Complex numbers, P&C, Binomial Expansion NDA Pyqs

00:00 – Introduction & Session Overview (NDA 2018-2019 PYQs) 00:18 – Complex Numbers: Finding Principal Argument (Theory & Quadrant Rules) 02:18 – Complex Numbers: Modulus Properties & Formulas 03:00 – Solving PYQ: Principal Argument of $-1-i$ 03:46 – Binomial Expansion: General Term Formula & Total Terms 05:32 – Solving PYQ: Relation between $(2r+1)^{th}$ and $(r+2)^{th}$ terms 07:57 – Permutations & Combinations: Numbers between 100-1000 (Non-repetition) 08:50 – Binomial Expansion: Relation between coefficients of $a^m$ and $a^n$ 10:42 – Solving PYQ: Non-zero Integral Solutions of Modulus Equations 12:26 – Permutations & Combinations: 4-digit numbers divisible by 10 13:07 – Complex Numbers: Solving for Modulus $|(\alpha-\beta)/(1-\alpha\bar{\beta})|$ 17:51 – Properties of $i$ (Iota) and Consecutive Powers Sum Rule 21:10 – Solving PYQ: Polar Form (Modulus-Amplitude) of $\sqrt{3}+i$ 23:30 – Binomial Expansion: Number of Non-zero terms in combined expansions 25:52 – Combinatorial Identity Application: $^{n}C_{r} + 2 \cdot ^{n}C_{r-1} + ^{n}C_{r-2}$ 29:23 – Geometry-based P&C: Number of Triangles from 12 points (7 collinear) 31:38 – Complex Numbers: Summation of $i^n(1+i)$ from $n=2$ to 11 34:44 – Arithmetic Progression: Sum of 2-digit numbers (Remainder 2 when divided by 3) 35:58 – P&C Challenge: Integers with at least two equal digits (Complementary counting) 41:08 – Binomial Expansion: Identifying the Middle Term Coefficient 42:04 – P&C Selection: Selecting a Cricket Team with specific bowler constraints 43:39 – Complex Numbers: Cube Roots of Unity ($\omega$ and $\omega^2$) Properties 45:54 – Relation between Middle Term Coefficients (Alpha, Beta, Gamma) 48:51 – P&C: Total 5-digit numbers using digits 0-9 49:46 – P&C: Sum of all 3-digit numbers formed by 3, 4, and 5 51:07 – Complex Numbers: Finding Common Roots between two high-power equations 56:17 – Geometry-based P&C: Total Straight Lines from 10 points 58:10 – P&C Selection: Recruitment with "at least one typist" constraint 01:02:04 – Solving for '$n$' and '$a$' using the first three terms of an expansion 01:04:52 – Binomial Expansion: Finding the Term Independent of $x$ 01:07:11 – Evaluating polynomials using $x = -1$ substitution 01:09:35 – P&C: Maximum points of intersection of 5 non-overlapping circles