, Two-Port Matrices

AM, FM, Carson's Rule, PCM Quantization SNR, BPSK, QPSK, Shannon Channel Capacity

Diodes, Small-Signal BJT & MOSFET, Op-Amp Virtual Ground, Active Filters, Oscillators

Mason's Gain, 2nd Order Transient Specs, Routh-Hurwitz, Root Locus, Bode & Nyquist

K-Maps, MUX, Decoders, Flip-Flops, Synchronous Counters, FSM Mealy/Moore, ADC/DAC

Maxwell's Equations, Plane Wave Reflection, Transmission Lines, Smith Chart, Waveguides