Lecture Notes: Preparation for Railway Exams

Introduction

• Excitement for preparation is high among students and the lecturer.
• Free practice series announced on the YouTube channel "Maths Concept King".
• Today's lecture topic: Number System.

Importance of Number System in Railway Exams

• Railway exams frequently test on number system and simplification.
• Most railway exam papers contain in-depth questions from these topics.
• Best 50 must-do previous questions selected from various railway exams (e.g., Group D, NTPC, RPF).

Structure of the Lecture

• Students are advised to watch the video from start to end for a good revision.
• Unique and fresh concepts will be taught.
• The lecture is beneficial for anyone preparing for railway exams.
• Content also useful for police exams due to similar levels.

Additional Resources

• PDF of questions available on the Telegram channel "Maths by Gangadhar Pratap".
• Daily shorts on the YouTube channel with best questions posted twice a day.

Key Concepts Discussed

1. Divisibility Rules

   • Understanding rules for numbers like 125, 5, 25.
   • Example: Determining if a number is divisible by 8, 9.
   • Rule of divisibility by 11 explained with examples.

2. Prime Numbers and Twin Primes

   • Definition of twin prime numbers.
   • Examples provided to identify twin primes.

3. Sum of Two Numbers and Product of Numbers

   • Example problems involving sum and product calculations.

4. Concept of Co-primes

   • Explanation of co-prime numbers: two numbers having no common factor other than 1.

5. Factorization and Perfect Squares

   • Techniques for finding the number of factors.
   • Differences between perfect squares and cubes.

6. Complex Numbers and Real Numbers

   • Introduction to complex numbers (e.g., a + bi).
   • Real-world applications in mathematics.

7. Special Number Properties

   • Discussion on properties of even, odd, and prime numbers.
   • Problem-solving using these properties.

Homework

• Extra practice questions will be provided.
• Students are encouraged to engage with the practice materials for better understanding.

Conclusion

• The lecture provides a comprehensive overview of the number system for railway exams.
• Students are advised to subscribe to the channel for ongoing lessons and updates.
• Simplification will be covered in the next session.