✨ Introduction: What If Losing Is a Mathematical Certainty? You’re sitting across from a friend.A table holds three small piles of coins — maybe 5, 3, and 1. It’s your turn. You can remove any number of coins from any single pile.The only rule: whoev...
1. Mean (Arithmetic Mean - A.M.) Used in: Q2, Q7, Q12, Q13, Q15, Q24, Q25, Q32, Q33, Q38, Q39, Q41, Q48, Q49 Concept: A.M = Sum of observations / Number of observations Arithmetic Mean 2. Median Used in: Q6, Q14, Q17, Q21, Q26, Q35, Q42, Q49 ...
All matrices things are here. Question : 1. Symmetric & Skew-Symmetric Matrices 18 is not important. Used in: Q1, Q13, Q18 Concept: A matrix A is symmetric if A = Aᵗ, skew-symmetric if A = -Aᵗ. Symmetric and Skew-Symmetric Matrices 2. Sin...
What is Linear Algebra ? Linear Algebra is a branch of math that deals with numbers organised in lines, tables, and grids — called vectors and matrices — and how we can transform them. It’s the math behind how computers understand and manipulate da...
Reference link : https://jmp.sh/s/oZN1QLomLJ9YzxbFxuzG To-Do question: q3,4,20,21 1. Arithmetic Mean (A.M.) 🔹 For Ungrouped Data: Formula: $$\text{A.M.} = \frac{x_1 + x_2 + \cdots + x_n}{n}$$Example: Marks: 10, 15, 20, 25, 30 $$\text{A.M.} = \fra...
Was ist das Trachtenberg-System? Das Trachtenberg-System ist eine besondere Methode, mit der man Rechenaufgaben sehr schnell im Kopf lösen kann – oft sogar schneller als mit einem Taschenrechner. Entwickelt wurde es von Jakow Trachtenberg. Es beruht ...
¿Qué es el Sistema Trachtenberg? El Sistema Trachtenberg de cálculo mental rápido es una forma única de hacer operaciones matemáticas de manera veloz, muchas veces incluso más rápido que usando una calculadora. Desarrollado por Jakow Trachtenberg, es...
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Naive: Time Complexity: O(log₁₀(n)) Space Complexity: O(1) def countDigits(n:int) -> int: int res = 0 while (x>0): x = x//10 res += 1 return res Recursive Way: Time Complexity: O(log₁₀(n)) Space Complexity: O(log₁₀(n)) de...
String Built in Function MethodDescriptionExamples charAt(index)Returns the character at the specified index"Hello".charAt(1) → "e" concat(str1, str2, ...)Joins two or more strings"Hello".concat(" World") → "Hello World" includes(substring...
