HCF = Highest Common Factor GCD = Greatest Common Divisor Example: Find HCF/GCD of 12 and 18 Method 1: List the factors Factors of 12: 1, 2, 3, 4, 6, 12 Factors of 18: 1, 2, 3, 6, 9, 18 Common factors: 1, 2, 3, 6 The highest common factor is 6 . So: HCF(12, 18) = GCD(12, 18) = 6 Euclidean algorithm For larger numbers, this is faster. Find GCD of 48 and 18 : 48 ÷ 18 = 2 remainder 12 18 ÷ 12 = 1 remainder 6 12 ÷ 6 = 2 remainder 0 When the remainder becomes 0 , the last non-zero remainder is the GCD. Answer = 6 For Decimal Numbers Example: HCF of 1.2 and 1.8 Step 1: Count decimal places Both numbers have 1 decimal place. Step 2: Multiply both by 10 1.2 × 10 = 12 1.8 × 10 = 18 Step 3: Find the HCF of 12 and 18 HCF = 6 Step 4: Divide by 10 6 ÷ 10 = 0.6 HCF of 1.2 and 1.8 = 0.6 Another example: 2.4 and 3.6 Multiply by 10: 2.4 → 24 3.6 → 36 HCF of 24 and 36 = 12 Divide by 10: 12 ÷ 10 = 1.2 So, HCF = 1.2 . If the numbers have different numbers of decimal...

Finding affordable student accommodation in Delhi can be challenging, especially if you want to stay close to your college, coaching centre, metro station and everyday essentials. The best area depends largely on where you study and how much you can spend each month. For students looking for a PG in Delhi , popular options include GTB Nagar and Hudson Lane near Delhi University’s North Campus, Mukherjee Nagar for competitive-exam preparation, Satya Niketan for South Campus, Laxmi Nagar for budget accommodation, and the IIT Delhi–JNU belt of Katwaria Sarai, Jia Sarai, Ber Sarai and Munirka . Best Areas for Student Accommodation in Delhi Area Best for Approx. monthly PG budget* Overall take GTB Nagar / Hudson Lane DU North Campus ₹7,000–₹16,000 ⭐ Best overall for North Campus Kamla Nagar / Vijay Nagar DU North Campus ₹8,000–₹15,000 ⭐ Excellent student environment Mukherjee Nagar UPSC, SSC and North Campus ₹7,000–₹13,000 ⭐ Good for serious study Satya Niketan DU South Campus ₹8,000–₹...

  Q. The area bounded by the curves y = |x – 1| + |x – 2| and y = 3 is equal to   (1) 3   (2) 4   (3) 5   (4) 6 Area Between the Curves We are given: \[ y = |x-1| + |x-2| \] and \[ y = 3 \] 1. Find the points of intersection At the points of intersection: \[ |x-1| + |x-2| = 3 \] Case 1: \(x \leq 1\) Here both expressions inside the modulus are negative: \[ |x-1| = 1-x \] \[ |x-2| = 2-x \] Therefore: \[ (1-x)+(2-x)=3 \] \[ 3-2x=3 \] \[ x=0 \] First intersection: \[ \boxed{(0,3)} \] Case 2: \(1 \leq x \leq 2\) In this interval: \[ |x-1|=x-1 \] ...

  Is India’s Telecom Pricing Becoming a Burden for the Common Man? Every few months, we see changes in mobile plans, pricing, and affordable recharge options. For an individual, ₹20–₹50 may seem like a small amount. But for a family with multiple connections, the impact adds up every month. Today, mobile connectivity is essential—not a luxury. UPI, banking, education, jobs, government services, and even emergency communication depend on it. Telecom companies have every right to grow and earn profits. But the question is: Where should the balance be between business growth and consumer affordability? If prices continue to increase while cheaper options disappear, the burden ultimately falls on ordinary families. This is not just about Airtel. It is about the affordability of essential digital connectivity in India. Why Is Mobile Data Becoming More Expensive in India? Mobile data and recharge prices in India have been trending upward...

Why Signal Power is A²/2R: Mathematical Proof & Intuitive Guide Why is the Power of a Carrier Signal Equal to \( \frac{A^2}{2R} \)? If you are studying electrical engineering, telecommunications, or RF (Radio Frequency) design, you have undoubtedly encountered the formula for the average power of a sinusoidal signal: \( P = \frac{A^2}{2R} \) . At first glance, it looks similar to the standard DC power formula (\( P = V^2/R \)), but with a mysterious factor of 2 in the denominator. Where does that 2 come from? Is it just a constant we have to memorize? In this guide, we’ll break down the mathematical derivation and the intuition behind it. The Short Answer: The factor of 2 comes from the average value of the square of a sine (or cosine) wave over one complete cycle. A sine wave doesn't stay at its peak; it oscillates, delivering exactly half the power of a constant DC signal wi...

VOH, VOL, VIH, and VIL Explained VOH, VOL, VIH, and VIL — Simple Explanation These terms are used in digital electronics to describe what voltage a logic gate considers a 0 (LOW) or a 1 (HIGH) . Think of two people talking: The first gate is the sender . The second gate is the receiver . The sender outputs a voltage and the receiver must correctly understand whether that voltage means HIGH (1) or LOW (0). The Four Important Voltages Symbol Meaning VOH Minimum guaranteed output voltage when output is HIGH VOL Maximum guaranteed output voltage when output is LOW VIH Minimum input voltage that will be accepted as HIGH VIL Maximum input voltage that will be accepted as LOW Easy Example (5V Logic) Suppose: VOH = 4.4 V VOL = 0.4 V VIH = 2.0 V VIL = 0.8 V If a gate outputs 4.4 V, the next gate sees it as HIGH because 4.4 V is greater than VIH (2.0 V). If a gate outputs 0.4 V, the next gate sees it as LOW because 0.4...

  Understanding Pressure, Heat, and Refrigeration Have you ever wondered why refrigerators and air conditioners use a very thin pipe between the condenser and evaporator? It may look insignificant, but this tiny tube is one of the most important components in the entire cooling system. Without it, your refrigerator would not cool, your air conditioner would not produce cold air, and the refrigeration cycle would completely fail. In this article, we'll explore: Why pressure and temperature are connected How the compressor and condenser work together Why a small-diameter capillary tube reduces pressure How pressure reduction creates cooling Real-world examples and calculations Understanding the Relationship Between Pressure and Temperature Before understanding refrigeration, we must first understand the relationship between pressure and temperature. For a gas confined in a fixed volume: P₁/T₁ = P₂/T₂ Where: P = Pressure T = Absolute Temp...

  Flux of Water Through Rectangular Surface Flux of Water Through a Rectangular Surface The water flow is along the x-direction with flow rate density: B x = 3yz   liters/min/m² The rectangular surface lies in the yz-plane at x = 0, with: 0 ≤ y ≤ 3 0 ≤ z ≤ 2 Step 1: Write the Flux Integral Φ = ∫ 0 3 ∫ 0 2 3yz dz dy Step 2: Integrate with Respect to z Φ = ∫ 0 3 3y [ z² / 2 ] 0 2 dy = ∫ 0 3 3y × 2 dy = ∫ 0 3 6y dy Step 3: Integrate with Respect to y Φ = 6 [ y² / 2 ] 0 3 = 3 × 9 = 27 Total Flux = 27 liters/min

Sales Analytics Project An End-to-End Data Pipeline from Raw CSV to Power BI Intelligence SQL Setup Data Cleaning Queries Dashboard Project Overview This project demonstrates a full data analytics pipeline: CSV Data → SQL Import Data Cleaning using SQL Data Analysis Queries Dashboard in Power BI Step 1: CSV Input Data The raw source data used for this project: order_id,order_date,product,category,sales,quantity,customer 1001,2023-01-05,Phone,Electronics,500,1,Amit 1002,2023-01-06,Laptop,Electronics,1200,1,Rahul Step 2: SQL Table Creation Initial staging table to hold raw string data: CR...

  Harvard vs Von Neumann Architecture 1. Basic Idea Feature Von Neumann Harvard Memory for instructions and data Same memory Separate memories Bus system One shared bus Separate buses Can fetch instruction and data together? No Yes Speed Slower Faster Complexity Simpler More complex 2. Von Neumann Architecture In this design, instructions and data are stored in the same memory. The CPU uses the same bus for both instruction fetch and data transfer. Example Address Content 100 Instruction: ADD 101 Data = 5 102 Data = 7 CP...

AMT Encoder AMT Encoder usually refers to the AMT series of rotary encoders made by CUI Devices / Same Sky. These are used in robotics, CNC machines, motors, and automation systems to measure: Shaft position Rotation speed Direction Angular displacement The AMT series is known for using capacitive sensing technology instead of traditional optical sensing. What Makes AMT Encoders Special? 1. Capacitive Sensing Unlike optical encoders, AMT encoders are: Resistant to dust, oil, and dirt More rugged in industrial environments Less sensitive to vibration 2. High Precision They can provide very fine rotational measurements: Incremental outputs (A/B quadrature) Absolute position outputs Multi-turn tracking in some models 3. Programm...

  Audio Files: Original vs WAV vs MP3 1. The Original Signal The true original signal is a continuous analog sound wave (air pressure variations over time). That’s what your ears hear. 2. WAV File A .wav file stores audio using Pulse-Code Modulation (PCM) : The analog signal is sampled (measured many times per second) Each sample is quantized into numbers Stored as digital data WAV = digitized version of the original signal, not modulated in the radio sense ✔ Very close to original (especially at high sample rates like 44.1 kHz) 3. MP3 File An .mp3 file uses Perceptual Coding : Starts from PCM audio (like WAV) Removes parts humans are less likely to hear Compresses the data significantly MP3 = compressed and modified version of the original signal ✔ Smaller size ❌ Some information permanen...