Notes, summaries, assignments, exams, and problems

National Company Law Tribunal (NCLT): An Introduction

The National Company Law Tribunal (NCLT) is a quasi-judicial body established under the Companies Act, 2013 to consolidate and handle all matters related to company law, insolvency, and corporate disputes. It was constituted on June 1, 2016, and functions as a replacement for multiple earlier bodies such as the Company Law Board (CLB), the Board for Industrial and Financial Reconstruction (BIFR), the Appellate Authority for Industrial and Financial Reconstruction (AAIFR), and High Court jurisdictions in certain corporate matters.

NCLT aims to provide speedy, efficient, and specialized adjudication in corporate matters, thereby improving the corporate governance and insolvency resolution framework... Continue reading "National Company Law Tribunal (NCLT): Functions and Role in India" »

Data Structure Trees: Fundamentals

A tree is a non-linear data structure that represents data in a hierarchical form. It consists of nodes connected by edges.

Key Tree Terminology

• Root Node: The topmost node (has no parent).
• Parent Node: A node that has child nodes.
• Child Node: Nodes that have a parent.
• Leaf Node: Nodes with no children.
• Edge: The connection between two nodes.
• Level: Distance from the root (root = level 0).
• Height: The length of the longest path from the root to a leaf.

C++ Node Structure Example

This structure defines a basic node for a binary tree:

#include <iostream>
using namespace std;

struct Node {
    int data;
    Node* left;
    Node* right;

    Node(int val) {
        data = val;
        left = right = nullptr;
    }

Introduction to Industrial Control Systems

Control systems are fundamental to industrial automation, with a primary focus on Distributed Control Systems (DCS). This document covers the core components, variables, and applications of these systems.

Learning Outcomes

• Describe the components of a control system.
• Define the three types of variables associated with a control system.
• Provide examples of common control systems.
• Explain distributed control systems and their industrial applications.
• List and define components of DCS, including SCADA, communication, and alarms.

Components of an Automation System

A modern automation system is composed of several interconnected components:

• Control System: The brain of the operation, processing inputs and making

Operating System Fundamentals

The Operating System (OS) serves several critical roles:

• It acts as a resource manager, controlling access to the hardware.
• It provides an abstraction layer, allowing user processes to call functions that access hardware via system calls.

User Mode vs. Supervisor Mode (Kernel Mode)

The CPU enforces separation between user processes and the OS kernel:

• User Mode: Prohibits privileged instructions.
• Kernel Mode (Supervisor Mode): Allows access to all hardware and privileged operations.

Program Status Word (PSW)

The PSW is a special register holding vital information, such as:

• Access privilege mode.
• Runtime execution conditions (e.g., condition codes).
• Program Counter (PC) and Stack Pointer (SP).

Simplified Interrupt Handling Flow

1. A

Fundamental Sorting Algorithms in C

This document provides standard C implementations for three essential comparison-based sorting algorithms: Merge Sort, Quick Sort, and Heap Sort. These examples demonstrate the core logic and structure of each algorithm.

Merge Sort Implementation

Merge Sort is a stable, divide-and-conquer algorithm known for its consistent O(n log n) time complexity.

#include <stdio.h>

void merge(int a[], int l, int m, int r) {
    int i=l, j=m+1, k=0, b[100];
    while(i<=m && j<=r) {
        if(a[i]<a[j]) b[k++]=a[i++];
        else b[k++]=a[j++];
    }
    while(i<=m) b[k++]=a[i++];
    while(j<=r) b[k++]=a[j++];
    for(i=l,k=0;i<=r;i++,k++) a[i]=b[k];
}

void mergesort(int a[], int l, int

Ancient Indian Literature: Shruti and Smriti

The literature of ancient India is a vast and glorious treasure, forming the foundation of Indian civilization and deeply influencing global thought. It is traditionally categorized into two main groups: Shruti (that which is heard/revealed) and Smriti (that which is remembered/transmitted).

1. Vedic Literature (Shruti)

This is the oldest stratum of Indian literature, considered eternal knowledge revealed to ancient sages.

The Vedas

The four foundational texts of Hinduism:

• Rigveda: The oldest Veda, a collection of 1,028 hymns in praise of various deities.
• Yajurveda: Contains formulas for rituals and sacrifices.
• Samaveda: A collection of melodies and chants, mostly drawn from the Rigveda.
• Atharvaveda: Deals

Chapter 11 – Unemployment & Labor Markets

BLS Household Survey

• 60,000 households monthly

• Population: 333,287,557

  • Age 17+: 269,523,012

  • Children: 63,764,545

  • Civilian Noninstitutional Population: 263,973,000

  • Labor Force: 164,287,000

    • Employed: 158,291,000

    • Unemployed: 5,996,000

    • Not in Labor Force: 99,686,000

Key Formulas:

• Unemployment Rate (UR) = (Unemployed / Labor Force) × 100 → 3.7%

• Labor Force Participation Rate (LFPR) = (Labor Force / Civilian Noninstitutional Pop) × 100 → 62.2%

Alternate Measures of Unemployment (U1–U6):

• U3: Official unemployment rate

• Marginally attached: sought work in the past year but no longer looking

• Underskilled: working below qualifications or hours desired

• Involuntarily part-time: want full-time but work part-time

• US Unemployed

Contract Definition and Validity Requirements

Definition of a Contract

A contract is an agreement between two or more parties which is legally enforceable when executed in accordance with requirements. An agreement will be enforced when the following essential elements exist:

• Offer and acceptance
• Intention to create legal relations
• Legality
• Possibility of performance
• Capacity of the parties
• Consent must be genuine
• Consideration must be present

All the elements must be present for a valid contract.

Remedies for Non-Performance (Schema)

Remedies available upon non-performance include:

• General remedies
• Cure by debtor of non-conforming performance
• Right to enforce performance
• Withholding performance
• Termination
  • Grounds for termination
  • Scope, exercise, and loss of

1. Span of Array

Problem Statement:
Find the span of an array (the difference between the maximum and minimum elements).

Example:
Input: [3, 4, 7, 10, 1]
Output: 9 (since 10 - 1 = 9)

Approach:

• Initialize max = -∞ and min = +∞.
• Traverse the array once:
  • Update max if the current element is greater than max.
  • Update min if the current element is less than min.
• Return max - min.

Time Complexity: O(n)
Space Complexity: O(1)

2. Second Largest Element

Problem Statement:
Find the second largest element in an array without sorting it.

Example:
Input: [20, 42, 99, 10, 88, 6]
Output: 88

Approach:

• Initialize two variables: max1 (largest) and max2 (second largest).
• Compare the first two elements to set initial values for max1 and max2.
• From the third element onward, iterate:

1. Vector Databases — High-Dimensional Embeddings

Store and search high-dimensional vector embeddings. Used in semantic search, similarity search, and RAG pipelines.

Indexing Techniques

• Flat Index (Brute Force) → accurate but slow.
• Approximate Nearest Neighbor (ANN) → fast and scalable.
  • Algorithms: HNSW, FAISS, Annoy.
  • 

3. Retrieval-Augmented Generation (RAG)

Overview

Enhances LLM output by integrating retrieved external knowledge.

• Reduces hallucination and outdated responses.
• Improves factual grounding.

RAG Workflow

1. Indexing: Convert raw data (PDF, HTML, Word) → embeddings.
2. Retrieval: Retrieve relevant document chunks using similarity search.
3. Generation: LLM synthesizes results with the query to produce the final answer.

Retrieval Types