updated content

Author: aryan

content/blog/math/Geometery-Made-Easy.md

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+
+## Geometry Made Easy! 📐✨
+
+Here’s a simple, emoji-filled summary of all the key geometry concepts from your PDF, perfect for SSC CHSL Quant Aptitude prep! [^1][^2]
+
+---
+
+### **Basic Concepts** 🟢
+
+- **Point**: An exact location, no size—just a dot! ⚫
+- **Line Segment**: Straight path between two points (A \& B) with a fixed length. 📏
+- **Ray**: Starts at a point and goes on forever in one direction. ➡️
+- **Intersecting Lines**: Cross at a point. ✖️
+- **Concurrent Lines**: 3+ lines meeting at the same point. 🌟
+
+---
+
+### **Angles** 🔺
+
+- **Angle**: Formed when two lines meet at a point. (∠AOB) 🧭
+- **Right Angle**: 90° ⬛
+- **Acute Angle**: Less than 90° 🔽
+- **Obtuse Angle**: Between 90° and 180° 🔼
+- **Reflex Angle**: Between 180° and 360° 🔄
+- **Complementary Angles**: Add up to 90°. 60° + 30° = 90° 🤝
+- **Supplementary Angles**: Add up to 180°. 130° + 50° = 180° 👫
+- **Vertically Opposite Angles**: Equal when two lines cross. 🔁
+- **Bisector**: Divides an angle into two equal parts. ✂️
+
+---
+
+### **Lines \& Parallelism** 🟦
+
+- **Parallel Lines**: Never meet, always same distance apart. 〰️〰️
+- **Transversal**: Cuts across two or more lines. ➖
+- **Alternate Angles**: Equal when lines are parallel. 🔄
+- **Corresponding Angles**: Equal when lines are parallel. 🟰
+- **Sum of Angles on a Straight Line**: 180° ➡️
+
+---
+
+### **Triangles** 🔺
+
+- **Triangle**: 3 sides, 3 angles. △
+- **Sum of Angles**: Always 180° 🔢
+- **Side Rule**: Any two sides’ sum > third side. ➕
+- **Exterior Angle**: Equals sum of two opposite interior angles. 🔄
+
+
+#### **Area of Triangle** 📏
+
+- \$ Area = \frac{1}{2} \times base \times height \$ 🏕️
+- \$ Area = \frac{1}{2} ab \sin C \$ (using sine) 🟢
+- **Heron’s Formula**: \$ \sqrt{s(s-a)(s-b)(s-c)} \$, where \$ s = \frac{a+b+c}{2} \$ 🧮
+
+
+#### **Special Segments in Triangles** 📐
+
+- **Median**: Vertex to midpoint of opposite side. Intersect at centroid (divides median 2:1). 🔹
+- **Altitude**: Perpendicular from vertex to opposite side. Meet at orthocenter. ⬆️
+- **Angle Bisector**: Divides angle into two equal parts, meet at incentre. ✂️
+- **Perpendicular Bisector**: Cuts side into two equal parts at 90°, meet at circumcentre. ➕
+
+
+#### **Similarity \& Area** 🟠
+
+- **Similar Triangles**: Angles equal, sides in proportion. 🔁
+- **Area Ratio**: Ratio of areas = (ratio of sides)² 📊
+
+---
+
+### **Polygons** 🟣
+
+- **Regular Polygon**: All sides \& angles equal. 🛑
+- **Sum of Angles**: \$ 180(n-2) \$, where n = number of sides. 🔢
+- **Interior Angle**: \$ \frac{180(n-2)}{n} \$ 🧮
+- **Example**: Octagon (8 sides): Each angle = 135° 🛑
+
+---
+
+### **Quadrilaterals** 🟤
+
+- **Square**: All sides equal, all angles 90°. Area = \$ a^2 \$, Diagonal = \$ a\sqrt{2} \$ ⬛
+- **Rectangle**: Opposite sides equal, all angles 90°. Area = length × breadth 🟦
+- **Parallelogram**: Opposite sides equal \& parallel. Area = base × height 🔲
+- **Rhombus**: All sides equal, diagonals perpendicular. Area = \$ \frac{1}{2} \times d_1 \times d_2 \$ 💎
+- **Trapezium**: One pair of parallel sides. Area = \$ \frac{1}{2} \times (sum of parallel sides) \times height \$ 🟫
+
+---
+
+### **Circle** ⚪
+
+- **Center**: Fixed point (O) 🟢
+- **Radius (r)**: Distance from center to edge. 📏
+- **Diameter (d)**: \$ 2r \$ ⬅️➡️
+- **Circumference**: \$ 2\pi r \$ 🔵
+- **Area**: \$ \pi r^2 \$ 🧮
+- **Chord**: Line joining two points on the circle. ➖
+- **Arc**: Part of circumference. 🟠
+- **Sector**: 'Pizza slice' of the circle. Area = \$ \frac{\theta}{360} \times \pi r^2 \$ 🍕
+- **Tangent**: Touches circle at one point, perpendicular to radius. 🚏
+
+
+#### **Key Circle Properties** 🟡
+
+- **Equal chords = equal distance from center** 🟰
+- **Angle in a semicircle = 90°** ⬛
+- **Angles in same arc = equal** 🔁
+- **Angle at center = 2 × angle at circumference (same arc)** 🔄
+- **Intersecting Chords Rule**: \$ AP \times PB = CP \times PD \$ ✖️
+- **Tangents from same point are equal** 🟰
+
+---
+
+### **Important Examples \& Tricks** 🏆
+
+- **Sum of Third Side in Triangle**: If two sides are 12 \& 7, possible third sides = 6 to 18 (integers), sum = 156.
+- **Area of Hexagon**: \$ \frac{3\sqrt{3}}{2} a^2 \$ for side a. 🟩
+- **Circle Chord Example**: Chord of length 8 cm is twice as far from center as chord of 10 cm. Use Pythagoras to solve!
+- **Parallel Chords Example**: Distance between two chords = add/subtract their distances from center.
+
+---
+
+### **Emoji Legend** 🗺️
+
+- ⚫ Point
+- 📏 Line/Length
+- ➡️ Ray/Direction
+- ✖️ Intersect
+- 🌟 Concurrent
+- ⬛ Right angle/Square
+- 🔽 Acute/Small
+- 🔼 Obtuse/Large
+- 🔄 Reflex/Alternate
+- 🤝 Complementary
+- 👫 Supplementary
+- 🔁 Equal/Vertically opposite/Similar
+- ✂️ Bisector
+- 〰️ Parallel
+- ➖ Chord/Transversal
+- △ Triangle
+- 🏕️ Area
+- 🧮 Calculation
+- 🔹 Median/Centroid
+- ⬆️ Altitude/Orthocenter
+- 🛑 Polygon
+- 🟦 Rectangle
+- 🔲 Parallelogram
+- 💎 Rhombus
+- 🟫 Trapezium
+- ⚪ Circle
+- 🍕 Sector
+- 🚏 Tangent
+- 🟰 Equal
+- 🟡 Key Point
+- 🏆 Example
+
+---
+
+Use this guide for quick revision and easy understanding of all geometry basics for your exam! Good luck! 🍀[^1][^2]
+
+<div style="text-align: center">⁂</div>
+
+[^1]: Geometery.pdf
+
+[^2]: education.study_materials
+

content/blog/reasoning/Key-Calendar-Concepts-for-Exams.md

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+---
+title: Key Calendar Concepts for Exams 📅
+description: To excel in calendar reasoning questions for exams like SSC CHSL, focus on these essential concepts:-
+date: 2025-05-17
+authors:
+  - name: Aryan
+    link: https://github.com/simplearyan
+    image: https://github.com/simplearyan.png
+tags:
+  - Reasoning
+excludeSearch: true
+width: nomral
+image: "/images/svg/github-wallpaper.svg"
+---
+
+## Key Calendar Concepts for Exams 📅
+
+To excel in calendar reasoning questions for exams like SSC CHSL, focus on these essential concepts:
+
+---
+
+### **1. Days of the Week** 🗓️
+
+- There are 7 days: Sunday, Monday, Tuesday, Wednesday, Thursday, Friday, and Saturday.
+- Days repeat every 7 days, forming a cycle[^1].
+
+---
+
+### **2. Months of the Year** 📆
+
+- 12 months: January to December.
+- Each month has a fixed number of days (28, 29, 30, or 31)[^1].
+
+---
+
+### **3. Ordinary Year vs. Leap Year** 🔄
+
+- **Ordinary Year:** 365 days (52 weeks + 1 day). That 1 extra day is called an **odd day**.
+- **Leap Year:** 366 days (52 weeks + 2 days). That 2 extra days are called **odd days**.
+- Leap year rule: Divisible by 4, but century years must also be divisible by 400 (e.g., 2000 is leap, 1900 is not)[^2][^3].
+
+---
+
+### **4. Odd Days Concept** 🤔
+
+- **Odd days** are the extra days left after counting complete weeks in a period.
+- Used to calculate the day of the week for any given date[^2][^3].
+- Example: 365 days ÷ 7 = 52 weeks + 1 odd day.
+
+---
+
+### **5. Day Coding for Fast Calculation** 🔢
+
+| Day | Code |
+| :-- | :-- |
+| Sunday | 0 |
+| Monday | 1 |
+| Tuesday | 2 |
+| Wednesday | 3 |
+| Thursday | 4 |
+| Friday | 5 |
+| Saturday | 6 |
+
+- Use these codes to quickly find the day after a certain number of days[^2].
+
+---
+
+### **6. Century Odd Days \& Repetition** 🔁
+
+- 100 years: 5 odd days
+- 200 years: 3 odd days
+- 300 years: 1 odd day
+- 400 years: 0 odd days (calendar repeats every 400 years)[^2][^3].
+
+---
+
+### **7. Types of Calendar Questions** ❓
+
+- **Finding the Day on a Given Date:** With or without a reference date[^3][^2].
+- **Matching Calendars:** Which year/month will have the same calendar as another[^2].
+- **Counting Odd Days:** To determine the weekday for a date[^3].
+- **Leap Year Calculations:** Identifying leap years and their effect on the calendar[^2].
+
+---
+
+### **8. Tricks \& Shortcuts** 🪄
+
+- The same calendar repeats after 6 or 11 years for ordinary years and after 28 years for leap years[^3].
+- The first day of a century is always Monday, Wednesday, Friday, or Saturday[^3].
+- Use odd days to quickly find the weekday for any date.
+
+---
+
+## 📝 Quick Practice Question
+
+**Q:** Today is Monday. What day will it be after 61 days?
+**Solution:** 61 ÷ 7 = 8 weeks + 5 odd days. Monday + 5 = **Saturday**[^2] 🛍️
+
+---
+
+**Remember:**
+
+- Mastering these concepts with practice will help you solve calendar questions quickly and accurately in exams! 🚀[^4]
+
+<div style="text-align: center">⁂</div>
+
+[^1]: http://www.placementpreparation.io/logical-reasoning/calendar/concepts/
+
+[^2]: https://byjus.com/govt-exams/calendars-logical-reasoning/
+
+[^3]: https://testbook.com/reasoning/calendar-reasoning
+
+[^4]: education.study_materials
+
+[^5]: Blood-and-Relation.pdf
+
+[^6]: https://www.youtube.com/watch?v=ILqGmlKJkmE
+
+[^7]: https://www.scribd.com/document/599910211/Calendar-Concept-and-Tricks
+
+[^8]: https://www.hitbullseye.com/Calendar-Tricks.php
+
+[^9]: https://www.indiabix.com/aptitude/calendar/
+
+[^10]: https://www.youtube.com/watch?v=mLD41elDRTE
+
+[^11]: https://www.creativeteaching.com/collections/calendars-accessories/products/emoji-fun-calendar-set-bulletin-board
+
+[^12]: https://www.facultyfocus.com/articles/course-design-ideas/creating-a-course-calendar-that-aligns-to-the-rhythms-of-the-semester/
+

content/notes/chsl-exam-syllabus/english/_index.md

@@ -5,7 +5,7 @@ tags:
   - Notes 
   - SSC Exam
 excludeSearch: false
-type: cards
+type: chapters
 width: wide
 cascade:
  series: ["SSC-CHSL", "English"]

content/notes/chsl-exam-syllabus/english/active-passive-voice.md

@@ -248,3 +248,5 @@ voice than mentioned in the question.
    4. By whom your bike stolen?
 
 **Answer**: ✅ 2. By whom was your bike stolen?
+
+