Chinese Civilization: History, Culture & Major Achievements
Chinese Civilization — 16 Marks
Chinese civilization, one of the world’s oldest continuous cultures, developed along the Huang He (Yellow River) around c. 2000 BCE. Known for its dynastic rule, philosophical systems, architectural achievements, writing system, and technological innovations, it has contributed greatly to world heritage.
1. Geographical Setting
- Originated in the fertile Yellow River Valley.
- Expanded to the Yangtze River region.
- Natural barriers like the Himalayas, the Gobi Desert,
Letter Templates, Article & Short Story Examples
Formal Letter (Carta Formal)
Dear Sir or Madam, I am writing to inform you about [motivo], which has recently become a matter of concern. Little did I expect that the situation would develop in such an unexpected way, especially considering the information I had previously received. To begin with, […] Despite my efforts to address the issue promptly and follow the correct procedures, the outcome has not been satisfactory. Furthermore, I would like to request [propuesta]. I would greatly appreciate
Read MoreExpress Authentication Methods: Syntax and Results
1. Basic Authentication (Stateless)
What it is: A very simple authentication where a username and password are sent in the Authorization header (Base64 encoded). Not safe unless over HTTPS.
Example (express-basic-auth)
const express = require("express");
const basicAuth = require("express-basic-auth");
const app = express();
app.use(
basicAuth({
users: { admin: "pass123" },
challenge: true,
unauthorizedResponse: "Invalid credentials"
})
);
app.get("/", (req, res) => {
res.send(Food Economics: Demand, Supply, Elasticity & Population
Lecture 7: Demand, Supply, Elasticity
Lectures:
Lecture 7: Economic frameworks to study the world food problem — demand, supply, and elasticity.
Demand Curve
The demand curve follows the Law of Demand: as price falls, quantity demanded rises, producing a downward slope. This occurs because of:
- Diminishing marginal utility — less satisfaction from extra units;
- Heterogeneity in demand — different people have different willingness to pay.
The entire demand curve can shift based on changes in consumer
Read More7 Cs of Business Communication for Legal Professionals
Effective communication is a vital component of business success, especially in the legal and corporate environment. Business communication ensures smooth coordination, builds professional relationships, and supports decision-making. For law students and legal professionals, mastering business communication is essential when dealing with clients, organizations, courts, and regulatory bodies. The 7 C’s of Business Communication—Clarity, Conciseness, Concreteness, Correctness, Completeness, Courtesy,
Read MoreCivil Procedure Code: Jurisdiction, Transfer, Decrees & Venue
Q1: Types of Jurisdiction under CPC
The Civil Procedure Code (CPC) recognizes several types of jurisdiction, which determine a court’s authority to hear and decide cases. Here are the main kinds:
Types of Jurisdiction
- Subject-Matter Jurisdiction: Refers to a court’s authority to hear cases of a specific type. For example, a Rent Controller cannot decide divorce cases, and Consumer Forums handle cases related to consumer rights and disputes.
- Pecuniary Jurisdiction: Based on the monetary value of the
Aristotle & M.N. Roy: Political Thought on Democracy
Aristotle & M.N. Roy: Political Thought on Democracy
Aristotle: Father of Political Science
Aristotle is called the father of political science because he studied politics through observation and practical reasoning. He believed that humans are political beings who can achieve their highest moral and intellectual development only within the state, whose purpose is to promote the good life.
Slavery and Greek social context: His justification of slavery was based on the idea of natural slavery, where
Read MoreIndus Valley Civilization: Harappan Cities, Architecture & Economy
Indus Valley Civilization – Detailed 16-Mark Answer
Introduction
The Indus Valley Civilization (IVC), also known as the Harappan Civilization, flourished from 2600 BCE to 1900 BCE along the Indus River and its tributaries in present-day India and Pakistan. It is one of the world’s earliest urban civilizations, known for its scientific city planning, advanced drainage systems, standardized bricks, and organized socio-economic life.
1. Geographical Extent
- Spread over 1.3 million sq. km — larger
Advanced Vector Calculus and Matrix Algebra Problems
Cayley-Hamilton Theorem: Verification and Inverse
Problem 1: Verify Cayley-Hamilton theorem for A and find A-1
Given matrix: A = [[2, 1, 1], [0, 1, 0], [1, 1, 2]]
Step 1: Find the Characteristic Equation |A – λI| = 0
A – λI = [[2-λ, 1, 1], [0, 1-λ, 0], [1, 1, 2-λ]]
Expand along the 2nd row (which has two zeros):
|A – λI| = (1-λ) × |[2-λ, 1], [1, 2-λ]|
= (1-λ) × [(2-λ)(2-λ) – 1×1]
= (1-λ) × [(2-λ)2 – 1]
= (1-λ) × [4 – 4λ + λ2 – 1]
= (1-λ)(λ2 – 4λ + 3)
= (1-λ)(λ-1)(λ-3)
= -(λ-1)2(
Read MoreSoftware Design Principles and Coding Best Practices
Software Design and Coding Best Practices for Developers
1. Basic Principles of Software Design
Basic principles of software design help create software that is simple, maintainable, and easy to understand. The major principles are:
- Abstraction – Show only important details and hide unnecessary information. It helps reduce complexity.
- Modularity – Break the system into small modules so each module handles one purpose.
- Information Hiding – Keep internal details of a module hidden to protect data