Delhi Police – Chapter 1: Number System / संख्या पद्धति

🎙 Teacher-Style Introduction

Number System is one of the simplest and most scoring chapters in the Delhi Police Constable Exam. Agar aap is chapter ko dhyan se kar lete ho, toh 2–3 number almost pakke ho jaate hain.

यहीं से पेपर में सामान्यत: 2–3 आसान प्रश्न आते हैं – isliye is chapter ko strong banana bahut zaroori hai.

📘 Important Formulas / महत्वपूर्ण सूत्र

• Place Value = digit × positional value (ones, tens, hundreds, thousands…)
• HCF (GCD) = Highest Common Factor of given numbers.
• LCM = Least Common Multiple of given numbers.
• Fraction → Decimal = numerator ÷ denominator.
• Prime Number = Only 2 factors: 1 and the number itself.
• Composite Number = More than 2 factors.

• स्थानिक मान = अंक × स्थान (इकाई, दहाई, सैकड़ा, हज़ार…)
• HCF = दो या अधिक संख्याओं का सबसे बड़ा सामान्य गुणनखंड।
• LCM = दो या अधिक संख्याओं का सबसे छोटा सामान्य गुणज।
• भिन्न → दशमलव = अंश ÷ हर।
• अभाज्य संख्या = जिसके केवल दो गुणनखंड हों – 1 और वही संख्या।
• मिश्र संख्या = जिसके दो से अधिक गुणनखंड हों।

⚡ Tricks & Shortcuts / ट्रिक्स व शॉर्टकट

• Fractions ko compare karne ke liye unhe decimal me convert kar lo (divide karke).
• Chhoti numbers ka LCM nikalte waqt multiples list karna sabse fast hai.
• Prime check ke liye sirf 2, 3, 5, 7 se divide karke dekhna kaafi hota hai (small numbers me).
• Remainder questions basic division se mentally ho sakte hain – likhne ki zaroorat kam padti hai.

🎯 Exam Angle – Delhi Police

Last 5–6 saal ke Delhi Police Constable papers me Number System se lagbhag 2–3 sawal aaye hain:

• Prime / Composite pe 1 question
• LCM / HCF direct pe 1 question
• Remainder ya decimal–fraction pe 1 question

Yeh saare questions ek–do step ke hote hain – isliye yeh chapter high-scoring hai.

✔ Solved Examples / हल प्रश्न

Example 1: Find the LCM of 3, 4 and 6.
Solution (English): Multiples of 6: 6, 12, 18… 12 is divisible by 3 and 4 and 6 → LCM = 12.
समाधान (Hindi): 6 के गुणज: 6, 12, 18… 12 संख्या 3, 4 और 6 तीनों से विभाज्य है, अतः LCM = 12।

Example 2: What is the remainder when 85 is divided by 7?
Solution: 7 × 12 = 84, so remainder = 1.
समाधान: 7 × 12 = 84, इसलिए शेष = 1।

Example 3: Find the place value of 7 in 7,542.
Solution: 7 is in thousands place → 7 × 1000 = 7000.
समाधान: 7 हज़ार वाले स्थान पर है → 7 × 1000 = 7000।

Example 4: Convert 3/4 to decimal.
Solution: 3 ÷ 4 = 0.75.
समाधान: 3 ÷ 4 = 0.75।

Example 5: Which is greater: 3/5 or 4/7?
3/5 = 0.60, 4/7 ≈ 0.57 → 3/5 is greater.
समाधान: 3/5 = 0.60, 4/7 ≈ 0.57 इसलिए 3/5 बड़ा है।

Example 6: Which of these is prime: 21, 17, 27?
21, 27 have more than 2 factors; only 17 has exactly 2 factors → 17 is prime.
समाधान: 21 और 27 मिश्र संख्याएँ हैं; केवल 17 के दो ही गुणनखंड (1 और 17) हैं → 17 अभाज्य है।

✔ MCQs (Delhi Police Level) / बहुविकल्पीय प्रश्न

1. Which of the following is a prime number?
   39, 35, 31, 21
   Correct Answer: 31
2. What is the remainder when 92 is divided by 6?
   Correct Answer: 2
3. LCM of 5 and 20 is –
   Correct Answer: 20
4. HCF of 12 and 18 is –
   Correct Answer: 6
5. 0.45 is equal to –
   Correct Answer: 45/100
6. Which fraction is greater?
   7/9 or 5/7 → 7/9
7. Place value of 5 in 5,816 is –
   Correct Answer: 5000
8. Which of the following is an even number?
   47, 63, 82, 57 → 82

💡 Motivation: Aaj aapne ek chapter complete kiya – aap apne Delhi Police ke sapne ke aur ek mazboot kadam badh chuke hain.