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đŸŽ¯ English āĻļ⧇āĻ–āĻžāϰ āϏāĻ āĻŋāĻ• Roadmap — Zero āĻĨ⧇āϕ⧇ AdvancedāĻ…āύ⧇āϕ⧇āχ English āĻļāĻŋāĻ–āϤ⧇ āϚāĻžāύ, āĻ•āĻŋāĻ¨ā§āϤ⧁ āϕ⧋āĻĨāĻž āĻĨ⧇āϕ⧇ āĻļ⧁āϰ⧁ āĻ•āϰāĻŦ⧇āύ āĻŦ⧁āĻāϤ⧇ āĻĒāĻžāϰ⧇āύ āύāĻžāĨ¤ Y...
27/08/2026

đŸŽ¯ English āĻļ⧇āĻ–āĻžāϰ āϏāĻ āĻŋāĻ• Roadmap — Zero āĻĨ⧇āϕ⧇ Advanced

āĻ…āύ⧇āϕ⧇āχ English āĻļāĻŋāĻ–āϤ⧇ āϚāĻžāύ, āĻ•āĻŋāĻ¨ā§āϤ⧁ āϕ⧋āĻĨāĻž āĻĨ⧇āϕ⧇ āĻļ⧁āϰ⧁ āĻ•āϰāĻŦ⧇āύ āĻŦ⧁āĻāϤ⧇ āĻĒāĻžāϰ⧇āύ āύāĻžāĨ¤ YouTube-āĻ āĻāϕ⧇āĻ•āĻĻāĻŋāύ āĻāϕ⧇āĻ• āϧāϰāύ⧇āϰ āĻ­āĻŋāĻĄāĻŋāĻ“ āĻĻ⧇āĻ–āϞ⧇ āĻļ⧇āĻ–āĻžāϰ āĻĒāϰāĻŋāĻŦāĻ°ā§āϤ⧇ āĻ…āύ⧇āĻ• āϏāĻŽā§Ÿ Confusion āϤ⧈āϰāĻŋ āĻšā§ŸāĨ¤

āϤāĻžāχ English āĻļ⧇āĻ–āĻžāϰ āϜāĻ¨ā§āϝ Level āĻ…āύ⧁āϝāĻžā§Ÿā§€ āĻāĻ—āĻŋā§Ÿā§‡ āϚāϞ⧁āύāĨ¤ 👇

🔰 Level 1 — Alphabet & Pronunciation
YouTube-āĻ āϏāĻžāĻ°ā§āϚ āĻ•āϰ⧁āύ:
👉 "English Alphabet & Pronunciation for Beginners Bangla"
👉 "English Phonics Bangla"

đŸŸĸ Level 2 — Vocabulary
👉 "English Vocabulary for Beginners Bangla"
👉 "Daily Use English Words Bangla"

đŸŸĸ Level 3 — Sentence Making
👉 "English Sentence Making from Basic Bangla"
👉 "English Sentence Structure Bangla"

🟡 Level 4 — Basic Grammar
👉 "Basic English Grammar Bangla"
👉 "English Grammar for Beginners Bangla"

🟡 Level 5 — Tense
👉 "Tense in English Grammar Bangla"
👉 "12 Tense Bangla"

🟠 Level 6 — Reading
👉 "English Reading Practice for Beginners"
👉 "English Reading from Basic Bangla"

🟠 Level 7 — Listening
👉 "English Listening Practice for Beginners"
👉 "Slow English Listening Practice"

đŸ”ĩ Level 8 — Speaking
👉 "Spoken English for Beginners Bangla"
👉 "Daily English Conversation Bangla"

đŸ”ĩ Level 9 — Intermediate English
👉 "Intermediate English Grammar Bangla"
👉 "Intermediate English Speaking"

🔴 Level 10 — Advanced English
👉 "Advanced English Grammar Bangla"
👉 "Advanced English Speaking & Fluency"

⭐ āĻŽāύ⧇ āϰāĻžāĻ–āĻŦ⧇āύ

Alphabet → Pronunciation → Vocabulary → Sentence Making → Grammar → Tense → Reading → Listening → Speaking → Intermediate → Advanced

❌ āĻāĻ•āĻĻāĻŋāύ⧇ āϏāĻŦāĻ•āĻŋāϛ⧁ āĻļ⧇āĻ–āĻžāϰ āĻšā§‡āĻˇā§āϟāĻž āĻ•āϰāĻŦ⧇āύ āύāĻžāĨ¤
✅ āĻāĻ•āϟāĻŋ Level āĻ­āĻžāϞ⧋āĻ­āĻžāĻŦ⧇ āĻļāĻŋāϖ⧁āύ, Practice āĻ•āϰ⧁āύ, āϤāĻžāϰāĻĒāϰ āĻĒāϰ⧇āϰ Level-āĻ āϝāĻžāύāĨ¤

English āĻļ⧇āĻ–āĻžāϰ āĻŽā§‚āϞāĻŽāĻ¨ā§āĻ¤ā§āϰ:
📚 Learn → âœī¸ Practice → đŸ—Ŗī¸ Speak → 🔄 Repeat

āĻļ⧁āϰ⧁āϤ⧇ āϭ⧁āϞ āĻšāĻŦ⧇āχāĨ¤ āϭ⧁āϞ āĻ•āϰ⧇āχ English āĻļ⧇āĻ–āĻž āϝāĻžā§ŸāĨ¤ āϤāĻžāχ āϭ⧟ āύāĻž āĻĒā§‡ā§Ÿā§‡ āĻĒā§āϰāϤāĻŋāĻĻāĻŋāύ āĻāĻ•āϟ⧁ āĻāĻ•āϟ⧁ āĻ•āϰ⧇ Practice āĻ•āϰ⧁āύāĨ¤ â¤ī¸

07/08/2026

āĻ­ā§‹āĻ•āĻžāĻŦ⧁āϞāĻžāϰāĻŋ āĻŽāύ⧇ āϰāĻžāĻ–āϤ⧇ āϚāĻžāχāϞ⧇ āĻāĻ­āĻžāĻŦ⧇ āĻĒ⧜⧁āύāσ
| 1. Win (āωāχāύ) | āϜ⧟ | Fail (āĻĢ⧇āχāϞ) | āĻŦā§āϝāĻ°ā§āĻĨ |
| 2. Happy (āĻšā§āϝāĻžāĻĒāĻŋ) | āϏ⧁āĻ–ā§€ | Sad (āĻ¸ā§āϝāĻžāĻĄ) | āĻĻ⧁āσāĻ–ā§€ |
| 3. Hot (āĻšāϟ) | āĻ—āϰāĻŽ | Cold (āϕ⧋āĻ˛ā§āĻĄ) | āĻ āĻžāĻ¨ā§āĻĄāĻž |
| 4. Day (āĻĄā§‡) | āĻĻāĻŋāύ | Night (āύāĻžāχāϟ) | āϰāĻžāϤ |
| 5. Big (āĻŦāĻŋāĻ—) | āĻŦ⧜ | Small (āĻ¸ā§āĻŽāϞ) | āϛ⧋āϟ |
| 6. Good (āϗ⧁āĻĄ) | āĻ­āĻžāϞ⧋ | Bad (āĻŦā§āϝāĻžāĻĄ) | āĻ–āĻžāϰāĻžāĻĒ |
| 7. Fast (āĻĢāĻžāĻ¸ā§āϟ) | āĻĻā§āϰ⧁āϤ | Slow (āĻ¸ā§āϞ⧋) | āϧ⧀āϰ |
| 8. Up (āφāĻĒ) | āωāĻĒāϰ⧇ | Down (āĻĄāĻžāωāύ) | āύāĻŋāĻšā§‡ |
| 9. Yes (āĻ‡ā§Ÿā§‡āϏ) | āĻšā§āϝāĻžāρ | No (āύ⧋) | āύāĻž |
| 10. Open (āĻ“āĻĒ⧇āύ) | āĻ–ā§‹āϞāĻž | Close (āĻ•ā§āϞ⧋āϜ) | āĻŦāĻ¨ā§āϧ |
| 11. Rich (āϰāĻŋāϚ) | āϧāύ⧀ | Poor (āĻĒ⧁āĻ“āϰ) | āĻ—āϰāĻŋāĻŦ |
| 12. New (āύāĻŋāω) | āύāϤ⧁āύ | Old (āĻ“āĻ˛ā§āĻĄ) | āĻĒ⧁āϰāύ⧋ |
| 13. High (āĻšāĻžāχ) | āωāρāϚ⧁ | Low (āϞ⧋) | āύāĻŋāϚ⧁ |
| 14. Tall (āϟāϞ) | āϞāĻŽā§āĻŦāĻž | Short (āĻļāĻ°ā§āϟ) | āĻ–āĻžāĻŸā§‹ |
| 15. Light (āϞāĻžāχāϟ) | āφāϞ⧋ | Dark (āĻĄāĻžāĻ°ā§āĻ•) | āĻ…āĻ¨ā§āϧāĻ•āĻžāϰ |
| 16. Black (āĻŦā§āĻ˛ā§āϝāĻžāĻ•) | āĻ•āĻžāϞ⧋ | White (āĻšā§‹ā§ŸāĻžāχāϟ) | āϏāĻžāĻĻāĻž | 17. Left (āϞ⧇āĻĢāϟ) | āĻŦāĻžāĻŽ | Right (āϰāĻžāχāϟ) | āĻĄāĻžāύ |
| 18. Soft (āϏāĻĢāϟ) | āύāϰāĻŽ | Hard (āĻšāĻžāĻ°ā§āĻĄ) | āĻļāĻ•ā§āϤ |
| 19. Full (āĻĢ⧁āϞ) | āĻĒā§‚āĻ°ā§āĻŖ | Empty (āĻāĻŽā§āĻĒāϟāĻŋ) | āĻ–āĻžāϞāĻŋ |
| 20. Clean (āĻ•ā§āϞāĻŋāύ) | āĻĒāϰāĻŋāĻˇā§āĻ•āĻžāϰ | Dirty (āĻĄāĻžāĻ°ā§āϟāĻŋ) | āύ⧋āĻ‚āϰāĻž |
| 21. Boy (āĻŦ⧟) | āĻŦāĻžāϞāĻ• | Girl (āĻ—āĻžāĻ°ā§āϞ) | āĻŦāĻžāϞāĻŋāĻ•āĻž |
| 22. Man (āĻŽā§āϝāĻžāύ) | āĻĒ⧁āϰ⧁āώ | Woman (āĻ“āĻŽā§āϝāĻžāύ) | āĻŽāĻšāĻŋāϞāĻž |
| 23. Easy (āχāϜāĻŋ) | āϏāĻšāϜ | Hard/Difficult | āĻ•āĻ āĻŋāύ |
| 24. Early (āφāĻ°ā§āϞāĻŋ) | āĻ­ā§‹āϰ⧇ | Late (āϞ⧇āϟ) | āĻĻ⧇āϰāĻŋāϤ⧇ |
| 25. Near (āύāĻŋ⧟āĻžāϰ) | āĻ•āĻžāϛ⧇ | Far (āĻĢāĻžāϰ) | āĻĻā§‚āϰ⧇ |
| 26. In (āχāύ) | āϭ⧇āϤāϰ⧇ | Out (āφāωāϟ) | āĻŦāĻžāχāϰ⧇ |
| 27. Laugh (āϞāĻžāĻĢ) | āĻšāĻžāϏāĻž | Cry (āĻ•ā§āϰāĻžāχ) | āĻ•āĻžāρāĻĻāĻž |
| 28. Smile (āĻ¸ā§āĻŽāĻžāχāϞ) | āĻšāĻžāϏāĻŋ | Frown (āĻĢā§āϰāĻžāωāύ) | āĻŽā§āĻ– āĻ­āĻžāϰ āĻ•āϰāĻž |
| 29. Start (āĻ¸ā§āϟāĻžāĻ°ā§āϟ) | āĻļ⧁āϰ⧁ | Stop (āĻ¸ā§āϟāĻĒ) | āĻĨāĻžāĻŽāĻž |
| 30. First (āĻĢāĻžāĻ°ā§āĻ¸ā§āϟ) | āĻĒā§āϰāĻĨāĻŽ | Last (āϞāĻžāĻ¸ā§āϟ) | āĻļ⧇āώ |
| 31. Give (āĻ—āĻŋāĻ­) | āĻĻ⧇āĻ“ā§ŸāĻž | Take (āĻŸā§‡āĻ•) | āύ⧇āĻ“ā§ŸāĻž |
| 32. Buy (āĻŦāĻžāχ) | āϕ⧇āύāĻž | Sell (āϏ⧇āϞ) | āĻŦāĻŋāĻ•ā§āϰāĻŋ āĻ•āϰāĻž |
| 33. Love (āϞāĻžāĻ­) | āĻ­āĻžāϞ⧋āĻŦāĻžāϏāĻž | Hate (āĻšā§‡āϟ) | āϘ⧃āĻŖāĻž āĻ•āϰāĻž |
| 34. Friend (āĻĢā§āϰ⧇āĻ¨ā§āĻĄ) | āĻŦāĻ¨ā§āϧ⧁ | Enemy (āĻāύāĻŋāĻŽāĻŋ) | āĻļāĻ¤ā§āϰ⧁ |
| 35. Push (āĻĒ⧁āĻļ) | āϧāĻžāĻ•ā§āĻ•āĻž āĻĻ⧇āĻ“ā§ŸāĻž | Pull (āĻĒ⧁āϞ) | āϟāĻžāύāĻž |
| 36. Sweet (āϏ⧁āχāϟ) | āĻŽāĻŋāĻˇā§āϟāĻŋ | Sour (āϏāĻžāĻ“ā§ŸāĻžāϰ) | āϟāĻ• |
| 37. Alive (āĻāϞāĻžāχāĻ­) | āĻœā§€āĻŦāĻŋāϤ | Dead (āĻĄā§‡āĻĄ) | āĻŽā§ƒāϤ |
| 38. Smart (āĻ¸ā§āĻŽāĻžāĻ°ā§āϟ) | āĻŦ⧁āĻĻā§āϧāĻŋāĻŽāĻžāύ | Stupid (āĻ¸ā§āϟ⧁āĻĒāĻŋāĻĄ) | āĻŦā§‹āĻ•āĻž |
| 39. Beautiful (āĻŦāĻŋāωāϟāĻŋāĻĢ⧁āϞ) | āϏ⧁āĻ¨ā§āĻĻāϰ | Ugly (āφāĻ—āϞāĻŋ) | āĻ•ā§ā§ŽāϏāĻŋāϤ |
| 40. True (āĻŸā§āϰ⧁) | āϏāĻ¤ā§āϝ | False (āĻĢāϞāϏ) | āĻŽāĻŋāĻĨā§āϝāĻž |
ā§Ēā§§ āĻĨ⧇āϕ⧇ ā§Žā§Ļ: āϗ⧁āĻŖāĻžāϗ⧁āĻŖ āĻ“ āĻŦ⧈āĻļāĻŋāĻˇā§āĻŸā§āϝ

āχāĻ‚āϰ⧇āϜāĻŋ (English) āĻŦāĻžāĻ‚āϞāĻž āĻ…āĻ°ā§āĻĨ āĻŦāĻŋāĻĒāϰ⧀āϤ āĻļāĻŦā§āĻĻ (Opposite) āĻŦāĻžāĻ‚āϞāĻž āĻ…āĻ°ā§āĻĨ

41. Fat (āĻĢā§āϝāĻžāϟ) āĻŽā§‹āϟāĻž Thin (āĻĨāĻŋāύ) āĻĒāĻžāϤāϞāĻž
42. Heavy (āĻšā§‡āĻ­āĻŋ) āĻ­āĻžāϰ⧀ Light (āϞāĻžāχāϟ) āĻšāĻžāϞāĻ•āĻž
43. Strong (āĻ¸ā§āĻŸā§āϰāĻ‚) āĻļāĻ•ā§āϤāĻŋāĻļāĻžāϞ⧀ Weak (āωāχāĻ•) āĻĻ⧁āĻ°ā§āĻŦāϞ
44. Brave (āĻŦā§āϰ⧇āĻ­) āϏāĻžāĻšāϏ⧀ Coward (āĻ•āĻžāĻ“ā§ŸāĻžāĻ°ā§āĻĄ) āĻ­ā§€āϰ⧁
45. Kind (āĻ•āĻžāχāĻ¨ā§āĻĄ) āĻĻ⧟āĻžāϞ⧁ Cruel (āĻ•ā§āĻ°ā§ā§Ÿā§‡āϞ) āύāĻŋāĻˇā§āϠ⧁āϰ
46. Safe (āϏ⧇āĻĢ) āύāĻŋāϰāĻžāĻĒāĻĻ Danger (āĻĄā§‡āĻžā§āϜāĻžāϰ) āĻŦāĻŋāĻĒāĻĻ
47. Active (āĻ…ā§āϝāĻžāĻ•ā§āϟāĻŋāĻ­) āĻ•āĻ°ā§āĻŽāĻ  Lazy (āϞ⧇āϜāĻŋ) āĻ…āϞāϏ
48. Wide (āĻ“ā§ŸāĻžāχāĻĄ) āĻĒā§āϰāĻļāĻ¸ā§āϤ Narrow (āĻ¨ā§āϝāĻžāϰ⧋) āϏāĻ‚āϕ⧀āĻ°ā§āĻŖ
49. Deep (āĻĄāĻŋāĻĒ) āĻ—āĻ­ā§€āϰ Shallow (āĻļā§āϝāĻžāϞ⧋) āĻ…āĻ—āĻ­ā§€āϰ
50. Quiet (āĻ•ā§‹ā§ŸāĻžāχāϟ) āĻļāĻžāĻ¨ā§āϤ Noisy (āĻ¨ā§Ÿā§‡āϜāĻŋ) āĻļā§‹āϰāĻ—ā§‹āϞ
51. Wise (āĻ“ā§ŸāĻžāχāϜ) āĻœā§āĻžāĻžāύ⧀ Foolish (āĻĢ⧁āϞāĻŋāĻļ) āĻŽā§‚āĻ°ā§āĻ–
52. Young (āĻ‡ā§ŸāĻžāĻ‚) āϤāϰ⧁āĻŖ Old (āĻ“āĻ˛ā§āĻĄ) āĻŦ⧃āĻĻā§āϧ
53. Healthy (āĻšā§‡āϞāĻĻāĻŋ) āĻ¸ā§āĻŦāĻžāĻ¸ā§āĻĨā§āϝāĻŦāĻžāύ Sick (āϏāĻŋāĻ•) āĻ…āϏ⧁āĻ¸ā§āĻĨ
54. Honest (āĻ…āύ⧇āĻ¸ā§āϟ) āĻ¸ā§Ž Dishonest (āĻĄāĻŋāϏāĻ…āύ⧇āĻ¸ā§āϟ) āĻ…āĻ¸ā§Ž
55. Useful (āχāωāϜāĻĢ⧁āϞ) āĻĻāϰāĻ•āĻžāϰ⧀ Useless (āχāωāϜāϞ⧇āϏ) āĻ…āϕ⧇āĻœā§‹
56. Careful (āĻ•ā§‡ā§ŸāĻžāϰāĻĢ⧁āϞ) āϏāϤāĻ°ā§āĻ• Careless (āĻ•ā§‡ā§ŸāĻžāϰāϞ⧇āϏ) āĻ…āϏāϤāĻ°ā§āĻ•
57. Right (āϰāĻžāχāϟ) āϏāĻ āĻŋāĻ• Wrong (āϰāĻ‚) āϭ⧁āϞ
58. Cheap (āϚāĻŋāĻĒ) āϏāĻ¸ā§āϤāĻž Expensive (āĻāĻ•ā§āϏāĻĒ⧇āĻ¨ā§āϏāĻŋāĻ­) āĻĻāĻžāĻŽāĻŋ
59. Dry (āĻĄā§āϰāĻžāχ) āĻļ⧁āĻ•āύ⧋ Wet (āĻ“ā§Ÿā§‡āϟ) āϭ⧇āϜāĻž
60. Smooth (āĻ¸ā§āĻŽā§āĻĻ) āĻŽāϏ⧃āĻŖ Rough (āϰāĻžāĻĢ) āĻ…āĻŽāϏ⧃āĻŖ
61. Top (āϟāĻĒ) āĻļā§€āĻ°ā§āώ Bottom (āĻŦāϟāĻŽ) āϤāϞāĻĻ⧇āĻļ
62. Front (āĻĢā§āϰāĻ¨ā§āϟ) āϏāĻžāĻŽāύ⧇ Back (āĻŦā§āϝāĻžāĻ•) āĻĒ⧇āĻ›āύ⧇
63. Before (āĻŦāĻŋāĻĢā§‹āϰ) āφāϗ⧇ After (āφāĻĢāϟāĻžāϰ) āĻĒāϰ⧇
64. More (āĻŽā§‹āϰ) āĻŦ⧇āĻļāĻŋ Less (āϞ⧇āϏ) āĻ•āĻŽ
65. All (āĻ…āϞ) āϏāĻŦ None (āύāĻžāύ) āĻ•āĻŋāϛ⧁āχ āύāĻž
66. Always (āĻ…āϞāĻ“ā§Ÿā§‡āϜ) āϏāĻŦāϏāĻŽā§Ÿ Never (āύ⧇āĻ­āĻžāϰ) āĻ•āĻ–āύ⧋āχ āύāĻž
67. Together (āϟ⧁āϗ⧇āĻĻāĻžāϰ) āĻāĻ•āĻ¤ā§āϰ⧇ Apart (āĻ…ā§āϝāĻžāĻĒāĻžāĻ°ā§āϟ) āφāϞāĻžāĻĻāĻž
68. Same (āϏ⧇āĻŽ) āĻāĻ•āχ Different (āĻĄāĻŋāĻĢāĻžāϰ⧇āĻ¨ā§āϟ) āĻ­āĻŋāĻ¨ā§āύ
69. Often (āĻ…āĻĢ⧇āύ) āĻĒā§āϰāĻžā§Ÿāχ Seldom (āϏ⧇āϞāĻĄāĻŽ) āĻ•āĻĻāĻžāϚāĻŋā§Ž
70. Loud (āϞāĻžāωāĻĄ) āωāĻšā§āϚāĻ¸ā§āĻŦāϰ Whisper (āĻšā§āχāĻ¸ā§āĻĒāĻžāϰ) āĻĢāĻŋāϏāĻĢāĻŋāϏ
71. Sharp (āĻļāĻžāĻ°ā§āĻĒ) āϧāĻžāϰāĻžāϞ⧋ Blunt (āĻŦā§āϞāĻžāĻ¨ā§āϟ) āĻ­ā§‹āρāϤāĻž
72. Bright (āĻŦā§āϰāĻžāχāϟ) āωāĻœā§āĻœā§āĻŦāϞ Dull (āĻĄāĻžāϞ) āĻ…āύ⧁āĻœā§āĻœā§āĻŦāϞ
73. Heavy (āĻšā§‡āĻ­āĻŋ) āĻ“āϜāύāĻĻāĻžāϰ Light (āϞāĻžāχāϟ) āĻ“āϜāύ⧇ āĻšāĻžāϞāĻ•āĻž
74. Thick (āĻĨāĻŋāĻ•) āĻĒ⧁āϰ⧁ Thin (āĻĨāĻŋāύ) āϏāϰ⧁
75. North (āύāĻ°ā§āĻĨ) āωāĻ¤ā§āϤāϰ South (āϏāĻžāωāĻĨ) āĻĻāĻ•ā§āώāĻŋāĻŖ
76. East (āχāĻ¸ā§āϟ) āĻĒā§‚āĻ°ā§āĻŦ West (āĻ“ā§Ÿā§‡āĻ¸ā§āϟ) āĻĒāĻļā§āϚāĻŋāĻŽ
77. Hello (āĻšā§āϝāĻžāϞ⧋) āĻ“āĻšā§‡ Goodbye (āϗ⧁āĻĄāĻŦāĻžāχ) āĻŦāĻŋāĻĻāĻžā§Ÿ
78. Question (āĻ•ā§‹ā§Ÿā§‡āĻļā§āϚāύ) āĻĒā§āϰāĻļā§āύ Answer (āĻ…ā§āϝāĻžāύāϏāĻžāϰ) āωāĻ¤ā§āϤāϰ
79. Victory (āĻ­āĻŋāĻ•ā§āϟāϰāĻŋ) āĻŦāĻŋāϜ⧟ Defeat (āĻĄāĻŋāĻĢāĻŋāϟ) āĻĒāϰāĻžāϜ⧟
80. Peace (āĻĒāĻŋāϏ) āĻļāĻžāĻ¨ā§āϤāĻŋ War (āĻ“ā§ŸāĻžāϰ) āϝ⧁āĻĻā§āϧ
ā§Žā§§ āĻĨ⧇āϕ⧇ ⧧⧍ā§Ļ: āĻ•āĻžāϜ āĻ“ āĻ…āĻŦāĻ¸ā§āĻĨāĻž (Verbs & States)
āχāĻ‚āϰ⧇āϜāĻŋ (English) āĻŦāĻžāĻ‚āϞāĻž āĻ…āĻ°ā§āĻĨ āĻŦāĻŋāĻĒāϰ⧀āϤ āĻļāĻŦā§āĻĻ (Opposite) āĻŦāĻžāĻ‚āϞāĻž āĻ…āĻ°ā§āĻĨ
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81. Come (āĻ•āĻžāĻŽ) āφāϏāĻž Go (āĻ—ā§‹) āϝāĻžāĻ“ā§ŸāĻž
82. Sit (āϏāĻŋāϟ) āĻŦāϏāĻž Stand (āĻ¸ā§āĻŸā§āϝāĻžāĻ¨ā§āĻĄ) āĻĻāĻžāρ⧜āĻžāύ⧋
83. Sleep (āĻ¸ā§āϞāĻŋāĻĒ) āϘ⧁āĻŽāĻžāύ⧋ Wake (āĻ“ā§Ÿā§‡āĻ•) āĻœā§‡āϗ⧇ āĻ“āĻ āĻž
84. Push (āĻĒ⧁āĻļ) āϠ⧇āϞāĻž Pull (āĻĒ⧁āϞ) āϟāĻžāύāĻž
85. Lift (āϞāĻŋāĻĢāϟ) āϤ⧋āϞāĻž Drop (āĻĄā§āϰāĻĒ) āĻĢ⧇āϞ⧇ āĻĻ⧇āĻ“ā§ŸāĻž
86. Build (āĻŦāĻŋāĻ˛ā§āĻĄ) āύāĻŋāĻ°ā§āĻŽāĻžāĻŖ āĻ•āϰāĻž Destroy (āĻĄā§‡āĻ¸ā§āĻŸā§āϰ⧟) āĻ§ā§āĻŦāĻ‚āϏ āĻ•āϰāĻž
87. Catch (āĻ•ā§āϝāĻžāϚ) āϧāϰāĻž Throw (āĻĨā§āϰ⧋) āϛ⧁āĻā§œā§‡ āĻŽāĻžāϰāĻž
88. Find (āĻĢāĻžāχāĻ¨ā§āĻĄ) āϖ⧁āρāĻœā§‡ āĻĒāĻžāĻ“ā§ŸāĻž Lose (āϞ⧁āϜ) āĻšāĻžāϰāĻžāύ⧋
89. Remember (āϰāĻŋāĻŽā§‡āĻŽā§āĻŦāĻžāϰ) āĻŽāύ⧇ āϰāĻžāĻ–āĻž Forget (āĻĢāϰāϗ⧇āϟ) āϭ⧁āϞ⧇ āϝāĻžāĻ“ā§ŸāĻž
90. Learn (āϞāĻžāĻ°ā§āύ) āĻļ⧇āĻ–āĻž Teach (āϟāĻŋāϚ) āĻļ⧇āĻ–āĻžāύ⧋
91. Live (āϞāĻŋāĻ­) āĻŦāĻžāϏ āĻ•āϰāĻž Die (āĻĄāĻžāχ) āĻŽāĻžāϰāĻž āϝāĻžāĻ“ā§ŸāĻž
92. Ask (āφāĻ¸ā§āĻ•) āϜāĻŋāĻœā§āĻžāĻžāϏāĻž āĻ•āϰāĻž Reply (āϰāĻŋāĻĒā§āϞāĻžāχ) āωāĻ¤ā§āϤāϰ āĻĻ⧇āĻ“ā§ŸāĻž
93. Work (āĻ“ā§ŸāĻžāĻ°ā§āĻ•) āĻ•āĻžāϜ āĻ•āϰāĻž Play (āĻĒā§āϞ⧇) āϖ⧇āϞāĻž āĻ•āϰāĻž
94. Send (āϏ⧇āĻ¨ā§āĻĄ) āĻĒāĻžāĻ āĻžāύ⧋ Receive (āϰāĻŋāϏāĻŋāĻ­) āĻ—ā§āϰāĻšāĻŖ āĻ•āϰāĻž
95. Save (āϏ⧇āĻ­) āϜāĻŽāĻžāύ⧋/āϰāĻ•ā§āώāĻž Spend (āĻ¸ā§āĻĒ⧇āĻ¨ā§āĻĄ) āĻ–āϰāϚ āĻ•āϰāĻž
96. Win (āωāχāύ) āĻœā§‡āϤāĻž Lose (āϞ⧁āϜ) āĻšāĻžāϰāĻž
97. Attack (āĻ…ā§āϝāĻžāϟāĻžāĻ•) āφāĻ•ā§āϰāĻŽāĻŖ āĻ•āϰāĻž Defend (āĻĄāĻŋāĻĢ⧇āĻ¨ā§āĻĄ) āϰāĻ•ā§āώāĻž āĻ•āϰāĻž
98. Add (āĻ…ā§āϝāĻžāĻĄ) āϝ⧋āĻ— āĻ•āϰāĻž Subtract (āϏāĻžāĻŦāĻŸā§āĻ°ā§āϝāĻžāĻ•ā§āϟ) āĻŦāĻŋā§Ÿā§‹āĻ— āĻ•āϰāĻž
99. Agree (āĻāĻ—ā§āϰāĻŋ) āϰāĻžāϜāĻŋ āĻšāĻ“ā§ŸāĻž Disagree (āĻĄāĻŋāϏāĻāĻ—ā§āϰāĻŋ) āĻ…āϏāĻŽā§āĻŽāϤ āĻšāĻ“ā§ŸāĻž
100. Arrive (āĻ…ā§āϝāĻžāϰāĻžāχāĻ­) āĻĒ⧌āρāĻ›āĻžāύ⧋ Depart (āĻĄāĻŋāĻĒāĻžāĻ°ā§āϟ) āϰāĻ“āύāĻž āĻšāĻ“ā§ŸāĻž
101. Admit (āĻ…ā§āϝāĻžāĻĄāĻŽāĻŋāϟ) āĻ¸ā§āĻŦā§€āĻ•āĻžāϰ āĻ•āϰāĻž Deny (āĻĄāĻŋāύāĻžāχ) āĻ…āĻ¸ā§āĻŦā§€āĻ•āĻžāϰ āĻ•āϰāĻž
102. Break (āĻŦā§āϰ⧇āĻ•) āĻ­āĻžāĻ™āĻž Fix (āĻĢāĻŋāĻ•ā§āϏ) āĻŽā§‡āϰāĻžāĻŽāϤ āĻ•āϰāĻž
103. Create (āĻ•ā§āϰāĻŋā§Ÿā§‡āϟ) āϤ⧈āϰāĻŋ āĻ•āϰāĻž Destroy (āĻĄā§‡āĻ¸ā§āĻŸā§āϰ⧟) āĻ§ā§āĻŦāĻ‚āϏ āĻ•āϰāĻž
104. Enter (āĻāĻ¨ā§āϟāĻžāϰ) āĻĒā§āϰāĻŦ⧇āĻļ āĻ•āϰāĻž Exit (āĻāĻ•ā§āϏāĻŋāϟ) āĻŦ⧇āϰ āĻšāĻ“ā§ŸāĻž
105. Fill (āĻĢāĻŋāϞ) āĻĒā§‚āĻ°ā§āĻŖ āĻ•āϰāĻž Empty (āĻāĻŽā§āĻĒāϟāĻŋ) āĻ–āĻžāϞāĻŋ āĻ•āϰāĻž
106. Float (āĻĢā§āϞ⧋āϟ) āĻ­āĻžāϏāĻž Sink (āϏāĻŋāĻ™ā§āĻ•) āĻĄā§‹āĻŦāĻž
107. Follow (āĻĢāϞ⧋) āĻ…āύ⧁āϏāϰāĻŖ āĻ•āϰāĻž Lead (āϞāĻŋāĻĄ) āύ⧇āϤ⧃āĻ¤ā§āĻŦ āĻĻ⧇āĻ“ā§ŸāĻž
108. Forget (āĻĢāϰāϗ⧇āϟ) āĻ­ā§‹āϞāĻž Remember (āϰāĻŋāĻŽā§‡āĻŽā§āĻŦāĻžāϰ) āĻŽāύ⧇ āϰāĻžāĻ–āĻž
109. Hire (āĻšāĻžāϝāĻŧāĻžāϰ) āĻ­āĻžā§œāĻž āĻ•āϰāĻž Fire (āĻĢāĻžā§ŸāĻžāϰ) āĻ›āĻžāρāϟāĻžāχ āĻ•āϰāĻž
110. Import (āχāĻŽāĻĒā§‹āĻ°ā§āϟ) āφāĻŽāĻĻāĻžāύāĻŋ Export (āĻāĻ•ā§āϏāĻĒā§‹āĻ°ā§āϟ) āϰāĻĒā§āϤāĻžāύāĻŋ
111. Join (āĻœā§Ÿā§‡āύ) āϝ⧋āĻ— āĻĻ⧇āĻ“ā§ŸāĻž Separate (āϏ⧇āĻĒāĻžāϰ⧇āϟ) āφāϞāĻžāĻĻāĻž āĻšāĻ“ā§ŸāĻž
112. Lend (āϞ⧇āĻ¨ā§āĻĄ) āϧāĻžāϰ āĻĻ⧇āĻ“ā§ŸāĻž Borrow (āĻŦāϰ⧋) āϧāĻžāϰ āύ⧇āĻ“ā§ŸāĻž
113. Marry (āĻŽā§āϝāĻžāϰāĻŋ) āĻŦāĻŋā§Ÿā§‡ āĻ•āϰāĻž Divorce (āĻĄāĻŋāĻ­ā§‹āĻ°ā§āϏ) āĻŦāĻŋāĻšā§āϛ⧇āĻĻ
114. Pass (āĻĒāĻžāϏ) āϏāĻĢāϞ āĻšāĻ“ā§ŸāĻž Fail (āĻĢ⧇āχāϞ) āĻŦā§āϝāĻ°ā§āĻĨ āĻšāĻ“ā§ŸāĻž
115. Raise (āϰ⧇āχāϜ) āϤ⧋āϞāĻž Lower (āϞ⧋āϝāĻŧāĻžāϰ) āύāĻžāĻŽāĻžāύ⧋
116. Rise (āϰāĻžāχāϜ) āωāĻĻāĻŋāϤ āĻšāĻ“ā§ŸāĻž Set (āϏ⧇āϟ) āĻ…āĻ¸ā§āϤ āϝāĻžāĻ“ā§ŸāĻž
117. Shout (āĻļāĻžāωāϟ) āϚāĻŋā§ŽāĻ•āĻžāϰ āĻ•āϰāĻž Whisper (āĻšā§āχāĻ¸ā§āĻĒāĻžāϰ) āĻĢāĻŋāϏāĻĢāĻŋāϏ āĻ•āϰāĻž
118. Tight (āϟāĻžāχāϟ) āĻļāĻ•ā§āϤ/āφāρāϟāϏāĻžāρāϟ Loose (āϞ⧁āϜ) āφāϞāĻ—āĻž
119. Wild (āĻ“āϝāĻŧāĻžāχāĻ˛ā§āĻĄ) āĻŦāĻ¨ā§āϝ Tame (āĻŸā§‡āĻŽ) āĻ—ā§ƒāĻšāĻĒāĻžāϞāĻŋāϤ/āĻļāĻžāĻ¨ā§āϤ
120. Sunny (āϏāĻžāύāĻŋ) āϰ⧋āĻĻ⧇āϞāĻž Cloudy (āĻ•ā§āϞāĻžāωāĻĄāĻŋ) āĻŽā§‡āϘāϞāĻž
⧧⧍⧧ āĻĨ⧇āϕ⧇ ā§§ā§Ŧā§Ļ: āĻ…āύ⧁āĻ­ā§‚āϤāĻŋ āĻ“ āϏāĻžāĻŽāĻžāϜāĻŋāĻ• āĻļāĻŦā§āĻĻ
āχāĻ‚āϰ⧇āϜāĻŋ (English) āĻŦāĻžāĻ‚āϞāĻž āĻ…āĻ°ā§āĻĨ āĻŦāĻŋāĻĒāϰ⧀āϤ āĻļāĻŦā§āĻĻ (Opposite) āĻŦāĻžāĻ‚āϞāĻž āĻ…āĻ°ā§āĻĨ
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121. Brave (āĻŦā§āϰ⧇āĻ­) āϏāĻžāĻšāϏ⧀ Afraid (āφāĻĢā§āϰ⧇āχāĻĄ) āĻ­ā§€āϤ
122. Calm (āĻ•āĻžāĻŽ) āĻļāĻžāĻ¨ā§āϤ Excited (āĻāĻ•ā§āϏāĻžāχāĻŸā§‡āĻĄ) āωāĻ¤ā§āϤ⧇āϜāĻŋāϤ
123. Cool (āϕ⧁āϞ) āĻļā§€āϤāϞ Warm (āĻ“ā§ŸāĻžāĻ°ā§āĻŽ) āωāĻˇā§āĻŖ
124. Clever (āĻ•ā§āϞ⧇āĻ­āĻžāϰ) āϚāĻžāϞāĻžāĻ• Stupid (āĻ¸ā§āϟ⧁āĻĒāĻŋāĻĄ) āύāĻŋāĻ°ā§āĻŦā§‹āϧ
125. Complex (āĻ•āĻŽāĻĒā§āϞ⧇āĻ•ā§āϏ) āϜāϟāĻŋāϞ Simple (āϏāĻŋāĻŽā§āĻĒāϞ) āϏāϰāϞ
126. Correct (āĻ•āĻžāϰ⧇āĻ•ā§āϟ) āϏāĻ āĻŋāĻ• Incorrect (āχāύāĻ•āĻžāϰ⧇āĻ•ā§āϟ) āϭ⧁āϞ
127. Dangerous (āĻĄā§‡āĻžā§āϜāĻžāϰāĻžāϏ) āĻŦāĻŋāĻĒāĻœā§āϜāύāĻ• Safe (āϏ⧇āĻĢ) āύāĻŋāϰāĻžāĻĒāĻĻ
128. Eager (āχāĻ—āĻžāϰ) āφāĻ—ā§āϰāĻšā§€ Reluctant (āϰāĻŋāĻ˛ā§āϝāĻžāĻ•ā§āĻŸā§āϝāĻžāĻ¨ā§āϟ) āĻ…āύāĻŋāĻšā§āϛ⧁āĻ•
129. Even (āχāϭ⧇āύ) āĻœā§‹ā§œ Odd (āĻ…āĻĄ) āĻŦāĻŋāĻœā§‹ā§œ
130. Famous (āĻĢ⧇āĻŽāĻžāϏ) āĻŦāĻŋāĻ–ā§āϝāĻžāϤ Unknown (āφāύāύ⧋āύ) āĻ…āĻĒāϰāĻŋāϚāĻŋāϤ
131. Fast (āĻĢāĻžāĻ¸ā§āϟ) āĻĻā§āϰ⧁āϤ Slow (āĻ¸ā§āϞ⧋) āϧ⧀āϰ
132. Final (āĻĢāĻžāχāύāĻžāϞ) āĻšā§‚ā§œāĻžāĻ¨ā§āϤ Initial (āχāύāĻŋāĻļāĻŋ⧟āĻžāϞ) āĻĒā§āϰāĻžāĻĨāĻŽāĻŋāĻ•
133. Fresh (āĻĢā§āϰ⧇āĻļ) āϏāϤ⧇āϜ Stale (āĻ¸ā§āĻŸā§‡āϞ) āĻŦāĻžāϏāĻŋ
134. Funny (āĻĢāĻžāύāĻŋ) āĻŽāϜāĻžāĻĻāĻžāϰ Serious (āϏāĻŋāϰāĻŋ⧟āĻžāϏ) āĻ—āĻŽā§āĻ­ā§€āϰ
135. Generous (āĻœā§‡āύāĻžāϰāĻžāϏ) āωāĻĻāĻžāϰ Mean/Stingy āĻ•ā§ƒāĻĒāĻŖ
136. Giant (āϜāĻžā§ŸāĻžāĻ¨ā§āϟ) āĻĻāĻžāύāĻŦā§€ā§Ÿ/āĻŦāĻŋāĻļāĻžāϞ Tiny (āϟāĻžāχāύāĻŋ) āĻ•ā§āώ⧁āĻĻā§āϰ
137. Guilty (āĻ—āĻŋāĻ˛ā§āϟāĻŋ) āĻĻā§‹āώ⧀ Innocent (āχāύ⧋āϏ⧇āĻ¨ā§āϟ) āύāĻŋāĻ°ā§āĻĻā§‹āώ
138. Hope (āĻšā§‹āĻĒ) āφāĻļāĻž Despair (āĻĄā§‡āϏāĻĒ⧇āϝāĻŧāĻžāϰ) āĻšāϤāĻžāĻļāĻž
139. Huge (āĻšāĻŋāωāϜ) āĻŦāĻŋāĻļāĻžāϞ Tiny (āϟāĻžāχāύāĻŋ) āĻ…āϤāĻŋ āĻ•ā§āώ⧁āĻĻā§āϰ
140. Humble (āĻšāĻžāĻŽā§āĻŦāϞ) āĻŦāĻŋāĻ¨ā§Ÿā§€ Proud (āĻĒā§āϰāĻžāωāĻĄ) āĻ…āĻšāĻ‚āĻ•āĻžāϰ⧀
141. Important (āχāĻŽā§āĻĒāϰāĻŸā§āϝāĻžāĻ¨ā§āϟ) āϗ⧁āϰ⧁āĻ¤ā§āĻŦāĻĒā§‚āĻ°ā§āĻŖ Trivial (āĻŸā§āϰāĻŋāĻ­āĻŋ⧟āĻžāϞ) āϤ⧁āĻšā§āĻ›
142. Inside (āχāύāϏāĻžāχāĻĄ) āϭ⧇āϤāϰ⧇ Outside (āφāωāϟāϏāĻžāχāĻĄ) āĻŦāĻžāχāϰ⧇
143. Joy (āϜ⧟) āφāύāĻ¨ā§āĻĻ Sorrow (āϏāϰ⧋) āĻŦ⧇āĻĻāύāĻž
144. King (āĻ•āĻŋāĻ‚) āϰāĻžāϜāĻž Queen (āϕ⧁āχāύ) āϰāĻžāύ⧀
145. Master (āĻŽāĻžāĻ¸ā§āϟāĻžāϰ) āĻŽāĻžāϞāĻŋāĻ•/āĻĒā§āϰāϭ⧁ Servant (āϏāĻžāĻ°ā§āϭ⧇āĻ¨ā§āϟ) āϚāĻžāĻ•āϰ
146. Melt (āĻŽā§‡āĻ˛ā§āϟ) āĻ—āϞāĻž Freeze (āĻĢā§āϰāĻŋāϜ) āϜāĻŽāĻžāϟ āĻŦāĻžāρāϧāĻž
147. Modern (āĻŽāĻĄāĻžāĻ°ā§āύ) āφāϧ⧁āύāĻŋāĻ• Ancient (āĻāύāĻļāĻŋā§Ÿā§‡āĻ¨ā§āϟ) āĻĒā§āϰāĻžāĻšā§€āύ
148. Natural (āĻ¨ā§āϝāĻžāϚāĻžāϰāĻžāϞ) āĻĒā§āϰāĻžāĻ•ā§ƒāϤāĻŋāĻ• Artificial (āφāĻ°ā§āϟāĻŋāĻĢāĻŋāĻļāĻŋ⧟āĻžāϞ) āĻ•ā§ƒāĻ¤ā§āϰāĻŋāĻŽ
149. Normal (āύāϰāĻŽāĻžāϞ) āĻ¸ā§āĻŦāĻžāĻ­āĻžāĻŦāĻŋāĻ• Strange (āĻ¸ā§āĻŸā§āϰ⧇āĻžā§āϜ) āĻ…āĻĻā§āϭ⧁āϤ
150. Peace (āĻĒāĻŋāϏ) āĻļāĻžāĻ¨ā§āϤāĻŋ Noise (āĻ¨ā§Ÿā§‡āϜ) āĻ—ā§‹āϞāĻŽāĻžāϞ
151. Polite (āĻĒā§‹āϞāĻžāχāϟ) āĻ­āĻĻā§āϰ Rude (āϰ⧁āĻĄ) āĻ…āĻ­āĻĻā§āϰ
152. Possible (āĻĒāϏāĻŋāĻŦāϞ) āϏāĻŽā§āĻ­āĻŦ Impossible (āχāĻŽāĻĒāϏāĻŋāĻŦāϞ) āĻ…āϏāĻŽā§āĻ­āĻŦ
153. Private (āĻĒā§āϰāĻžāχāϭ⧇āϟ) āĻŦā§āϝāĻ•ā§āϤāĻŋāĻ—āϤ Public (āĻĒāĻžāĻŦāϞāĻŋāĻ•) āϏāϰāĻ•āĻžāϰāĻŋ/āϜāύāϏāĻžāϧāĻžāϰāĻŖ
154. Pretty (āĻĒā§āϰāĻŋāϟāĻŋ) āϏ⧁āĻ¨ā§āĻĻāϰ⧀ Ugly (āφāĻ—āϞāĻŋ) āĻ•ā§ā§ŽāϏāĻŋāϤ
155. Profit (āĻĒā§āϰāĻĢāĻŋāϟ) āϞāĻžāĻ­ Loss (āϞāϏ) āĻ•ā§āώāϤāĻŋ
156. Real (āϰāĻŋā§Ÿā§‡āϞ) āĻŦāĻžāĻ¸ā§āϤāĻŦ Fake (āĻĢ⧇āĻ•) āύāĻ•āϞ
157. Regular (āϰ⧇āϗ⧁āϞāĻžāϰ) āύāĻŋ⧟āĻŽāĻŋāϤ Irregular (āχāϰ⧇āϗ⧁āϞāĻžāϰ) āĻ…āύāĻŋ⧟āĻŽāĻŋāϤ
158. Senior (āϏāĻŋāύāĻŋ⧟āϰ) āĻŦ⧜/āĻœā§‡āĻˇā§āĻ ā§āϝ Junior (āϜ⧁āύāĻŋ⧟āϰ) āϛ⧋āϟ/āĻ•āύāĻŋāĻˇā§āĻ 
159. Single (āϏāĻŋāĻ™ā§āϗ⧇āϞ) āĻāĻ•āĻžāϕ⧀ Married (āĻŽā§āϝāĻžāϰāĻŋāĻĄ) āĻŦāĻŋāĻŦāĻžāĻšāĻŋāϤ
160. Success (āϏāĻžāĻ•āϏ⧇āϏ) āϏāĻĢāϞāϤāĻž Failure (āĻĢ⧇āχāϞāĻŋāĻ“āϰ) āĻŦā§āϝāĻ°ā§āĻĨāϤāĻž
ā§§ā§Ŧā§§ āĻĨ⧇āϕ⧇ ⧍ā§Ļā§Ļ: āĻŦāĻŋāĻŦāĻŋāϧ āĻļāĻŦā§āĻĻāĻŽāĻžāϞāĻž
āχāĻ‚āϰ⧇āϜāĻŋ (English) āĻŦāĻžāĻ‚āϞāĻž āĻ…āĻ°ā§āĻĨ āĻŦāĻŋāĻĒāϰ⧀āϤ āĻļāĻŦā§āĻĻ (Opposite) āĻŦāĻžāĻ‚āϞāĻž āĻ…āĻ°ā§āĻĨ
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161. Summer (āϏāĻžāĻŽāĻžāϰ) āĻ—ā§āϰ⧀āĻˇā§āĻŽ Winter (āωāχāĻ¨ā§āϟāĻžāϰ) āĻļā§€āϤ
162. Sun (āϏāĻžāύ) āϏ⧂āĻ°ā§āϝ Moon (āĻŽā§āύ) āϚāĻžāρāĻĻ
163. Tame (āĻŸā§‡āĻŽ) āĻĒā§‹āώāĻž Wild (āĻ“āϝāĻŧāĻžāχāĻ˛ā§āĻĄ) āĻŦ⧁āύ⧋
164. Temporary (āĻŸā§‡āĻŽā§āĻĒā§‹āϰāĻžāϰāĻŋ) āϏāĻžāĻŽāϝāĻŧāĻŋāĻ• Permanent (āĻĒāĻžāϰāĻŽāĻžāύ⧇āĻ¨ā§āϟ) āĻ¸ā§āĻĨāĻžā§Ÿā§€
165. Together (āϟ⧁āϗ⧇āĻĻāĻžāϰ) āĻāĻ•āϏāĻžāĻĨ⧇ Alone (āĻ…ā§āϝāĻžāϞ⧋āύ) āĻāĻ•āĻž
166. Top (āϟāĻĒ) āωāĻĒāϰ⧇ Bottom (āĻŦāϟāĻŽ) āύāĻŋāĻšā§‡
167. Tough (āϟāĻžāĻĢ) āĻ•āĻ āĻŋāύ Easy (āχāϜāĻŋ) āϏāĻšāϜ
168. Unity (āχāωāύāĻŋāϟāĻŋ) āĻāĻ•āϤāĻž Division (āĻĄāĻŋāĻ­āĻŋāĻļāύ) āĻŦāĻŋāϭ⧇āĻĻ
169. Up (āφāĻĒ) āωāĻĒāϰ⧇ Down (āĻĄāĻžāωāύ) āύāĻŋāĻšā§‡
170. Urban (āφāϰāĻŦāĻžāύ) āĻļāĻšā§āϰ⧇ Rural (āϰ⧁āϰāĻžāϞ) āĻ—ā§āϰāĻžāĻŽā§€āĻŖ
171. Vacant (āϭ⧇āĻ•ā§āϝāĻžāĻ¨ā§āϟ) āĻ–āĻžāϞāĻŋ Occupied (āĻ…āϕ⧁āĻĒāĻžāχāĻĄ) āĻĻāĻ–āϞāĻ•ā§ƒāϤ
172. Valuable (āĻ­ā§āϝāĻžāϞ⧁āϝāĻŧ⧇āĻŦāϞ) āĻĻāĻžāĻŽā§€ Worthless (āĻ“āϝāĻŧāĻžāĻ°ā§āĻĨāϞ⧇āϏ) āĻŽā§‚āĻ˛ā§āϝāĻšā§€āύ
173. Vertical (āĻ­āĻžāĻ°ā§āϟāĻŋāĻ•āĻžāϞ) āωāϞāĻŽā§āĻŦ Horizontal (āĻšāϰāĻžāχāϜāĻ¨ā§āϟāĻžāϞ) āφāύ⧁āĻ­ā§‚āĻŽāĻŋāĻ•
174. Village (āĻ­āĻŋāϞ⧇āϜ) āĻ—ā§āϰāĻžāĻŽ City (āϏāĻŋāϟāĻŋ) āĻļāĻšāϰ
175. Visible (āĻ­āĻŋāϜāĻŋāĻŦāϞ) āĻĻ⧃āĻļā§āϝāĻŽāĻžāύ Invisible (āχāύāĻ­āĻŋāϜāĻŋāĻŦāϞ) āĻ…āĻĻ⧃āĻļā§āϝ
176. Wealthy (āĻ“āϝāĻŧ⧇āϞāĻĻāĻŋ) āϧāύ⧀ Poor (āĻĒ⧁āĻ“āϰ) āĻ—āϰ⧀āĻŦ
177. Whole (āĻšā§‹āϞ) āĻĒ⧁āϰ⧋ Part (āĻĒāĻžāĻ°ā§āϟ) āĻ…āĻ‚āĻļ
178. Win (āωāχāύ) āϜ⧟ Loss (āϞāϏ) āĻĒāϰāĻžāϜ⧟
179. Wisdom (āωāχāϜāĻĄāĻŽ) āĻĒā§āϰāĻœā§āĻžāĻž Folly (āĻĢāϞāĻŋ) āĻŦā§‹āĻ•āĻžāĻŽāĻŋ
180. Within (āωāχāĻĻāĻŋāύ) āϭ⧇āϤāϰ⧇ Without (āωāχāĻĻāĻžāωāϟ) āĻ›āĻžā§œāĻž/āĻŦāĻžāχāϰ⧇
181. Yes (āχāϝāĻŧ⧇āϏ) āĻšā§āϝāĻžāρ No (āύ⧋) āύāĻž
182. Youth (āχāωāĻĨ) āϝ⧌āĻŦāύ Age (āĻāϜ) āĻŦāĻžāĻ°ā§āϧāĻ•ā§āϝ
183. Zenith (āĻœā§‡āύāĻŋāĻĨ) āĻšā§‚ā§œāĻž Nadir (āύāĻžāĻĻāĻŋāϰ) āĻĒāĻžāĻĻāĻŦāĻŋāĻ¨ā§āĻĻ⧁
184. Always (āĻ…āϞāĻ“āϝāĻŧ⧇āϜ) āϏāĻ°ā§āĻŦāĻĻāĻž Never (āύ⧇āĻ­āĻžāϰ) āĻ•āĻ–āύ⧋ āύāĻž
185. Animal (āĻ…ā§āϝāĻžāύāĻŋāĻŽā§‡āϞ) āĻĒāĻļ⧁ Human (āĻšāĻŋāωāĻŽā§āϝāĻžāύ) āĻŽāĻžāύ⧁āώ
186. Apart (āĻ…ā§āϝāĻžāĻĒāĻžāĻ°ā§āϟ) āφāϞāĻžāĻĻāĻž Together (āϟ⧁āϗ⧇āĻĻāĻžāϰ) āĻāĻ•āĻ¤ā§āϰ⧇
187. Beautiful (āĻŦāĻŋāωāϟāĻŋāĻĢ⧁āϞ) āϏ⧁āĻ¨ā§āĻĻāϰ Ugly (āφāĻ—āϞāĻŋ) āĻ•ā§ā§ŽāϏāĻŋāϤ
188. Better (āĻŦ⧇āϟāĻžāϰ) āφāϰāĻ“ āĻ­āĻžāϞ⧋ Worse (āĻ“āϝāĻŧāĻžāĻ°ā§āϏ) āφāϰāĻ“ āĻ–āĻžāϰāĻžāĻĒ
189. Bitter (āĻŦāĻŋāϟāĻžāϰ) āϤ⧇āϤ⧋ Sweet (āϏ⧁āχāϟ) āĻŽāĻŋāĻˇā§āϟāĻŋ
190. Borrow (āĻŦāϰ⧋) āϧāĻžāϰ āĻ•āϰāĻž Lend (āϞ⧇āĻ¨ā§āĻĄ) āϧāĻžāϰ āĻĻ⧇āĻ“ā§ŸāĻž
191. Busy (āĻŦāĻŋāϜāĻŋ) āĻŦā§āϝāĻ¸ā§āϤ Free (āĻĢā§āϰāĻŋ) āĻ…āĻŦāϏāϰ
192. Calm (āĻ•āĻžāĻŽ) āĻļāĻžāĻ¨ā§āϤ Stormy (āĻ¸ā§āϟāĻ°ā§āĻŽāĻŋ) āĻā§‹ā§œā§‹
193. Child (āϚāĻžāχāĻ˛ā§āĻĄ) āĻļāĻŋāĻļ⧁ Adult (āĻ…ā§āϝāĻžāĻĄāĻžāĻ˛ā§āϟ) āĻĒā§āϰāĻžāĻĒā§āϤāĻŦ⧟āĻ¸ā§āĻ•
194. Day (āĻĄā§‡) āĻĻāĻŋāύ Night (āύāĻžāχāϟ) āϰāĻžāϤ
195. Drunk (āĻĄā§āϰāĻžāĻ™ā§āĻ•) āĻŽāĻžāϤāĻžāϞ Sober (āϏ⧋āĻŦāĻžāϰ) āϏ⧁āĻ¸ā§āĻĨ/āĻ¸ā§āĻŦāĻžāĻ­āĻžāĻŦāĻŋāĻ•
196. Fat (āĻĢā§āϝāĻžāϟ) āĻŽā§‹āϟāĻž Slim (āĻ¸ā§āϞāĻŋāĻŽ) āĻĒāĻžāϤāϞāĻž
197. Heaven (āĻšā§‡āϭ⧇āύ) āĻ¸ā§āĻŦāĻ°ā§āĻ— Hell (āĻšā§‡āϞ) āύāϰāĻ•
198. Male (āĻŽā§‡āϞ) āĻĒ⧁āϰ⧁āώ Female (āĻĢāĻŋāĻŽā§‡āϞ) āĻŽāĻšāĻŋāϞāĻž
199. Ocean (āĻ“āĻļāĻžāύ) āϏāĻŽā§āĻĻā§āϰ Land (āĻ˛ā§āϝāĻžāĻ¨ā§āĻĄ) āĻ­ā§‚āĻŽāĻŋ
200. Solid (āϏāϞāĻŋāĻĄ) āĻ•āĻ āĻŋāύ Liquid (āϞāĻŋāϕ⧁āχāĻĄ) āϤāϰāϞ

📚 English Grammar | Word (āĻļāĻŦā§āĻĻ)📖 āχāĻ‚āϰ⧇āϜāĻŋ āĻļ⧇āĻ–āĻžāϰ āĻĒā§āϰāĻĨāĻŽ āϧāĻžāĻĒ āĻšāϞ⧋ Word (āĻļāĻŦā§āĻĻ) āϏāĻŽā§āĻĒāĻ°ā§āϕ⧇ āϏāĻ āĻŋāĻ• āϧāĻžāϰāĻŖāĻž āĻ…āĻ°ā§āϜāύ āĻ•āϰāĻžāĨ¤āφāĻŽāϰāĻž āϝ⧇āĻŽāύ āĻāĻ•āϟāĻŋ āĻŦāĻžāĻĄ...
05/06/2026

📚 English Grammar | Word (āĻļāĻŦā§āĻĻ)

📖 āχāĻ‚āϰ⧇āϜāĻŋ āĻļ⧇āĻ–āĻžāϰ āĻĒā§āϰāĻĨāĻŽ āϧāĻžāĻĒ āĻšāϞ⧋ Word (āĻļāĻŦā§āĻĻ) āϏāĻŽā§āĻĒāĻ°ā§āϕ⧇ āϏāĻ āĻŋāĻ• āϧāĻžāϰāĻŖāĻž āĻ…āĻ°ā§āϜāύ āĻ•āϰāĻžāĨ¤

āφāĻŽāϰāĻž āϝ⧇āĻŽāύ āĻāĻ•āϟāĻŋ āĻŦāĻžāĻĄāĻŧāĻŋ āϤ⧈āϰāĻŋāϰ āϜāĻ¨ā§āϝ āĻāϕ⧇āϰ āĻĒāϰ āĻāĻ• āχāϟ āĻŦā§āϝāĻŦāĻšāĻžāϰ āĻ•āϰāĻŋ, āĻ āĻŋāĻ• āϤ⧇āĻŽāύāĻŋ āχāĻ‚āϰ⧇āϜāĻŋ āĻ­āĻžāώāĻžāϝāĻŧ Letter (āĻŦāĻ°ā§āĻŖ) āĻāĻ•āĻ¤ā§āϰāĻŋāϤ āĻšāϝāĻŧ⧇ Word (āĻļāĻŦā§āĻĻ) āϤ⧈āϰāĻŋ āĻ•āϰ⧇ āĻāĻŦāĻ‚ Word āĻāĻ•āĻ¤ā§āϰāĻŋāϤ āĻšāϝāĻŧ⧇ Sentence (āĻŦāĻžāĻ•ā§āϝ) āĻ—āĻ āύ āĻ•āϰ⧇āĨ¤

🔹 Word (āĻļāĻŦā§āĻĻ) āϕ⧀?

āĻāĻ• āĻŦāĻž āĻāĻ•āĻžāϧāĻŋāĻ• Letter āϝāĻ–āύ āĻāĻ•āĻ¤ā§āϰāĻŋāϤ āĻšāϝāĻŧ⧇ āĻāĻ•āϟāĻŋ āĻ…āĻ°ā§āĻĨāĻĒā§‚āĻ°ā§āĻŖ āĻļāĻŦā§āĻĻ āϤ⧈āϰāĻŋ āĻ•āϰ⧇, āϤāĻ–āύ āϤāĻžāϕ⧇ Word āĻŦāϞāĻž āĻšāϝāĻŧāĨ¤

āωāĻĻāĻžāĻšāϰāĻŖ:
✅ Book = āĻŦāχ
✅ Pen = āĻ•āϞāĻŽ
✅ Nice = āϏ⧁āĻ¨ā§āĻĻāϰ
✅ Fast = āĻĻā§āϰ⧁āϤ

āϤāĻŦ⧇ āĻļ⧁āϧ⧁ āĻ•āϝāĻŧ⧇āĻ•āϟāĻŋ Letter āĻāĻ•āϏāĻžāĻĨ⧇ āĻĨāĻžāĻ•āϞ⧇āχ Word āĻšāϝāĻŧ āύāĻžāĨ¤ āϏ⧇āχ Letter-āϗ⧁āϞ⧋āϰ āĻ…āĻŦāĻļā§āϝāχ āĻāĻ•āϟāĻŋ āĻ…āĻ°ā§āĻĨ āĻĨāĻžāĻ•āϤ⧇ āĻšāĻŦ⧇āĨ¤

āϝ⧇āĻŽāύ:
❌ enam
❌ koob
❌ ecin

āĻāϗ⧁āϞ⧋ āĻĻ⧇āĻ–āϤ⧇ Word-āĻāϰ āĻŽāϤ⧋ āĻšāϞ⧇āĻ“ āφāϏāϞ⧇ Word āύāϝāĻŧ, āĻ•āĻžāϰāĻŖ āĻāϗ⧁āϞ⧋āϰ āϕ⧋āύ⧋ āĻ…āĻ°ā§āĻĨ āύ⧇āχāĨ¤

āϏāĻ āĻŋāĻ•āĻ­āĻžāĻŦ⧇ āϏāĻžāϜāĻžāĻ˛ā§‡â€”

âœ”ī¸ enam → Name
âœ”ī¸ koob → Book
âœ”ī¸ ecin → Nice

āĻ…āĻ°ā§āĻĨāĻžā§Ž, Letter-āĻāϰ āϏāĻŽāĻˇā§āϟāĻŋ āϝāĻĻāĻŋ āϕ⧋āύ⧋ āĻ…āĻ°ā§āĻĨ āĻĒā§āϰāĻ•āĻžāĻļ āύāĻž āĻ•āϰ⧇, āϤāĻžāĻšāϞ⧇ āϤāĻž Word āύāϝāĻŧāĨ¤

🔰 Word-āĻāϰ āϗ⧁āϰ⧁āĻ¤ā§āĻŦ

āχāĻ‚āϰ⧇āϜāĻŋ āĻ­āĻžāώāĻžāϰ āĻĒā§āϰāϤāĻŋāϟāĻŋ āĻ…āĻ‚āĻļ Word-āĻāϰ āĻŽāĻžāĻ§ā§āϝāĻŽā§‡ āĻĒā§āϰāĻ•āĻžāĻļ āĻ•āϰāĻž āĻšāϝāĻŧāĨ¤ āϝ⧇āĻŽāĻ¨â€”

🔹 Noun (āύāĻžāĻŽāĻŦāĻžāϚāĻ• āĻļāĻŦā§āĻĻ) → Man, Student, Book
🔹 Pronoun (āϏāĻ°ā§āĻŦāύāĻžāĻŽ) → He, She, They
🔹 Adjective (āĻŦāĻŋāĻļ⧇āώāĻŖ) → Good, Beautiful, Honest
🔹 Verb (āĻ•ā§āϰāĻŋāϝāĻŧāĻž) → Write, Read, Play
🔹 Adverb (āĻ•ā§āϰāĻŋāϝāĻŧāĻž āĻŦāĻŋāĻļ⧇āώāĻŖ) → Well, Quickly, Slowly
🔹 Preposition (āĻĒāĻĻāĻžāĻ¨ā§āĻŦāϝāĻŧā§€ āĻ…āĻŦā§āϝāϝāĻŧ) → In, On, At
🔹 Conjunction (āϏāĻ‚āϝ⧋āϜāĻ•) → And, But, Or
🔹 Interjection (āφāĻŦ⧇āĻ—āϏ⧂āϚāĻ• āĻļāĻŦā§āĻĻ) → Oh!, Hurrah!, Alas!

💡 āĻŽāύ⧇ āϰāĻžāĻ–āĻŦ⧇āύ:

"āϝ⧇ Letter āĻŦāĻž Letter-āĻāϰ āϏāĻŽāĻˇā§āϟāĻŋ āĻāĻ•āϟāĻŋ āĻ¸ā§āĻĒāĻˇā§āϟ āĻ…āĻ°ā§āĻĨ āĻĒā§āϰāĻ•āĻžāĻļ āĻ•āϰ⧇, āϏ⧇āϟāĻŋāχ WordāĨ¤"

āχāĻ‚āϰ⧇āϜāĻŋ Grammar āĻ­āĻžāϞ⧋āĻ­āĻžāĻŦ⧇ āĻļāĻŋāĻ–āϤ⧇ āĻšāϞ⧇ āĻĒā§āϰāĻĨāĻŽā§‡ Word āϏāĻŽā§āĻĒāĻ°ā§āϕ⧇ āĻĒāϰāĻŋāĻˇā§āĻ•āĻžāϰ āϧāĻžāϰāĻŖāĻž āĻĨāĻžāĻ•āϤ⧇ āĻšāĻŦ⧇āĨ¤ āĻ•āĻžāϰāĻŖ Word āĻšāϞ⧋ āĻ­āĻžāώāĻžāϰ āĻ­āĻŋāĻ¤ā§āϤāĻŋ, āφāϰ āĻļāĻ•ā§āϤ āĻ­āĻŋāĻ¤ā§āϤāĻŋ āĻ›āĻžāĻĄāĻŧāĻž āϏ⧁āĻ¨ā§āĻĻāϰ āĻ­āĻŦāύ āϝ⧇āĻŽāύ āϤ⧈āϰāĻŋ āĻšāϝāĻŧ āύāĻž, āϤ⧇āĻŽāύāĻŋ Word āύāĻž āϜāĻžāύāϞ⧇ āχāĻ‚āϰ⧇āϜāĻŋāϤ⧇āĻ“ āĻĻāĻ•ā§āώ āĻšāĻ“āϝāĻŧāĻž āĻ•āĻ āĻŋāύāĨ¤

📖 āĻĒā§āϰāϤāĻŋāĻĻāĻŋāύ āĻāĻ•āϟ⧁ āĻāĻ•āϟ⧁ āĻ•āϰ⧇ Grammar āĻļāĻŋāϖ⧁āύ, āχāĻ‚āϰ⧇āϜāĻŋāϕ⧇ āϏāĻšāϜ āĻ•āϰ⧇ āϤ⧁āϞ⧁āύāĨ¤





04/06/2026

📚 āĻĒāĻžā§āϚāĻŽ āĻļā§āϰ⧇āĻŖāĻŋ āĻ—āĻŖāĻŋāϤ (āĻ…āĻ§ā§āϝāĻžā§Ÿâ€“ā§Š)
‌ ‌‌āĻĒāĻ°ā§āĻŦ-ā§§(⧍ā§Ļ⧍ā§Ŧ) āϗ⧁āύāĻŋāϤāĻ• āĻ“ āϗ⧁āĻŖāύ⧀āϝāĻŧāĻ•

đŸ”ĸ (āϗ⧁āĻŖāĻŋāϤāĻ• āĻ“ āϗ⧁āĻŖāĻ¨ā§€ā§ŸāĻ•) āϏāĻšāϜ āĻĒāĻĻā§āϧāϤāĻŋāϤ⧇ āφāϞ⧋āϚāύāĻž āĻ•āϰāĻž āĻšā§Ÿā§‡āϛ⧇āĨ¤

āϝāĻžāϰāĻž āĻāχ āĻ…āĻ§ā§āϝāĻžā§ŸāϟāĻŋ āĻŦ⧁āĻāϤ⧇ āϏāĻŽāĻ¸ā§āϝāĻžā§Ÿ āĻĒ⧜āϛ⧋, āϤāĻžāĻĻ⧇āϰ āϜāĻ¨ā§āϝ āĻ­āĻŋāĻĄāĻŋāĻ“āϟāĻŋ āϖ⧁āĻŦāχ āωāĻĒāĻ•āĻžāϰ⧀ āĻšāĻŦ⧇āĨ¤ đŸ’¯

đŸŽ¯ āĻ­āĻŋāĻĄāĻŋāĻ“āϟāĻŋ āϏāĻŽā§āĻĒā§‚āĻ°ā§āĻŖ āĻĻ⧇āϖ⧁āύ āĻāĻŦāĻ‚ āύāϤ⧁āύ āύāϤ⧁āύ āĻļāĻŋāĻ•ā§āώāĻžāĻŽā§‚āϞāĻ• āĻ­āĻŋāĻĄāĻŋāĻ“ āĻĒ⧇āϤ⧇ āĻĒ⧇āϜāϟāĻŋ āĻĢāϞ⧋ āĻ•āϰ⧇ āĻĒāĻžāĻļ⧇ āĻĨāĻžāϕ⧁āύāĨ¤

#āĻĒāĻžā§āϚāĻŽ_āĻļā§āϰ⧇āĻŖāĻŋ #āĻ—āĻŖāĻŋāϤ #āϗ⧁āĻŖāĻŋāϤāĻ•_āĻ“_āϗ⧁āĻŖāĻ¨ā§€ā§ŸāĻ•

📚 āχāĻ‚āϰ⧇āϜāĻŋ āĻļ⧇āĻ–āĻžāϰ āĻļ⧁āϰ⧁ āĻšā§‹āĻ• Alphabet āĻĨ⧇āϕ⧇! 🔤āχāĻ‚āϰ⧇āϜāĻŋ āĻ­āĻžāώāĻžāϰ āĻ­āĻŋāĻ¤ā§āϤāĻŋ āĻšāϞ⧋ Letter (Alphabet)āĨ¤ā§¨ā§ŦāϟāĻŋ Letter, ā§ĢāϟāĻŋ Vowel, ⧍⧧āϟāĻŋ Consonant...
04/06/2026

📚 āχāĻ‚āϰ⧇āϜāĻŋ āĻļ⧇āĻ–āĻžāϰ āĻļ⧁āϰ⧁ āĻšā§‹āĻ• Alphabet āĻĨ⧇āϕ⧇! 🔤
āχāĻ‚āϰ⧇āϜāĻŋ āĻ­āĻžāώāĻžāϰ āĻ­āĻŋāĻ¤ā§āϤāĻŋ āĻšāϞ⧋ Letter (Alphabet)āĨ¤
⧍ā§ŦāϟāĻŋ Letter, ā§ĢāϟāĻŋ Vowel, ⧍⧧āϟāĻŋ Consonant āĻāĻŦāĻ‚ Y-āĻāϰ āĻŦāĻŋāĻļ⧇āώ āĻŦā§āϝāĻŦāĻšāĻžāϰ āϏāĻŽā§āĻĒāĻ°ā§āϕ⧇ āϏāĻšāϜ āĻ­āĻžāώāĻžāϝāĻŧ āϜāĻžāύ⧁āύāĨ¤
✅ Vowel āĻ“ Consonant-āĻāϰ āĻĒāĻžāĻ°ā§āĻĨāĻ•ā§āϝ
✅ Letter-āĻāϰ āϏāĻ āĻŋāĻ• āωāĻšā§āϚāĻžāϰāĻŖ
✅ āϗ⧁āϰ⧁āĻ¤ā§āĻŦāĻĒā§‚āĻ°ā§āĻŖ Grammar Tips
āĻļ⧇āĻ–āĻžāϰ āφāĻ—ā§āϰāĻš āĻĨāĻžāĻ•āϞ⧇ āĻĒā§‹āĻ¸ā§āϟāϟāĻŋ āϞāĻžāχāĻ•, āĻ•āĻŽā§‡āĻ¨ā§āϟ āĻ“ āĻļ⧇āϝāĻŧāĻžāϰ āĻ•āϰ⧁āύ āĻāĻŦāĻ‚ āύāϤ⧁āύ āύāϤ⧁āύ āĻļāĻŋāĻ•ā§āώāĻžāĻŽā§‚āϞāĻ• āĻĒā§‹āĻ¸ā§āϟ āĻĒ⧇āϤ⧇ āĻĒ⧇āχāϜāϟāĻŋ āĻĢāϞ⧋ āĻĻāĻŋāϝāĻŧ⧇ āĻĒāĻžāĻļ⧇ āĻĨāĻžāϕ⧁āύāĨ¤ â¤ī¸
#āĻŦāĻžāĻ‚āϞāĻž_āĻĨ⧇āϕ⧇_āχāĻ‚āϰ⧇āϜāĻŋ #āĻļāĻŋāĻ•ā§āώāĻžāĻŽā§‚āϞāĻ•_āĻĒā§‹āĻ¸ā§āϟ 📖✨

🇧🇩  āώāĻˇā§āĻ , āϏāĻĒā§āϤāĻŽ, āĻ…āĻˇā§āϟāĻŽ, āύāĻŦāĻŽ āĻ“ āĻĻāĻļāĻŽ āĻļā§āϰ⧇āĻŖāĻŋāϰ āĻ—āĻŖāĻŋāϤ đŸ‡¯đŸ‡ĩāĻŦā§€āϜāĻ—āĻŖāĻŋāĻ¤ā§€ā§Ÿ āϏ⧂āĻ¤ā§āϰāĻžāĻŦāϞ⧀ āĻ“ āĻĒā§āĻ°ā§Ÿā§‹āĻ—āϏ⧂āĻ¤ā§āϰ⧇āϰ āĻĒā§āϰāĻŽāĻžāĻŖ āϏāĻš āĻŦā§āϝāĻžāĻ–ā§āϝāĻžāĨ¤āĨ¤āύ⧋āϟāϟāĻŋ  āĻ­āĻžāϞ⧋ āϞāĻžāĻ—...
04/06/2026

🇧🇩 āώāĻˇā§āĻ , āϏāĻĒā§āϤāĻŽ, āĻ…āĻˇā§āϟāĻŽ, āύāĻŦāĻŽ āĻ“ āĻĻāĻļāĻŽ āĻļā§āϰ⧇āĻŖāĻŋāϰ āĻ—āĻŖāĻŋāϤ đŸ‡¯đŸ‡ĩ
āĻŦā§€āϜāĻ—āĻŖāĻŋāĻ¤ā§€ā§Ÿ āϏ⧂āĻ¤ā§āϰāĻžāĻŦāϞ⧀ āĻ“ āĻĒā§āĻ°ā§Ÿā§‹āĻ—
āϏ⧂āĻ¤ā§āϰ⧇āϰ āĻĒā§āϰāĻŽāĻžāĻŖ āϏāĻš āĻŦā§āϝāĻžāĻ–ā§āϝāĻžāĨ¤āĨ¤
āύ⧋āϟāϟāĻŋ āĻ­āĻžāϞ⧋ āϞāĻžāĻ—āϞ⧇ āĻĒ⧇āχāϜāϟāĻŋ āĻĢāϞ⧋ āĻĻāĻŋā§Ÿā§‡ āφāĻŽāĻžāϰ āĻĒāĻžāĻļ⧇ āĻĨāĻžāĻ•āĻŦ⧇āύ āχāύāĻļāĻžāφāĻ˛ā§āϞāĻžāĻšāĨ¤âœī¸

02/06/2026

📚✨ āĻĻ⧁āχāϝāĻŧ⧇āϰ āύāĻžāĻŽāϤāĻž āĻļāĻŋāĻ–āĻŋ āϏāĻšāĻœā§‡, āĻŦāϞāĻŋ āϏāĻ āĻŋāĻ• āωāĻšā§āϚāĻžāϰāϪ⧇ ✨📚
āĻļāĻŋāĻļ⧁āĻĻ⧇āϰ āĻĒā§āϰāĻžāĻĨāĻŽāĻŋāĻ• āĻļāĻŋāĻ•ā§āώāĻžāϰ āĻ…āĻ¨ā§āϝāϤāĻŽ āϗ⧁āϰ⧁āĻ¤ā§āĻŦāĻĒā§‚āĻ°ā§āĻŖ āϧāĻžāĻĒ āĻšāϞ⧋ āύāĻžāĻŽāϤāĻž āĻļ⧇āĻ–āĻžāĨ¤ āĻļ⧁āϧ⧁ āĻŽā§āĻ–āĻ¸ā§āĻĨ āĻ•āϰāϞ⧇āχ āĻšāĻŦ⧇ āύāĻž, āϏāĻ āĻŋāĻ• āωāĻšā§āϚāĻžāϰāĻŖ āĻ“ āĻŦā§‹āĻāĻžāϰ āĻŽāĻžāĻ§ā§āϝāĻŽā§‡ āύāĻžāĻŽāϤāĻž āĻļāĻŋāĻ–āϞ⧇ āĻ—āĻŖāĻŋāϤ⧇āϰ āĻ­āĻŋāĻ¤ā§āϤāĻŋ āφāϰāĻ“ āĻŽāϜāĻŦ⧁āϤ āĻšāϝāĻŧāĨ¤
🔸 ⧍ × ā§§ = ⧍
🔸 ⧍ × ⧍ = ā§Ē
🔸 ⧍ × ā§Š = ā§Ŧ
🔸 ⧍ × ā§Ē = ā§Ž
🔸 ⧍ × ā§Ģ = ā§§ā§Ļ
🔸 ⧍ × ā§Ŧ = ⧧⧍
🔸 ⧍ × ā§­ = ā§§ā§Ē
🔸 ⧍ × ā§Ž = ā§§ā§Ŧ
🔸 ⧍ × ⧝ = ā§§ā§Ž
🔸 ⧍ × ā§§ā§Ļ = ⧍ā§Ļ
āĻāĻ­āĻžāĻŦ⧇āχ āϧāĻžāĻĒ⧇ āϧāĻžāĻĒ⧇ āĻļāĻŋāĻļ⧁āϰāĻž āϏāĻ‚āĻ–ā§āϝāĻž āĻ“ āϗ⧁āϪ⧇āϰ āϧāĻžāϰāĻŖāĻž āϏāĻšāĻœā§‡ āφāϝāĻŧāĻ¤ā§āϤ āĻ•āϰāϤ⧇ āĻĒāĻžāϰ⧇āĨ¤
🌱 āϛ⧋āϟāĻŦ⧇āϞāĻžāϰ āĻāχ āĻļāĻŋāĻ•ā§āώāĻž āĻ­āĻŦāĻŋāĻˇā§āϝāϤ⧇āϰ āĻŦāĻĄāĻŧ āϏāĻžāĻĢāĻ˛ā§āϝ⧇āϰ āĻ­āĻŋāĻ¤ā§āϤāĻŋ āĻ—āĻĄāĻŧ⧇ āĻĻ⧇āϝāĻŧāĨ¤ āϤāĻžāχ āφāϏ⧁āύ, āφāύāĻ¨ā§āĻĻ⧇āϰ āϏāĻžāĻĨ⧇ āĻļāĻŋāĻļ⧁āĻĻ⧇āϰ āύāĻžāĻŽāϤāĻž āĻļ⧇āĻ–āĻžāχ āĻāĻŦāĻ‚ āĻ—āĻŖāĻŋāϤāĻ­ā§€āϤāĻŋ āĻĻā§‚āϰ āĻ•āϰāĻŋāĨ¤
📝 āφāĻĒāύāĻžāϰ āϏāĻ¨ā§āϤāĻžāύ āĻ•āĻŋ āĻĻ⧁āχāϝāĻŧ⧇āϰ āύāĻžāĻŽāϤāĻž āĻŦāϞāϤ⧇ āĻĒāĻžāϰ⧇? āĻ•āĻŽā§‡āĻ¨ā§āĻŸā§‡ āϜāĻžāύāĻžāϤ⧇ āĻĒāĻžāϰ⧇āύāĨ¤
#āĻĻ⧁āχāϝāĻŧ⧇āϰ_āύāĻžāĻŽāϤāĻž #āϏāĻ āĻŋāĻ•_āωāĻšā§āϚāĻžāϰāĻŖ #āĻļāĻŋāĻļ⧁āĻļāĻŋāĻ•ā§āώāĻž #āĻ—āĻŖāĻŋāϤāĻļāĻŋāĻ•ā§āώāĻž #āύāĻžāĻŽāϤāĻž_āĻļāĻŋāĻ–āĻŋ #āĻĒā§āϰāĻžāĻĨāĻŽāĻŋāĻ•_āĻļāĻŋāĻ•ā§āώāĻž #āĻŦāĻžāĻ‚āϞāĻž_āĻļāĻŋāĻ•ā§āώāĻž

āĻ•āĻŽā§āĻĒāĻŋāωāϟāĻžāϰāϰ⧇āϰ āĻŦāĻžāĻ‚āϞāĻž āϟāĻžāχāĻĒāĻŋāĻ‚-āĻ āϕ⧋āύ āĻ…āĻ•ā§āώāϰ āĻĻāĻŋā§Ÿā§‡ āĻ•āĻŋāĻ­āĻžāĻŦ⧇ āϟāĻžāχāĻĒ āĻ•āϰāϤ⧇ āĻšā§Ÿ āϏāĻŦāĻ•āĻŋāϛ⧁ āĻāĻ•āϏāĻžāĻĨ⧇āĨ¤āϏāĻ‚āĻ—ā§ƒāĻšā§€āϤ āĻĒā§‹āĻ¸ā§āϟāĨ¤
04/05/2026

āĻ•āĻŽā§āĻĒāĻŋāωāϟāĻžāϰāϰ⧇āϰ āĻŦāĻžāĻ‚āϞāĻž āϟāĻžāχāĻĒāĻŋāĻ‚-āĻ āϕ⧋āύ āĻ…āĻ•ā§āώāϰ āĻĻāĻŋā§Ÿā§‡ āĻ•āĻŋāĻ­āĻžāĻŦ⧇ āϟāĻžāχāĻĒ āĻ•āϰāϤ⧇ āĻšā§Ÿ āϏāĻŦāĻ•āĻŋāϛ⧁ āĻāĻ•āϏāĻžāĻĨ⧇āĨ¤

āϏāĻ‚āĻ—ā§ƒāĻšā§€āϤ āĻĒā§‹āĻ¸ā§āϟāĨ¤

**āĻ—āĻŖāĻŋāϤ⧇āϰ āϏāĻ•āϞ āϏ⧂āĻ¤ā§āϰ**📖āĻŦā§€āϜāĻ—āĻžāĻŖāĻŋāϤāĻŋāĻ• āϏ⧂āĻ¤ā§āϰāĻžāĻŦāĻ˛ā§€đŸ“–1.🚩 (a+b)²= a²+2ab+b²2.🚩 (a+b)²= (a-b)²+4ab3.🚩 (a-b)²= a²-2ab+b²4.🚩 (a-b)²= (a...
28/04/2026

**āĻ—āĻŖāĻŋāϤ⧇āϰ āϏāĻ•āϞ āϏ⧂āĻ¤ā§āϰ**
📖āĻŦā§€āϜāĻ—āĻžāĻŖāĻŋāϤāĻŋāĻ• āϏ⧂āĻ¤ā§āϰāĻžāĻŦāĻ˛ā§€đŸ“–
1.🚩 (a+b)²= a²+2ab+b²
2.🚩 (a+b)²= (a-b)²+4ab
3.🚩 (a-b)²= a²-2ab+b²
4.🚩 (a-b)²= (a+b)²-4ab
5.🚩 a² + b²= (a+b)²-2ab.
6.🚩 a² + b²= (a-b)²+2ab.
7.🚩 a²-b²= (a +b)(a -b)
8.🚩 2(a²+b²)= (a+b)²+(a-b)²
9.🚩 4ab = (a+b)²-(a-b)²
10.🚩 ab = {(a+b)/2}²-{(a-b)/2}²
11.🚩 (a+b+c)² = a²+b²+c²+2(ab+bc+ca)
12.🚩 (a+b)Âŗ = aÂŗ+3a²b+3ab²+bÂŗ
13.🚩 (a+b)Âŗ = aÂŗ+bÂŗ+3ab(a+b)
14.🚩 a-b)Âŗ= aÂŗ-3a²b+3ab²-bÂŗ
15.🚩 (a-b)Âŗ= aÂŗ-bÂŗ-3ab(a-b)
16.🚩 aÂŗ+bÂŗ= (a+b) (a²-ab+b²)
17.🚩 aÂŗ+bÂŗ= (a+b)Âŗ-3ab(a+b)
18.🚩 aÂŗ-bÂŗ = (a-b) (a²+ab+b²)
19.🚩 aÂŗ-bÂŗ = (a-b)Âŗ+3ab(a-b)
20. (a² + b² + c²) = (a + b + c)² – 2(ab + bc + ca)
21.🚩 2 (ab + bc + ca) = (a + b + c)² – (a² + b² + c²)
22.🚩 (a + b + c)Âŗ = aÂŗ + bÂŗ + cÂŗ + 3 (a + b) (b + c) (c + a)
23.🚩 aÂŗ + bÂŗ + cÂŗ – 3abc =(a+b+c)(a² + b²+ c²–ab–bc– ca)
24.🚩 a3 + b3 + c3 – 3abc =ÂŊ (a+b+c) { (a–b)²+(b–c)²+(c–a)²}
25.🚩(x + a) (x + b) = x² + (a + b) x + ab
26.🚩 (x + a) (x – b) = x² + (a – b) x – ab
27.🚩 (x – a) (x + b) = x² + (b – a) x – ab
28.🚩 (x – a) (x – b) = x² – (a + b) x + ab
29.🚩 (x+p) (x+q) (x+r) = xÂŗ + (p+q+r) x² + (pq+qr+rp) x +pqr
30.🚩 bc (b-c) + ca (c- a) + ab (a - b) = - (b - c) (c- a) (a - b)
31.🚩 a² (b- c) + b² (c- a) + c² (a - b) = -(b-c) (c-a) (a - b)
32.🚩 a (b² - c²) + b (c² - a²) + c (a² - b²) = (b - c) (c- a) (a - b)
33.🚩 aÂŗ (b - c) + bÂŗ (c-a) +cÂŗ (a -b) =- (b-c) (c-a) (a - b)(a + b + c)
34.🚩 b²-c² (b²-c²) + c²a²(c²-a²)+a²b²(a²-b²)=-(b-c) (c-a) (a-b) (b+c) (c+a) (a+b)
35.🚩 (ab + bc+ca) (a+b+c) - abc = (a + b)(b + c) (c+a)
36.🚩 (b + c)(c + a)(a + b) + abc = (a + b +c) (ab + bc + ca)
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📖āφāϝāĻŧāϤāĻ•ā§āώ⧇āĻ¤ā§āĻ°đŸ“–
1.āφāϝāĻŧāϤāĻ•ā§āώ⧇āĻ¤ā§āϰ⧇āϰ āĻ•ā§āώ⧇āĻ¤ā§āϰāĻĢāϞ = (āĻĻ⧈āĻ°ā§āĻ˜ā§āϝ × āĻĒā§āϰāĻ¸ā§āĻĨ) āĻŦāĻ°ā§āĻ— āĻāĻ•āĻ•
2.āφāϝāĻŧāϤāĻ•ā§āώ⧇āĻ¤ā§āϰ⧇āϰ āĻĒāϰāĻŋāϏ⧀āĻŽāĻž = 2 (āĻĻ⧈āĻ°ā§āĻ˜ā§āϝ+āĻĒā§āϰāĻ¸ā§āĻĨ)āĻāĻ•āĻ•
3.āφāϝāĻŧāϤāĻ•ā§āώ⧇āĻ¤ā§āϰ⧇āϰ āĻ•āĻ°ā§āĻŖ = √(āĻĻ⧈āĻ°ā§āĻ˜ā§āĻ¯Â˛+āĻĒā§āϰāĻ¸ā§āĻĨ²)āĻāĻ•āĻ•
4.āφāϝāĻŧāϤāĻ•ā§āώ⧇āĻ¤ā§āϰ⧇āϰ āĻĻ⧈āĻ°ā§āĻ˜ā§āϝ= āĻ•ā§āώ⧇āĻ¤ā§āϰāĻĢāĻ˛ÃˇāĻĒā§āϰāĻ¸ā§āϤ āĻāĻ•āĻ•
5.āφāϝāĻŧāϤāĻ•ā§āώ⧇āĻ¤ā§āϰ⧇āϰ āĻĒā§āϰāĻ¸ā§āϤ= āĻ•ā§āώ⧇āĻ¤ā§āϰāĻĢāĻ˛ÃˇāĻĻ⧈āĻ°ā§āĻ˜ā§āϝ āĻāĻ•āĻ•
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📖āĻŦāĻ°ā§āĻ—āĻ•ā§āώ⧇āĻ¤ā§āĻ°đŸ“–
1.āĻŦāĻ°ā§āĻ—āĻ•ā§āώ⧇āĻ¤ā§āϰ⧇āϰ āĻ•ā§āώ⧇āĻ¤ā§āϰāĻĢāϞ = (āϝ⧇ āϕ⧋āύ āĻāĻ•āϟāĻŋ āĻŦāĻžāĻšā§āϰ āĻĻ⧈āĻ°ā§āĻ˜ā§āϝ)² āĻŦāĻ°ā§āĻ— āĻāĻ•āĻ•
2.āĻŦāĻ°ā§āĻ—āĻ•ā§āώ⧇āĻ¤ā§āϰ⧇āϰ āĻĒāϰāĻŋāϏ⧀āĻŽāĻž = 4 × āĻāĻ• āĻŦāĻžāĻšā§āϰ āĻĻ⧈āĻ°ā§āĻ˜ā§āϝ āĻāĻ•āĻ•
3.āĻŦāĻ°ā§āĻ—āĻ•ā§āώ⧇āĻ¤ā§āϰ⧇āϰ āĻ•āĻ°ā§āĻŖ=√2 × āĻāĻ• āĻŦāĻžāĻšā§āϰ āĻĻ⧈āĻ°ā§āĻ˜ā§āϝ āĻāĻ•āĻ•
4.āĻŦāĻ°ā§āĻ—āĻ•ā§āώ⧇āĻ¤ā§āϰ⧇āϰ āĻŦāĻžāĻšā§=√āĻ•ā§āώ⧇āĻ¤ā§āϰāĻĢāϞ āĻŦāĻž āĻĒāϰāĻŋāϏ⧀āĻŽāĻžÃˇ4 āĻāĻ•
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â­•đŸ—Ŗī¸āĻ¤ā§āϰāĻŋāĻ­ā§‚āĻœđŸšŠ
1.āϏāĻŽāĻŦāĻžāĻšā§ āĻ¤ā§āϰāĻŋāĻ­ā§‚āĻœā§‡āϰ āĻ•ā§āώ⧇āĻ¤ā§āϰāĻĢāϞ = √ž×(āĻŦāĻžāĻšā§)²
2.āϏāĻŽāĻŦāĻžāĻšā§ āĻ¤ā§āϰāĻŋāĻ­ā§‚āĻœā§‡āϰ āωāĻšā§āϚāϤāĻž = √3/2×(āĻŦāĻžāĻšā§)
3.āĻŦāĻŋāώāĻŽāĻŦāĻžāĻšā§ āĻ¤ā§āϰāĻŋāϭ⧁āĻœā§‡āϰ āĻ•ā§āώ⧇āĻ¤ā§āϰāĻĢāϞ = √s(s-a) (s-b) (s-c)
āĻāĻ–āĻžāύ⧇ a, b, c āĻ¤ā§āϰāĻŋāϭ⧁āĻœā§‡āϰ āϤāĻŋāύāϟāĻŋ āĻŦāĻžāĻšā§āϰ āĻĻ⧈āĻ°ā§āĻ˜ā§āϝ, s=āĻ…āĻ°ā§āϧāĻĒāϰāĻŋāϏ⧀āĻŽāĻž
★āĻĒāϰāĻŋāϏ⧀āĻŽāĻž 2s=(a+b+c)
4āϏāĻžāϧāĻžāϰāĻŖ āĻ¤ā§āϰāĻŋāĻ­ā§‚āĻœā§‡āϰ āĻ•ā§āώ⧇āĻ¤ā§āϰāĻĢāϞ = ÂŊ
(āĻ­ā§‚āĻŽāĻŋ×āωāĻšā§āϚāϤāĻž) āĻŦāĻ°ā§āĻ— āĻāĻ•āĻ•
5.āϏāĻŽāϕ⧋āĻŖā§€ āĻ¤ā§āϰāĻŋāĻ­ā§‚āĻœā§‡āϰ āĻ•ā§āώ⧇āĻ¤ā§āϰāĻĢāϞ = ÂŊ(a×b)
āĻāĻ–āĻžāύ⧇ āĻ¤ā§āϰāĻŋāϭ⧁āĻœā§‡āϰ āϏāĻŽāϕ⧋āĻŖ āϏāĻ‚āϞāĻ—ā§āύ āĻŦāĻžāĻšā§āĻĻā§āĻŦāϝāĻŧ a āĻāĻŦāĻ‚ b.
6.āϏāĻŽāĻĻā§āĻŦāĻŋāĻŦāĻžāĻšā§ āĻ¤ā§āϰāĻŋāĻ­ā§‚āĻœā§‡āϰ āĻ•ā§āώ⧇āĻ¤ā§āϰāĻĢāϞ = 2√4b²-a²/4 āĻāĻ–āĻžāύ⧇, a= āĻ­ā§‚āĻŽāĻŋ; b= āĻ…āĻĒāϰ āĻŦāĻžāĻšā§āĨ¤
7.āĻ¤ā§āϰāĻŋāϭ⧁āĻœā§‡āϰ āωāĻšā§āϚāϤāĻž = 2(āĻ•ā§āώ⧇āĻ¤ā§āϰāĻĢāϞ/āĻ­ā§‚āĻŽāĻŋ)
8.āϏāĻŽāϕ⧋āĻŖā§€ āĻ¤ā§āϰāĻŋāϭ⧁āĻœā§‡āϰ āĻ…āϤāĻŋāϭ⧁āϜ =√ āϞāĻŽā§āĻŦ²+āĻ­ā§‚āĻŽāĻŋ²
9.āϞāĻŽā§āĻŦ =√āĻ…āϤāĻŋāĻ­ā§‚āĻœÂ˛-āĻ­ā§‚āĻŽāĻŋ²
10.āĻ­ā§‚āĻŽāĻŋ = √āĻ…āϤāĻŋāĻ­ā§‚āĻœÂ˛-āϞāĻŽā§āĻŦ²
11.āϏāĻŽāĻĻā§āĻŦāĻŋāĻŦāĻžāĻšā§ āĻ¤ā§āϰāĻŋāϭ⧁āĻœā§‡āϰ āωāĻšā§āϚāϤāĻž = √b² - a²/4
āĻāĻ–āĻžāύ⧇ a= āĻ­ā§‚āĻŽāĻŋ; b= āϏāĻŽāĻžāύ āĻĻ⧁āχ āĻŦāĻžāĻšā§āϰ āĻĻ⧈āĻ°ā§āĻ˜ā§āϝāĨ¤
12.★āĻ¤ā§āϰāĻŋāϭ⧁āĻœā§‡āϰ āĻĒāϰāĻŋāϏ⧀āĻŽāĻž=āϤāĻŋāύ āĻŦāĻžāĻšā§āϰ āϏāĻŽāĻˇā§āϟāĻŋ
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â­•đŸ—Ŗī¸āϰāĻŽā§āĻŦāĻ¸đŸšŠ
1.āϰāĻŽā§āĻŦāϏ⧇āϰ āĻ•ā§āώ⧇āĻ¤ā§āϰāĻĢāϞ = ÂŊ× (āĻ•āĻ°ā§āĻŖāĻĻ⧁āχāϟāĻŋāϰ āϗ⧁āĻŖāĻĢāϞ)
2.āϰāĻŽā§āĻŦāϏ⧇āϰ āĻĒāϰāĻŋāϏ⧀āĻŽāĻž = 4× āĻāĻ• āĻŦāĻžāĻšā§āϰ āĻĻ⧈āĻ°ā§āĻ˜ā§āϝ
_____________________________________________â­•đŸ—Ŗī¸āϏāĻžāĻŽāĻžāĻ¨ā§āϤāϰāĻŋāĻ•đŸšŠ
1.āϏāĻžāĻŽāĻžāĻ¨ā§āϤāϰāĻŋāϕ⧇āϰ āĻ•ā§āώ⧇āĻ¤ā§āϰāĻĢāϞ = āĻ­ā§‚āĻŽāĻŋ × āωāĻšā§āϚāϤāĻž =
2.āϏāĻžāĻŽāĻžāĻ¨ā§āϤāϰāĻŋāϕ⧇āϰ āĻĒāϰāĻŋāϏ⧀āĻŽāĻž = 2×(āϏāĻ¨ā§āύāĻŋāĻšāĻŋāϤ āĻŦāĻžāĻšā§āĻĻā§āĻŦāϝāĻŧ⧇āϰ āϏāĻŽāĻˇā§āϟāĻŋ)
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â­•đŸ—Ŗī¸āĻŸā§āϰāĻžāĻĒāĻŋāϜāĻŋāϝāĻŧāĻžāĻŽđŸšŠ
1. āĻŸā§āϰāĻžāĻĒāĻŋāϜāĻŋāϝāĻŧāĻžāĻŽā§‡āϰ āĻ•ā§āώ⧇āĻ¤ā§āϰāĻĢāϞ =ÂŊ×(āϏāĻŽāĻžāĻ¨ā§āϤāϰāĻžāϞ āĻŦāĻžāĻšā§ āĻĻ⧁āχāϟāĻŋāϰ āϝāĻžā§‡āĻ—āĻĢāϞ)×āωāĻšā§āϚāϤāĻž
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â­•đŸ—Ŗī¸ āϘāύāĻ•đŸšŠ
1.āϘāύāϕ⧇āϰ āϘāύāĻĢāϞ = (āϝ⧇āϕ⧋āύ āĻŦāĻžāĻšā§)Âŗ āϘāύ āĻāĻ•āĻ•
2.āϘāύāϕ⧇āϰ āϏāĻŽāĻ—ā§āϰāϤāϞ⧇āϰ āĻ•ā§āώ⧇āĻ¤ā§āϰāĻĢāϞ = 6× āĻŦāĻžāĻšā§Â˛ āĻŦāĻ°ā§āĻ— āĻāĻ•āĻ•
3.āϘāύāϕ⧇āϰ āĻ•āĻ°ā§āĻŖ = √3×āĻŦāĻžāĻšā§ āĻāĻ•āĻ•
Samir Kumar Bardhan
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â­•đŸ—Ŗī¸āφāϝāĻŧāϤāϘāύāĻ•đŸšŠ
1.āφāϝāĻŧāϤāϘāύāϕ⧇āϰ āϘāύāĻĢāϞ = (āĻĻā§ˆā§°ā§āϘāĻžÃ—āĻĒā§āϰāĻ¸ā§āĻ¤Ã—āωāĻšā§āϚāϤāĻž) āϘāύ āĻāĻ•āĻ•
2.āφāϝāĻŧāϤāϘāύāϕ⧇āϰ āϏāĻŽāĻ—ā§āϰāϤāϞ⧇āϰ āĻ•ā§āώ⧇āĻ¤ā§āϰāĻĢāϞ = 2(ab + bc + ca) āĻŦāĻ°ā§āĻ— āĻāĻ•āĻ•
[ āϝ⧇āĻ–āĻžāύ⧇ a = āĻĻ⧈āĻ°ā§āĻ˜ā§āϝ b = āĻĒā§āϰāĻ¸ā§āϤ c = āωāĻšā§āϚāϤāĻž ]
3.āφāϝāĻŧāϤāϘāύāϕ⧇āϰ āĻ•āĻ°ā§āĻŖ = √a²+b²+c² āĻāĻ•āĻ•
4. āϚāĻžāϰāĻŋ āĻĻ⧇āĻ“āϝāĻŧāĻžāϞ⧇āϰ āĻ•ā§āώ⧇āĻ¤ā§āϰāĻĢāϞ = 2(āĻĻ⧈āĻ°ā§āĻ˜ā§āϝ + āĻĒā§āϰāĻ¸ā§āĻĨ)×āωāĻšā§āϚāϤāĻž
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â­•đŸ—Ŗī¸āĻŦ⧃āĻ¤ā§āĻ¤đŸšŠ
1.āĻŦ⧃āĻ¤ā§āϤ⧇āϰ āĻ•ā§āώ⧇āĻ¤ā§āϰāĻĢāϞ = Ī€r²=22/7r² {āĻāĻ–āĻžāύ⧇ Ī€=āĻ§ā§āϰ⧁āĻŦāĻ• 22/7, āĻŦ⧃āĻ¤ā§āϤ⧇āϰ āĻŦā§āϝāĻžāϏāĻžāĻ°ā§āϧ= r}
2. āĻŦ⧃āĻ¤ā§āϤ⧇āϰ āĻĒāϰāĻŋāϧāĻŋ = 2Ī€r
3. āĻ—ā§‹āϞāϕ⧇āϰ āĻĒ⧃āĻˇā§āĻ āϤāϞ⧇āϰ āĻ•ā§āώ⧇āĻ¤ā§āϰāĻĢāϞ = 4Ī€r² āĻŦāĻ°ā§āĻ— āĻāĻ•āĻ•
4. āĻ—ā§‹āϞāϕ⧇āϰ āφāϝāĻŧāϤāύ = 4Ī€rÂŗÃˇ3 āϘāύ āĻāĻ•āĻ•
5. h āωāĻšā§āϚāϤāĻžāϝāĻŧ āϤāϞāĻšā§āĻšā§‡āĻĻ⧇ āĻ‰ā§ŽāĻĒāĻ¨ā§āύ āĻŦ⧃āĻ¤ā§āϤ⧇āϰ āĻŦā§āϝāĻžāϏāĻžāĻ°ā§āϧ = √r²-h² āĻāĻ•āĻ•
6.āĻŦ⧃āĻ¤ā§āϤāϚāĻžāĻĒ⧇āϰ āĻĻ⧈āĻ°ā§āĻ˜ā§āϝ s=Ī€rθ/180° ,
āĻāĻ–āĻžāύ⧇ θ =āϕ⧋āĻŖ
Samir Kumar Bardhan
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đŸ—Ŗī¸āϏāĻŽāĻŦ⧃āĻ¤ā§āϤāĻ­ā§‚āĻŽāĻŋāĻ• āϏāĻŋāϞāĻŋāĻ¨ā§āĻĄāĻžāϰ / āĻŦ⧇āϞāĻ¨đŸšŠ
āϏāĻŽāĻŦ⧃āĻ¤ā§āϤāĻ­ā§‚āĻŽāĻŋāĻ• āϏāĻŋāϞāĻŋāĻ¨ā§āĻĄāĻžāϰ⧇āϰ āĻ­ā§‚āĻŽāĻŋāϰ āĻŦā§āϝāĻžāϏāĻžāĻ°ā§āϧ r āĻāĻŦāĻ‚ āωāĻšā§āϚāϤāĻž h āφāϰ āĻšā§‡āϞāĻžāύ⧋ āϤāϞ⧇āϰ āωāĻšā§āϚāϤāĻž l āĻšāϞ⧇,
1.āϏāĻŋāϞāĻŋāĻ¨ā§āĻĄāĻžāϰ⧇āϰ āφāϝāĻŧāϤāύ = Ī€r²h
2.āϏāĻŋāϞāĻŋāĻ¨ā§āĻĄāĻžāϰ⧇āϰ āĻŦāĻ•ā§āϰāϤāϞ⧇āϰ āĻ•ā§āώ⧇āĻ¤ā§āϰāĻĢāϞ (āϏāĻŋāĻāϏāĻ) = 2Ī€rhāĨ¤
3.āϏāĻŋāϞāĻŋāĻ¨ā§āĻĄāĻžāϰ⧇āϰ āĻĒ⧃āĻˇā§āĻ āϤāϞ⧇āϰ āĻ•ā§āώ⧇āĻ¤ā§āϰāĻĢāϞ (āϟāĻŋāĻāϏāĻ) = 2Ī€r (h + r)
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đŸ—Ŗī¸āϏāĻŽāĻŦ⧃āĻ¤ā§āϤāĻ­ā§‚āĻŽāĻŋāĻ• āϕ⧋āĻŖāĻ•đŸšŠ
āϏāĻŽāĻŦ⧃āĻ¤ā§āϤāĻ­ā§‚āĻŽāĻŋāĻ• āĻ­ā§‚āĻŽāĻŋāϰ āĻŦā§āϝāĻžāϏāĻžāĻ°ā§āϧ r āĻāĻŦāĻ‚ āωāĻšā§āϚāϤāĻž h āφāϰ āĻšā§‡āϞāĻžāύ⧋ āϤāϞ⧇āϰ āωāĻšā§āϚāϤāĻž l āĻšāϞ⧇,
1.āϕ⧋āĻŖāϕ⧇āϰ āĻŦāĻ•ā§āϰāϤāϞ⧇āϰ āĻ•ā§āώ⧇āĻ¤ā§āϰāĻĢāϞ= Ī€rl āĻŦāĻ°ā§āĻ— āĻāĻ•āĻ•
2.āϕ⧋āĻŖāϕ⧇āϰ āϏāĻŽāϤāϞ⧇āϰ āĻ•ā§āώ⧇āĻ¤ā§āϰāĻĢāϞ= Ī€r(r+l) āĻŦāĻ°ā§āĻ— āĻāĻ•āĻ•
3.āϕ⧋āĻŖāϕ⧇āϰ āφāϝāĻŧāϤāύ= â…“Ī€r²h āϘāύ āĻāĻ•āĻ•
🚩✮āĻŦāĻšā§āϭ⧁āĻœā§‡āϰ āĻ•āĻ°ā§āϪ⧇āϰ āϏāĻ‚āĻ–ā§āϝāĻž= n(n-3)/2
✮āĻŦāĻšā§āϭ⧁āĻœā§‡āϰ āϕ⧋āĻŖāϗ⧁āϞāĻŋāϰ āϏāĻŽāĻˇā§āϟāĻŋ=(2n-4)āϏāĻŽāϕ⧋āĻŖ
āĻāĻ–āĻžāύ⧇ n=āĻŦāĻžāĻšā§āϰ āϏāĻ‚āĻ–ā§āϝāĻž
★āϏ⧁āώāĻŽ āĻŦāĻšā§āϭ⧁āϜ āĻāϰ āĻ•ā§āώ⧇āĻ¤ā§āϰ⧇
āĻ…āĻ¨ā§āϤāσāϕ⧋āĻŖ + āĻŦāĻšāĻŋāσāϕ⧋āĻŖ=180°
āĻŦāĻžāĻšā§ āϏāĻ‚āĻ–ā§āϝāĻž=360°/āĻŦāĻšāĻŋāσ āϕ⧋āĻŖ
★āϚāϤ⧁āĻ°ā§āϭ⧁āĻœā§‡āϰ āĻĒāϰāĻŋāϏ⧀āĻŽāĻž=āϚāĻžāϰ āĻŦāĻžāĻšā§āϰ āϏāĻŽāĻˇā§āϟāĻŋ
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đŸ—Ŗī¸āĻ¤ā§āϰāĻŋāϕ⧋āĻŖāĻŽāĻŋāϤāĻŋāϰ āϏ⧂āĻ¤ā§āϰāĻžāĻŦāϞ⧀āĻƒđŸšŠ
1. sinθ=⤞āĻŽā§āĻŦ/āĻ…āϤāĻŋāĻ­ā§‚āϜ
2. cosθ=āĻ­ā§‚āĻŽāĻŋ/āĻ…āϤāĻŋāĻ­ā§‚āϜ
3. taneθ=⤞āĻŽā§āĻŦ/āĻ­ā§‚āĻŽāĻŋ
4. cotθ=āĻ­ā§‚āĻŽāĻŋ/āϞāĻŽā§āĻŦ
5. secθ=āĻ…āϤāĻŋāĻ­ā§‚āϜ/āĻ­ā§‚āĻŽāĻŋ
6. cosecθ=āĻ…āϤāĻŋāĻ­ā§‚āϜ/āϞāĻŽā§āĻŦ
7. sinθ=1/cosecθ, cosecθ=1/sinθ
8. cosθ=1/secθ, secθ=1/cosθ
9. tanθ=1/cotθ, cotθ=1/tanθ
10. sin²θ + cos²θ= 1
11. sin²θ = 1 - cos²θ
12. cos²θ = 1- sin²θ
13. sec²θ - tan²θ = 1
14. sec²θ = 1+ tan²θ
15. tan²θ = sec²θ - 1
16, cosec²θ - cot²θ = 1
17. cosec²θ = cot²θ + 1
18. cot²θ = cosec²θ - 1
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â­•đŸ—Ŗī¸ āĻŦāĻŋāϝāĻŧāĻžā§‡āϗ⧇āϰ āϏ⧂āĻ¤ā§āϰāĻžāĻŦāϞāĻŋ🚩
1. āĻŦāĻŋāϝāĻŧāĻžā§‡āϜāύ-āĻŦāĻŋāϝāĻŧā§‹āĻœā§āϝ =āĻŦāĻŋāϝāĻŧā§‹āĻ—āĻĢāϞāĨ¤
2.āĻŦāĻŋāϝāĻŧāĻžā§‡āϜāύ=āĻŦāĻŋāϝāĻŧāĻžā§‡āĻ—āĻĢ + āĻŦāĻŋāϝāĻŧāĻžā§‡āĻœā§āϝ
3.āĻŦāĻŋāϝāĻŧāĻžā§‡āĻœā§āϝ=āĻŦāĻŋāϝāĻŧāĻžā§‡āϜāύ-āĻŦāĻŋāϝāĻŧāĻžā§‡āĻ—āĻĢāϞ
Samir Kumar Bardhan
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â­•đŸ—Ŗī¸ āϗ⧁āϪ⧇āϰ āϏ⧂āĻ¤ā§āϰāĻžāĻŦāϞāĻŋ🚩
1.āϗ⧁āĻŖāĻĢāϞ =āϗ⧁āĻŖā§āϝ × āϗ⧁āĻŖāĻ•
2.āϗ⧁āĻŖāĻ• = āϗ⧁āĻŖāĻĢāϞ Ãˇ āϗ⧁āĻŖā§āϝ
3.āϗ⧁āĻŖā§āϝ= āϗ⧁āĻŖāĻĢāϞ Ãˇ āϗ⧁āĻŖāĻ•
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â­•đŸ—Ŗī¸ āĻ­āĻžāϗ⧇āϰ āϏ⧂āĻ¤ā§āϰāĻžāĻŦāϞāĻŋ🚩
āύāĻŋāσāĻļ⧇āώ⧇ āĻŦāĻŋāĻ­āĻžāĻœā§āϝ āύāĻž āĻšāϞ⧇āĨ¤
1.āĻ­āĻžāĻœā§āϝ= āĻ­āĻžāϜāĻ• × āĻ­āĻžāĻ—āĻĢāϞ + āĻ­āĻžāĻ—āĻļ⧇āώāĨ¤
2.āĻ­āĻžāϜāĻ•= (āĻ­āĻžāĻœā§āĻ¯â€” āĻ­āĻžāĻ—āĻļ⧇āώ) Ãˇ āĻ­āĻžāĻ—āĻĢāϞāĨ¤
3.āĻ­āĻžāĻ—āĻĢāϞ = (āĻ­āĻžāĻœā§āϝ — āĻ­āĻžāĻ—āĻļ⧇āώ)Ãˇ āĻ­āĻžāϜāĻ•āĨ¤
*āύāĻŋāσāĻļ⧇āώ⧇ āĻŦāĻŋāĻ­āĻžāĻœā§āϝ āĻšāϞ⧇āĨ¤
4.āĻ­āĻžāϜāĻ•= āĻ­āĻžāĻœā§āĻ¯Ãˇ āĻ­āĻžāĻ—āĻĢāϞāĨ¤
5.āĻ­āĻžāĻ—āĻĢāϞ = āĻ­āĻžāĻœā§āϝ Ãˇ āĻ­āĻžāϜāĻ•āĨ¤
6.āĻ­āĻžāĻœā§āϝ = āĻ­āĻžāϜāĻ• × āĻ­āĻžāĻ—āĻĢāϞāĨ¤
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â­•đŸ—Ŗī¸āĻ­āĻ—ā§āύāĻžāĻ‚āĻļ⧇āϰ āϞ.āϏāĻž.āϗ⧁ āĻ“ āĻ—.āϏāĻž.āϗ⧁ āϏ⧂āĻ¤ā§āϰāĻžāĻŦāϞ⧀ 🚩
1.āĻ­āĻ—ā§āύāĻžāĻ‚āĻļ⧇āϰ āĻ—.āϏāĻž.āϗ⧁ = āϞāĻŦāϗ⧁āϞāĻžā§‡āϰ āĻ—.āϏāĻž.āϗ⧁ / āĻšāϰāϗ⧁āϞāĻžā§‡āϰ āϞ.āϏāĻž.āϗ⧁
2.āĻ­āĻ—ā§āύāĻžāĻ‚āĻļ⧇āϰ āϞ.āϏāĻž.āϗ⧁ =āϞāĻŦāϗ⧁āϞāĻžā§‡āϰ āϞ.āϏāĻž.āϗ⧁ /āĻšāϰāϗ⧁āϞāĻžāϰ āĻ—.āϏāĻž.āϗ⧁
3.āĻ­āĻ—ā§āύāĻžāĻ‚āĻļāĻĻā§āĻŦāϝāĻŧ⧇āϰ āϗ⧁āĻŖāĻĢāϞ = āĻ­āĻ—ā§āύāĻžāĻ‚āĻļāĻĻā§āĻŦāϝāĻŧ⧇āϰ āϞ.āϏāĻž.āϗ⧁ × āĻ­āĻ—ā§āύāĻžāĻ‚āĻļāĻĻā§āĻŦāϝāĻŧ⧇āϰ āĻ—.āϏāĻž.āϗ⧁.
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đŸ—Ŗī¸āĻ—āĻĄāĻŧ āύāĻŋāĻ°ā§āĻŖāϝāĻŧ 🚩
1.āĻ—āĻĄāĻŧ = āϰāĻžāĻļāĻŋ āϏāĻŽāĻˇā§āϟāĻŋ /āϰāĻžāĻļāĻŋ āϏāĻ‚āĻ–ā§āϝāĻž
2.āϰāĻžāĻļāĻŋāϰ āϏāĻŽāĻˇā§āϟāĻŋ = āĻ—āĻĄāĻŧ ×āϰāĻžāĻļāĻŋāϰ āϏāĻ‚āĻ–ā§āϝāĻž
3.āϰāĻžāĻļāĻŋāϰ āϏāĻ‚āĻ–ā§āϝāĻž = āϰāĻžāĻļāĻŋāϰ āϏāĻŽāĻˇā§āϟāĻŋ Ãˇ āĻ—āĻĄāĻŧ
4.āφāϝāĻŧ⧇āϰ āĻ—āĻĄāĻŧ = āĻŽāĻžā§‡āϟ āφāϝāĻŧ⧇āϰ āĻĒāϰāĻŋāĻŽāĻžāĻŖ / āĻŽāĻžā§‡āϟ āϞāĻžā§‡āϕ⧇āϰ āϏāĻ‚āĻ–ā§āϝāĻž
5.āϏāĻ‚āĻ–ā§āϝāĻžāϰ āĻ—āĻĄāĻŧ = āϏāĻ‚āĻ–ā§āϝāĻžāϗ⧁āϞāĻžā§‡āϰ āϝāĻžā§‡āĻ—āĻĢāϞ /āϏāĻ‚āĻ–ā§āϝāĻžāϰ āĻĒāϰāĻŋāĻŽāĻžāύ āĻŦāĻž āϏāĻ‚āĻ–ā§āϝāĻž
6.āĻ•ā§āϰāĻŽāĻŋāĻ• āϧāĻžāϰāĻžāϰ āĻ—āĻĄāĻŧ =āĻļ⧇āώ āĻĒāĻĻ +ā§§āĻŽ āĻĒāĻĻ /2
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â­•đŸ—Ŗī¸āϏ⧁āĻĻāĻ•āώāĻžāϰ āĻĒāϰāĻŋāĻŽāĻžāύ āύāĻŋāĻ°ā§āύāϝāĻŧ⧇āϰ āϏ⧂āĻ¤ā§āϰāĻžāĻŦāĻ˛ā§€đŸšŠ
1. āϏ⧁āĻĻ = (āϏ⧁āĻĻ⧇āϰ āĻšāĻžāĻ°Ã—āφāϏāĻ˛Ã—āϏāĻŽāϝāĻŧ) Ãˇā§§ā§Ļā§Ļ
2. āϏāĻŽāϝāĻŧ = (100× āϏ⧁āĻĻ)Ãˇ (āφāϏāĻ˛Ã—āϏ⧁āĻĻ⧇āϰ āĻšāĻžāϰ)
3. āϏ⧁āĻĻ⧇āϰ āĻšāĻžāϰ = (100×āϏ⧁āĻĻ)Ãˇ(āφāϏāĻ˛Ã—āϏāĻŽāϝāĻŧ)
4. āφāϏāϞ = (100×āϏ⧁āĻĻ)Ãˇ(āϏāĻŽāϝāĻŧ×āϏ⧁āĻĻ⧇āϰ āĻšāĻžāϰ)
5. āφāϏāϞ = {100×(āϏ⧁āĻĻ-āĻŽā§‚āϞ)}Ãˇ(100+āϏ⧁āĻĻ⧇āϰ āĻšāĻžāĻ°Ã—āϏāĻŽāϝāĻŧ )
6. āϏ⧁āĻĻāĻžāϏāϞ = āφāϏāϞ + āϏ⧁āĻĻ
7. āϏ⧁āĻĻāĻžāϏāϞ = āφāϏāϞ ×(1+ āϏ⧁āĻĻ⧇āϰ āĻšāĻžāϰ)× āϏāĻŽāϝāĻŧ |[āϚāĻ•ā§āϰāĻŦ⧃āĻĻā§āϧāĻŋ āϏ⧁āĻĻ⧇āϰ āĻ•ā§āώ⧇āĻ¤ā§āϰ⧇]āĨ¤
Samir Kumar Bardhan
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â­•đŸ—Ŗī¸āϞāĻžāĻ­-āĻ•ā§āώāϤāĻŋāϰ āĻāĻŦāĻ‚ āĻ•ā§āϰāϝāĻŧ-āĻŦāĻŋāĻ•ā§āϰāϝāĻŧ⧇āϰ āϏ⧂āĻ¤ā§āϰāĻžāĻŦāĻ˛ā§€đŸšŠ
1. āϞāĻžāĻ­ = āĻŦāĻŋāĻ•ā§āϰāϝāĻŧāĻŽā§‚āĻ˛ā§āϝ-āĻ•ā§āϰāϝāĻŧāĻŽā§‚āĻ˛ā§āϝ
2.āĻ•ā§āώāϤāĻŋ = āĻ•ā§āϰāϝāĻŧāĻŽā§‚āĻ˛ā§āϝ-āĻŦāĻŋāĻ•ā§āϰāϝāĻŧāĻŽā§‚āĻ˛ā§āϝ
3.āĻ•ā§āϰāϝāĻŧāĻŽā§‚āĻ˛ā§āϝ = āĻŦāĻŋāĻ•ā§āϰāϝāĻŧāĻŽā§‚āĻ˛ā§āϝ-āϞāĻžāĻ­
āĻ…āĻĨāĻŦāĻž
āĻ•ā§āϰāϝāĻŧāĻŽā§‚āĻ˛ā§āϝ = āĻŦāĻŋāĻ•ā§āϰāϝāĻŧāĻŽā§‚āĻ˛ā§āϝ + āĻ•ā§āώāϤāĻŋ
4.āĻŦāĻŋāĻ•ā§āϰāϝāĻŧāĻŽā§‚āĻ˛ā§āϝ = āĻ•ā§āϰāϝāĻŧāĻŽā§‚āĻ˛ā§āϝ + āϞāĻžāĻ­
āĻ…āĻĨāĻŦāĻž
āĻŦāĻŋāĻ•ā§āϰāϝāĻŧāĻŽā§‚āĻ˛ā§āϝ = āĻ•ā§āϰāϝāĻŧāĻŽā§‚āĻ˛ā§āϝ-āĻ•ā§āώāϤāĻŋ
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â­•đŸ—Ŗī¸1-100 āĻĒāĻ°ā§āϝāĻ¨ā§āϤ āĻŽā§ŒāϞāĻŋāĻ• āϏāĻ‚āĻ–ā§āϝāĻžāĻŽāύ⧇ āϰāĻžāĻ–āĻžāϰ āϏāĻšāϜ āωāĻĒāĻžāϝāĻŧāĻƒđŸšŠ
āĻļāĻ°ā§āϟāĻ•āĻžāϟ :- 44 -22 -322-321
★1āĻĨ⧇āϕ⧇100āĻĒāĻ°ā§āϝāĻ¨ā§āϤ āĻŽā§ŒāϞāĻŋāĻ• āϏāĻ‚āĻ–ā§āϝāĻž=25āϟāĻŋ
★1āĻĨ⧇āϕ⧇10āĻĒāĻ°ā§āϝāĻ¨ā§āϤ āĻŽā§ŒāϞāĻŋāĻ• āϏāĻ‚āĻ–ā§āϝāĻž=4āϟāĻŋ 2,3,5,7
★11āĻĨ⧇āϕ⧇20āĻĒāĻ°ā§āϝāĻ¨ā§āϤ āĻŽā§ŒāϞāĻŋāĻ• āϏāĻ‚āĻ–ā§āϝāĻž=4āϟāĻŋ 11,13,17,19
★21āĻĨ⧇āϕ⧇30āĻĒāĻ°ā§āϝāĻ¨ā§āϤ āĻŽā§ŒāϞāĻŋāĻ• āϏāĻ‚āĻ–ā§āϝāĻž=2āϟāĻŋ 23,29
★31āĻĨ⧇āϕ⧇40āĻĒāĻ°ā§āϝāĻ¨ā§āϤ āĻŽā§ŒāϞāĻŋāĻ• āϏāĻ‚āĻ–ā§āϝāĻž=2āϟāĻŋ 31,37
★41āĻĨ⧇āϕ⧇50āĻĒāĻ°ā§āϝāĻ¨ā§āϤ āĻŽā§ŒāϞāĻŋāĻ• āϏāĻ‚āĻ–ā§āϝāĻž=3āϟāĻŋ 41,43,47
★51āĻĨ⧇āϕ⧇ 60āĻĒāĻ°ā§āϝāĻ¨ā§āϤ āĻŽā§ŒāϞāĻŋāĻ• āϏāĻ‚āĻ–ā§āϝāĻž=2āϟāĻŋ 53,59
★61āĻĨ⧇āϕ⧇70āĻĒāĻ°ā§āϝāĻ¨ā§āϤ āĻŽā§ŒāϞāĻŋāĻ• āϏāĻ‚āĻ–ā§āϝāĻž=2āϟāĻŋ 61,67
★71āĻĨ⧇āϕ⧇80 āĻĒāĻ°ā§āϝāĻ¨ā§āϤ āĻŽā§ŒāϞāĻŋāĻ• āϏāĻ‚āĻ–ā§āϝāĻž=3āϟāĻŋ 71,73,79
★81āĻĨ⧇āϕ⧇ 90āĻĒāĻ°ā§āϝāĻ¨ā§āϤ āĻŽā§ŒāϞāĻŋāĻ• āϏāĻ‚āĻ–ā§āϝāĻž=2āϟāĻŋ 83,89
★91āĻĨ⧇āϕ⧇100āĻĒāĻ°ā§āϝāĻ¨ā§āϤ āĻŽā§ŒāϞāĻŋāĻ• āϏāĻ‚āĻ–ā§āϝāĻž=1āϟāĻŋ 97
🚩1-100 āĻĒāĻ°ā§āϝāĻ¨ā§āϤ āĻŽā§ŒāϞāĻŋāĻ• āϏāĻ‚āĻ–ā§āϝāĻž 25 āϟāĻŋāσ
2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97
🚩1-100āĻĒāĻ°ā§āϝāĻ¨ā§āϤ āĻŽā§ŒāϞāĻŋāĻ• āϏāĻ‚āĻ–ā§āϝāĻžāϰ āϝ⧋āĻ—āĻĢāϞ
1060āĨ¤
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🚩1.āϕ⧋āύ āĻ•āĻŋāϛ⧁āϰ
āĻ—āϤāĻŋāĻŦ⧇āĻ—= āĻ…āϤāĻŋāĻ•ā§āϰāĻžāĻ¨ā§āϤ āĻĻā§‚āϰāĻ¤ā§āĻŦ/āϏāĻŽāϝāĻŧ
2.āĻ…āϤāĻŋāĻ•ā§āϰāĻžāĻ¨ā§āϤ āĻĻā§‚āϰāĻ¤ā§āĻŦ = āĻ—āϤāĻŋāĻŦ⧇āĻ—Ã—āϏāĻŽāϝāĻŧ
3.āϏāĻŽāϝāĻŧ= āĻŽā§‹āϟ āĻĻā§‚āϰāĻ¤ā§āĻŦ/āĻŦ⧇āĻ—
4.āĻ¸ā§āϰ⧋āϤ⧇āϰ āĻ…āύ⧁āϕ⧂āϞ⧇ āύ⧌āĻ•āĻžāϰ āĻ•āĻžāĻ°ā§āϝāĻ•āϰ⧀ āĻ—āϤāĻŋāĻŦ⧇āĻ— = āύ⧌āĻ•āĻžāϰ āĻĒā§āϰāĻ•ā§ƒāϤ āĻ—āϤāĻŋāĻŦ⧇āĻ— + āĻ¸ā§āϰ⧋āϤ⧇āϰ āĻ—āϤāĻŋāĻŦ⧇āĻ—āĨ¤
5.āĻ¸ā§āϰ⧋āϤ⧇āϰ āĻĒā§āϰāϤāĻŋāϕ⧂āϞ⧇ āύ⧌āĻ•āĻžāϰ āĻ•āĻžāĻ°ā§āϝāĻ•āϰ⧀ āĻ—āϤāĻŋāĻŦ⧇āĻ— = āύ⧌āĻ•āĻžāϰ āĻĒā§āϰāĻ•ā§ƒāϤ āĻ—āϤāĻŋāĻŦ⧇āĻ— - āĻ¸ā§āϰ⧋āϤ⧇āϰ āĻ—āϤāĻŋāĻŦ⧇āĻ—
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đŸ—Ŗī¸āϏāϰāϞ āϏ⧁āĻĻ🚩
āϝāĻĻāĻŋ āφāϏāϞ=P, āϏāĻŽāϝāĻŧ=T, āϏ⧁āĻĻ⧇āϰ āĻšāĻžāϰ=R, āϏ⧁āĻĻ-āφāϏāϞ=A āĻšāϝāĻŧ, āϤāĻžāĻšāϞ⧇
1.āϏ⧁āĻĻ⧇āϰ āĻĒāϰāĻŋāĻŽāĻžāĻŖ= PRT/100
2.āφāϏāϞ= 100×āϏ⧁āĻĻ-āφāϏāϞ(A)/100+TR
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⭕🚩āύ⧌āĻ•āĻžāϰ āĻ—āϤāĻŋ āĻ¸ā§āϰ⧋āϤ⧇āϰ āĻ…āύ⧁āϕ⧂āϞ⧇ āϘāĻ¨ā§āϟāĻžāϝāĻŧ 10 āĻ•āĻŋ.āĻŽāĻŋ. āĻāĻŦāĻ‚ āĻ¸ā§āϰ⧋āϤ⧇āϰ āĻĒā§āϰāϤāĻŋāϕ⧂āϞ⧇ 2 āĻ•āĻŋ.āĻŽāĻŋ.āĨ¤ āĻ¸ā§āϰ⧋āϤ⧇āϰ āĻŦ⧇āĻ— āĻ•āϤ?
★āĻŸā§‡āĻ•āύāĻŋāĻ•-
āĻ¸ā§āϰ⧋āϤ⧇āϰ āĻŦ⧇āĻ— = (āĻ¸ā§āϰ⧋āϤ⧇āϰ āĻ…āύ⧁āϕ⧂āϞ⧇ āύ⧌āĻ•āĻžāϰ āĻŦ⧇āĻ— - āĻ¸ā§āϰ⧋āϤ⧇āϰ āĻĒā§āϰāϤāĻŋāϕ⧂āϞ⧇ āύ⧌āĻ•āĻžāϰ āĻŦ⧇āĻ—) /2
= (10 - 2)/2=
= 4 āĻ•āĻŋ.āĻŽāĻŋ.
🚩āĻāĻ•āϟāĻŋ āύ⧌āĻ•āĻž āĻ¸ā§āϰ⧋āϤ⧇āϰ āĻ…āύ⧁āϕ⧂āϞ⧇ āϘāĻ¨ā§āϟāĻžāϝāĻŧ 8 āĻ•āĻŋ.āĻŽāĻŋ.āĻāĻŦāĻ‚ āĻ¸ā§āϰ⧋āϤ⧇āϰ āĻĒā§āϰāϤāĻŋāϕ⧂āϞ⧇ āϘāĻ¨ā§āϟāĻžāϝāĻŧ 4 āĻ•āĻŋ.āĻŽāĻŋ.
āϝāĻžāϝāĻŧāĨ¤ āύ⧌āĻ•āĻžāϰ āĻŦ⧇āĻ— āĻ•āϤ?
★ āĻŸā§‡āĻ•āύāĻŋāĻ•-
āύ⧌āĻ•āĻžāϰ āĻŦ⧇āĻ— = (āĻ¸ā§āϰ⧋āϤ⧇āϰ āĻ…āύ⧁āϕ⧂āϞ⧇ āύ⧌āĻ•āĻžāϰ āĻŦ⧇āĻ—+āĻ¸ā§āϰ⧋āϤ⧇āϰ āĻĒā§āϰāϤāĻŋāϕ⧂āϞ⧇ āύ⧌āĻ•āĻžāϰ āĻŦ⧇āĻ—)/2
= (8 + 4)/2
=6 āĻ•āĻŋ.āĻŽāĻŋ.
🚩āύ⧌āĻ•āĻž āĻ“ āĻ¸ā§āϰ⧋āϤ⧇āϰ āĻŦ⧇āĻ— āϘāĻ¨ā§āϟāĻžāϝāĻŧ āϝāĻĨāĻžāĻ•ā§āϰāĻŽā§‡ 10 āĻ•āĻŋ.āĻŽāĻŋ. āĻ“ 5 āĻ•āĻŋ.āĻŽāĻŋ.āĨ¤ āύāĻĻā§€āĻĒāĻĨ⧇ 45 āĻ•āĻŋ.āĻŽāĻŋ. āĻĒāĻĨ āĻāĻ•āĻŦāĻžāϰ āĻ—āĻŋāϝāĻŧ⧇ āĻĢāĻŋāϰ⧇ āφāϏāϤ⧇ āĻ•āϤ āϏāĻŽāϝāĻŧ āϞāĻžāĻ—āĻŦ⧇?
āĻŸā§‡āĻ•āύāĻŋāĻ•-
★āĻŽāĻžā§‡āϟ āϏāĻŽāϝāĻŧ = [(āĻŽāĻžā§‡āϟ āĻĻā§‚āϰāĻ¤ā§āĻŦ/ āĻ…āύ⧁āϕ⧂āϞ⧇ āĻŦ⧇āĻ—) + (āĻŽāĻžā§‡āϟ āĻĻā§‚āϰāĻ¤ā§āĻŦ/āĻĒā§āϰāϤāĻŋāϕ⧂āϞ⧇ āĻŦ⧇āĻ—)]
āωāĻ¤ā§āϤāϰ:āĻ¸ā§āϰ⧋āϤ⧇āϰ āĻ…āύ⧁āϕ⧂āϞ⧇ āύ⧌āĻ•āĻžāϰāĻŦ⧇āĻ— = (10+5) = 15 āĻ•āĻŋ.āĻŽāĻŋ.
āĻ¸ā§āϰ⧋āϤ⧇āϰ āĻĒā§āϰāϤāĻŋāϕ⧂āϞ⧇ āύ⧌āĻ•āĻžāϰ āĻŦ⧇āĻ— = (10-5) = 5āĻ•āĻŋ.āĻŽāĻŋ.
[(45/15) +(45/5)]
= 3+9
=12 āϘāĻ¨ā§āϟāĻž
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🚩★āϏāĻŽāĻžāĻ¨ā§āϤāϰ āϧāĻžāϰāĻžāϰ āĻ•ā§āϰāĻŽāĻŋāĻ• āϏāĻ‚āĻ–ā§āϝāĻžāϰ āϝ⧋āĻ—āĻĢāϞ-
(āϝāĻ–āύ āϏāĻ‚āĻ–ā§āϝāĻžāϟāĻŋ1 āĻĨ⧇āϕ⧇ āĻļ⧁āϰ⧁)1+2+3+4+......+n āĻšāϞ⧇ āĻāϰ⧂āĻĒ āϧāĻžāϰāĻžāϰ āϏāĻŽāĻˇā§āϟāĻŋ= [n(n+1)/2]
n=āĻļ⧇āώ āϏāĻ‚āĻ–ā§āϝāĻž āĻŦāĻž āĻĒāĻĻ āϏāĻ‚āĻ–ā§āϝāĻž s=āϝ⧋āĻ—āĻĢāϞ
🚩 āĻĒā§āϰāĻļā§āύāσ 1+2+3+....+100 =?
👍 āϏāĻŽāĻžāϧāĻžāύāσ[n(n+1)/2]
= [100(100+1)/2]
= 5050
🚩★āϏāĻŽāĻžāĻ¨ā§āϤāϰ āϧāĻžāϰāĻžāϰ āĻŦāĻ°ā§āĻ— āϝ⧋āĻ— āĻĒāĻĻā§āϧāϤāĻŋāϰ āĻ•ā§āώ⧇āĻ¤ā§āϰ⧇,-
āĻĒā§āϰāĻĨāĻŽ n āĻĒāĻĻ⧇āϰ āĻŦāĻ°ā§āϗ⧇āϰ āϏāĻŽāĻˇā§āϟāĻŋ
S= [n(n+1)2n+1)/6]
(āϝāĻ–āύ 1² + 2²+ 3² + 4²........ +n²)
🚩āĻĒā§āϰāĻļā§āύāσ(1² + 3²+ 5² + ....... +31²) āϏāĻŽāĻžāύ āĻ•āϤ?
👍āϏāĻŽāĻžāϧāĻžāύāσ S=[n(n+1)2n+1)/6]
= [31(31+1)2×31+1)/6]
=31
🚩★āϏāĻŽāĻžāĻ¨ā§āϤāϰ āϧāĻžāϰāĻžāϰ āϘāύāϝ⧋āĻ— āĻĒāĻĻā§āϧāϤāĻŋāϰ āĻ•ā§āώ⧇āĻ¤ā§āϰ⧇-
āĻĒā§āϰāĻĨāĻŽ n āĻĒāĻĻ⧇āϰ āϘāύ⧇āϰ āϏāĻŽāĻˇā§āϟāĻŋ S= [n(n+1)/2]2
(āϝāĻ–āύ 1Âŗ+2Âŗ+3Âŗ+.............+nÂŗ)
🚩āĻĒā§āϰāĻļā§āύāσ1Âŗ+2Âŗ+3Âŗ+4Âŗ+â€Ļâ€Ļâ€Ļâ€Ļ+10Âŗ=?
👍āϏāĻŽāĻžāϧāĻžāύāσ [n(n+1)/2]2
= [10(10+1)/2]2
= 3025
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🚩★āĻĒāĻĻ āϏāĻ‚āĻ–ā§āϝāĻž āĻ“ āĻĒāĻĻ āϏāĻ‚āĻ–ā§āϝāĻžāϰ āϏāĻŽāĻˇā§āϟāĻŋ āύāĻŋāĻ°ā§āύāϝāĻŧ⧇āϰ āĻ•ā§āώ⧇āĻ¤ā§āϰ⧇āσ
āĻĒāĻĻ āϏāĻ‚āĻ–ā§āϝāĻž N= [(āĻļ⧇āώ āĻĒāĻĻ â€“ āĻĒā§āϰāĻĨāĻŽ āĻĒāĻĻ)/āĻĒā§āϰāϤāĻŋ āĻĒāĻĻ⧇ āĻŦ⧃āĻĻā§āϧāĻŋ] +1
🚩āĻĒā§āϰāĻļā§āύāσ5+10+15+â€Ļâ€Ļâ€Ļâ€Ļ+50=?
👍āϏāĻŽāĻžāϧāĻžāύāσ āĻĒāĻĻāϏāĻ‚āĻ–ā§āϝāĻž = [(āĻļ⧇āώ āĻĒāĻĻ â€“ āĻĒā§āϰāĻĨāĻŽāĻĒāĻĻ)/āĻĒā§āϰāϤāĻŋ āĻĒāĻĻ⧇ āĻŦ⧃āĻĻā§āϧāĻŋ]+1
= [(50 – 5)/5] + 1
=10
āϏ⧁āϤāϰāĻžāĻ‚ āĻĒāĻĻ āϏāĻ‚āĻ–ā§āϝāĻžāϰ āϏāĻŽāĻˇā§āϟāĻŋ
= [(5 + 50)/2] ×10
= 275
🚩★ n āϤāĻŽ āĻĒāĻĻ=a + (n-1)d
āĻāĻ–āĻžāύ⧇, n =āĻĒāĻĻāϏāĻ‚āĻ–ā§āϝāĻž, a = 1āĻŽ āĻĒāĻĻ, d= āϏāĻžāϧāĻžāϰāĻŖ āĻ…āĻ¨ā§āϤāϰ
🚩āĻĒā§āϰāĻļā§āύāσ 5+8+11+14+.......āϧāĻžāϰāĻžāϟāĻŋāϰ āϕ⧋āύ āĻĒāĻĻ 302?
👍 āϏāĻŽāĻžāϧāĻžāύāσ āϧāϰāĻŋ, n āϤāĻŽ āĻĒāĻĻ =302
āĻŦāĻž, a + (n-1)d=302
āĻŦāĻž, 5+(n-1)3 =302
āĻŦāĻž, 3n=300
āĻŦāĻž, n=100
🚩āϏāĻŽāĻžāĻ¨ā§āϤāϰ āϧāĻžāϰāĻžāϰ āĻ•ā§āϰāĻŽāĻŋāĻ• āĻŦāĻŋāĻœā§‹āĻĄāĻŧ āϏāĻ‚āĻ–ā§āϝāĻžāϰ āϝ⧋āĻ—āĻĢāϞ-S=M² āĻāĻ–āĻžāύ⧇,M=āĻŽāĻ§ā§āϝ⧇āĻŽāĻž=(1āĻŽ āϏāĻ‚āĻ–ā§āϝāĻž+āĻļ⧇āώ āϏāĻ‚āĻ–ā§āϝāĻž)/2
🚩āĻĒā§āϰāĻļā§āύāσ1+3+5+.......+19=āĻ•āϤ? Biborno Sahin
👍 āϏāĻŽāĻžāϧāĻžāύāσ S=M²
={(1+19)/2}²
=(20/2)²
=100
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⭕🚩 āĻŦāĻ°ā§āĻ—đŸ‘
(1)²=1,(11)²=121,(111)²=12321,(1111)²=1234321,(11111)²=123454321
🚩👍āύāĻŋāϝāĻŧāĻŽ-āϝāϤāϗ⧁āϞ⧋ 1 āĻĒāĻžāĻļāĻžāĻĒāĻžāĻļāĻŋ āύāĻŋāϝāĻŧ⧇ āĻŦāĻ°ā§āĻ— āĻ•āϰāĻž āĻšāĻŦ⧇, āĻŦāĻ°ā§āĻ— āĻĢāϞ⧇ 1 āĻĨ⧇āϕ⧇ āĻļ⧁āϰ⧁ āĻ•āϰ⧇ āĻĒāϰ āĻĒāϰ āϏ⧇āχ āϏāĻ‚āĻ–ā§āϝāĻž āĻĒāĻ°ā§āϝāĻ¨ā§āϤ āϞāĻŋāĻ–āϤ⧇ āĻšāĻŦ⧇ āĻāĻŦāĻ‚ āϤāĻžāϰāĻĒāϰ āϏ⧇āχ āϏāĻ‚āĻ–ā§āϝāĻžāϰ āĻĒāϰ āĻĨ⧇āϕ⧇ āĻ…āϧāσāĻ•ā§āϰāĻŽā§‡ āĻĒāϰāĻĒāϰ āϏāĻ‚āĻ–ā§āϝāĻžāϗ⧁āϞ⧋ āϞāĻŋāϖ⧇ 1 āϏāĻ‚āĻ–ā§āϝāĻžāϝāĻŧ āĻļ⧇āώ āĻ•āϰāϤ⧇ āĻšāĻŦ⧇āĨ¤
🚩(3)²=9,(33)²=1089,(333)²=110889,(3333)²=11108889,(33333)²=1111088889
👍āϝāϤāϗ⧁āϞāĻŋ 3 āĻĒāĻžāĻļāĻžāĻĒāĻžāĻļāĻŋ āύāĻŋāϝāĻŧ⧇ āĻŦāĻ°ā§āĻ— āĻ•āϰāĻž āĻšāĻŦ⧇, āĻŦāĻ°ā§āĻ— āĻĢāϞ⧇ āĻāĻ•āϕ⧇āϰ āϘāϰ⧇ 9 āĻāĻŦāĻ‚ 9 āĻāϰ āĻŦāĻžāρāĻĻāĻŋāϕ⧇ āϤāĻžāϰ āĻšā§‡āϝāĻŧ⧇ (āϝāϤāϗ⧁āϞ⧋ 3 āĻĨāĻžāĻ•āĻŦ⧇) āĻāĻ•āϟāĻŋ āĻ•āĻŽ āϏāĻ‚āĻ–ā§āϝāĻ• 8, āϤāĻžāϰ āĻĒāϰ āĻŦāĻžāρāĻĻāĻŋāϕ⧇ āĻāĻ•āϟāĻŋ 0 āĻāĻŦāĻ‚ āĻŦāĻžāρāĻĻāĻŋāϕ⧇ 8 āĻāϰ āϏāĻŽāϏāĻ‚āĻ–ā§āϝāĻ• 1 āĻŦāϏāĻŦ⧇āĨ¤
🚩(6)²=36,(66)²=4356,(666)²=443556,(6666)²=44435556,(66666)²=4444355556
👍āϝāϤāϗ⧁āϞāĻŋ 6 āĻĒāĻžāĻļāĻžāĻĒāĻžāĻļāĻŋ āύāĻŋāϝāĻŧ⧇ āĻŦāĻ°ā§āĻ— āĻ•āϰāĻž āĻšāĻŦ⧇, āĻŦāĻ°ā§āĻ— āĻĢāϞ⧇ āĻāĻ•āϕ⧇āϰ āϘāϰ⧇ 6 āĻāĻŦāĻ‚ 6 āĻāϰ āĻŦāĻžāρāĻĻāĻŋāϕ⧇ āϤāĻžāϰ āĻšā§‡āϝāĻŧ⧇ (āϝāϤāϗ⧁āϞ⧋ 6 āĻĨāĻžāĻ•āĻŦ⧇) āĻāĻ•āϟāĻŋ āĻ•āĻŽ āϏāĻ‚āĻ–ā§āϝāĻ• 5, āϤāĻžāϰ āĻĒāϰ āĻŦāĻžāρāĻĻāĻŋāϕ⧇ āĻāĻ•āϟāĻŋ 3 āĻāĻŦāĻ‚ āĻŦāĻžāρāĻĻāĻŋāϕ⧇ 5 āĻāϰ āϏāĻŽāϏāĻ‚āĻ–ā§āϝāĻ• 4 āĻŦāϏāĻŦ⧇āĨ¤
🚩(9)²=81,(99)²=9801,(999)²=998001,(9999)²=99980001,(99999)²=9999800001
👍āϝāϤāϗ⧁āϞāĻŋ 9 āĻĒāĻžāĻļāĻžāĻĒāĻžāĻļāĻŋ āύāĻŋāϝāĻŧ⧇ āĻŦāĻ°ā§āĻ— āĻ•āϰāĻž āĻšāĻŦ⧇, āĻŦāĻ°ā§āĻ— āĻĢāϞ⧇ āĻāĻ•āϕ⧇āϰ āϘāϰ⧇ 1 āĻāĻŦāĻ‚ 1 āĻāϰ āĻŦāĻžāρāĻĻāĻŋāϕ⧇ āϤāĻžāϰ āĻšā§‡āϝāĻŧ⧇ (āϝāϤāϗ⧁āϞ⧋ 9 āĻĨāĻžāĻ•āĻŦ⧇) āĻāĻ•āϟāĻŋ āĻ•āĻŽ āϏāĻ‚āĻ–ā§āϝāĻ• 0, āϤāĻžāϰ āĻĒāϰ āĻŦāĻžāρāĻĻāĻŋāϕ⧇ āĻāĻ•āϟāĻŋ 8 āĻāĻŦāĻ‚ āĻŦāĻžāρāĻĻāĻŋāϕ⧇ 0 āĻāϰ āϏāĻŽāϏāĻ‚āĻ–ā§āϝāĻ• 9 āĻŦāϏāĻŦ⧇āĨ¤
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â­•đŸ—Ŗī¸đŸ‘‰āϜāύāĻ•â‰ Father
1)Numerology (āϏāĻ‚āĻ–ā§āϝāĻžāϤāĻ¤ā§āĻ¤ā§āĻŦ)- Pythagoras(āĻĒāĻŋāĻĨāĻžāĻ—ā§‹āϰāĻžāϏ)
2) Geometry(āĻœā§āϝāĻžāĻŽāĻŋāϤāĻŋ)- Euclid(āχāωāĻ•ā§āϞāĻŋāĻĄ)
3) Calculus(āĻ•ā§āϝāĻžāϞāϕ⧁āϞāĻžāϏ)- Newton(āύāĻŋāωāϟāύ)
4) Matrix(āĻŽā§āϝāĻžāĻŸā§āϰāĻŋāĻ•ā§āϏ) - Arthur Cayley(āĻ…āĻ°ā§āĻĨāĻžāϰ āĻ•ā§āϝāĻžāϞ⧇)
5)Trigonometry(āĻ¤ā§āϰāĻŋāϕ⧋āĻŖāĻŽāĻŋāϤāĻŋ)Hipparchus(āĻšāĻŋāĻĒā§āĻĒāĻžāϰāϚāĻžāϏ)
6) Asthmatic(āĻĒāĻžāϟāĻŋāĻ—āĻŖāĻŋāϤ) Brahmagupta(āĻŦā§āϰāĻšā§āĻŽāϗ⧁āĻĒā§āϤ)
7) Algebra(āĻŦā§€āϜāĻ—āĻŖāĻŋāϤ)- Muhammad ibn Musa al-Khwarizmi(āĻŽāĻžā§‡āĻšāĻžāĻŽā§āĻŽāĻĻ āĻŽā§āϏāĻž āφāϞ āĻ–āĻžāϰāĻŋāϜāĻŽā§€)
😎 Logarithm(āϞāĻ—āĻžāϰāĻŋāĻĻāĻŽ)- John Napier(āϜāύ āύ⧇āĻĒāĻŋāϝāĻŧāĻžāϰ)
9) Set theory(āϏ⧇āϟ āϤāĻ¤ā§āĻ¤ā§āĻŦ)- George Cantor(āϜāĻ°ā§āϜ āĻ•ā§āϝāĻžāĻ¨ā§āϟāϰ)
10) Zero(āĻļā§‚āĻ¨ā§āϝ)- Brahmagupta(āĻŦā§āϰāĻšā§āĻŽāϗ⧁āĻĒā§āϤ)
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🌟⭕👉āĻ…āĻ™ā§āϕ⧇āϰ āχāĻ‚āϰ⧇āϜāĻŋ āĻļāĻŦā§āĻĻ
āĻĒāĻžāϟāĻŋāĻ—āĻŖāĻŋāϤ āĻ“ āĻĒāϰāĻŋāĻŽāĻŋāϤāĻŋ
āĻ…āĻ™ā§āĻ•-Digit, āĻ…āύ⧁āĻĒāĻžāϤ-Ratio, āĻŽā§ŒāϞāĻŋāĻ• āϏāĻ‚āĻ–ā§āϝāĻžâ€”Prime number, āĻĒā§‚āĻ°ā§āĻŖāĻŦāĻ°ā§āĻ—-Perfect square,āĻ‰ā§ŽāĻĒāĻžāĻĻāĻ•-Factor,āĻ•ā§āϰāĻŽāĻŋāĻ• āϏāĻŽāĻžāύ⧁āĻĒāĻžāĻ¤ā§€â€”Continued proportion, āĻ•ā§āϰāϝāĻŧāĻŽā§‚āĻ˛ā§āϝ -Cost price, āĻ•ā§āώāϤāĻŋ-Loss, āĻ—āĻĄāĻŧ-Average, āĻ—āϤāĻŋāĻŦ⧇āĻ—-Velocity, āϗ⧁āĻŖāĻĢāϞ-Product, āĻ—,āϏāĻž,āϗ⧁-Highest Common Factor, āϘāĻžāϤ-Power, āϘāύāĻŽā§‚āĻ˛â€”Cube root, āϘāύāĻ•-Cube, āϘāύāĻĢāϞ-Volume, āĻĒā§‚āĻ°ā§āύāϏāĻ‚āĻ–ā§āϝāĻž-Integer, āϚāĻžāĻĒ-Arc, āĻšā§‹āĻ™-Cylinder, āĻœā§āϝāĻž-Chord, āĻœā§‹āĻĄāĻŧ āϏāĻ‚āĻ–ā§āϝāĻž-Even number, āĻ§ā§āϰ⧁āĻŦāĻ•-Constant, āĻĒāϰāĻŋāϏ⧀āĻŽāĻž-Perimeter, āĻŦāĻžāĻ¸ā§āϤāĻŦ-Real, āĻŦāĻ°ā§āĻ—āĻŽā§‚āϞ-Square root, āĻŦā§āϝāĻ¸ā§āϤ āĻ…āύ⧁āĻĒāĻžāĻ¤â€”Inverse ratio, āĻŦāĻŋāĻœā§‹āĻĄāĻŧāϏāĻ‚āĻ–ā§āϝāĻžâ€”Odd number, āĻŦāĻŋāĻ•ā§āϰāϝāĻŧāĻŽā§‚āĻ˛ā§āϝ -Selling price, āĻŦā§€āϜāĻ—āĻŖāĻŋāĻ¤â€”Algebra, āĻŽā§‚āϞāĻĻ Rational, āĻŽāĻ§ā§āϝ āϏāĻŽāĻžāύ⧁āĻĒāĻžāϤ⧀ -Mean proportional, āϝāĻžā§‡āĻ—āĻĢāϞ=Sum
āϞ,āϏāĻž,āϗ⧁-Lowest Common Multiple, āϞāĻŦ-Numerator, āĻļāϤāĻ•āϰāĻž-Percentage, āϏāĻŽāĻžāύ⧁āĻĒāĻžāϤ-Proportion, āϏāĻŽāĻžāύ⧁āĻĒāĻžāϤ⧀-Proportional, āϏ⧁āĻĻ-Interest, āĻšāϰ-Denominator,
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â¤ī¸āĻœā§āϝāĻžāĻŽāĻŋāϤāĻŋ
āĻ…āϤāĻŋāĻ­ā§‚āĻœâ€”Hypotenuse, āĻ…āĻ¨ā§āϤāσāϕ⧋āĻŖ-Internal angle, āĻ…āĻ°ā§āϧāĻŦ⧃āĻ¤ā§āϤ-Semi-circle, āĻ…āĻ¨ā§āϤ āĻŦā§āϝāĻžāϏāĻžāĻ°ā§āϧ-In-radius, āφāϝāĻŧāϤāĻ•ā§āώ⧇āĻ¤ā§āϰ-Rectangle, āωāĻšā§āϚāϤāĻž-Height, āĻ•āĻ°ā§āĻŖâ€“Diagonal, āϕ⧋āĻŖ-Angle, āϕ⧇āĻ¨ā§āĻĻā§āϰ-Centre, āĻ—āĻžā§‡āϞāĻ•-Sphere, āϚāϤ⧁āĻ°ā§āϭ⧁āϜ-Quadrilateral, āĻšā§‹āĻ™-Cylinder,āĻœā§āϝāĻžāĻŽāĻŋāϤāĻŋ-Geometry,āĻĻ⧈āĻ°ā§āĻ˜ā§āϝ-Length, āĻĒāĻžā§āϚāĻ­ā§‚āϜ -Pentagon, āĻĒā§āϰāĻ¸ā§āĻĨ-Breadth
āĻĒā§‚āϰāĻ•āϕ⧋āύ-Complementary angles, āĻŦāĻžāĻšā§-Side, āĻŦ⧃āĻ¤ā§āϤ-Circle, āĻŦā§āϝāĻžāϏāĻžāĻ°ā§āϧ-Radius, āĻŦā§āϝāĻžāϏ-Diameter, āĻŦāĻšā§āĻ­ā§‚āϜ-Polygon, āĻŦāĻ°ā§āĻ—āĻ•ā§āώ⧇āĻ¤ā§āĻ°â€”Square, āĻŦāĻšāĻŋ:āĻ¸ā§āĻĨ External, āĻļāĻ™ā§āϕ⧁-Cone, āϏāĻŽāϕ⧋āĻŖ-Right angle, āϏāĻŽāĻŦāĻžāĻšā§ āĻ¤ā§āϰāĻŋāĻ­ā§‚āϜ-Equilateral triangle, āĻ…āϏāĻŽāĻŦāĻžāĻšā§ āĻ¤ā§āϰāĻŋāĻ­ā§‚āĻœâ€”Scalene triangle, āϏāĻŽāĻĻā§āĻŦāĻŋāĻŦāĻžāĻšā§ āĻ¤ā§āϰāĻŋāĻ­ā§‚āϜ-isosceles Triangle,āϏāĻŽāϕ⧋āĻŖā§€ āĻ¤ā§āϰāĻŋāϭ⧁āϜ Right angled triangle, āϏ⧂āĻ•ā§āĻˇā§āĻŽāϕ⧋āĻŖā§€-Acute angled triangle, āĻ¸ā§āĻĨā§‚āϞāϕ⧋āĻŖā§€ āĻ¤ā§āϰāĻŋāϭ⧁āϜ Obtuse angled triangle, āϏāĻŽāĻžāĻ¨ā§āϤāϰāĻžāĻ˛â€”Parallel, āϏāϰāϞāϰ⧇āĻ–āĻžâ€”Straight line, āϏāĻŽā§āĻĒā§‚āϰāĻ• āϕ⧋āĻŖâ€”Supplementary angles, āϏāĻĻ⧃āĻļāϕ⧋āĻŖā§€-Equiangular
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🚩āϰ⧋āĻŽāĻžāύ āϏāĻ‚āĻ–ā§āϝāĻžâ‰  Roman numerals )
1:I
2: II
3: III
4: IV
5: V
6: VI
7: VII
8: VIII
9: IX
10: X
11: XI
12: XII
13: XIII
14: XIV
15: XV
16: XVI
17: XVII
18: XVIII
19: XIX
20: XX
30: ###
40: XL
50: L
60: LX
70: LXX
80: L###
90: XC
100: C
200: CC
300: CCC
400: CD
500: D
600: DC
700: DCC
800: DCCC
900: CM
1000:M
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â­•đŸ—Ŗī¸1. āĻœā§‹āĻĄāĻŧ āϏāĻ‚āĻ–ā§āϝāĻž + āĻœā§‹āĻĄāĻŧ āϏāĻ‚āĻ–ā§āϝāĻž = āĻœā§‹āĻĄāĻŧ
āϏāĻ‚āĻ–ā§āϝāĻžāĨ¤
āϝ⧇āĻŽāύāσ 2 + 6 = 8.
đŸ—Ŗī¸2. āĻœā§‹āĻĄāĻŧ āϏāĻ‚āĻ–ā§āϝāĻž + āĻŦāĻŋāĻœā§‹āĻĄāĻŧ āϏāĻ‚āĻ–ā§āϝāĻž = (āĻŦāĻŋāĻŦāĻ°ā§āĻŖ āĻļāĻžāĻšā§€āύ)
āĻŦāĻŋāĻœā§‹āĻĄāĻŧ āϏāĻ‚āĻ–ā§āϝāĻžāĨ¤
āϝ⧇āĻŽāύāσ 6 + 7 = 13.
đŸ—Ŗī¸3. āĻŦāĻŋāĻœā§‹āĻĄāĻŧ āϏāĻ‚āĻ–ā§āϝāĻž + āĻŦāĻŋāĻœā§‹āĻĄāĻŧ āϏāĻ‚āĻ–ā§āϝāĻž =
āĻœā§‹āĻĄāĻŧ āϏāĻ‚āĻ–ā§āϝāĻžāĨ¤
āϝ⧇āĻŽāύāσ 3 + 5 = 8.
đŸ—Ŗī¸4. āĻœā§‹āĻĄāĻŧ āϏāĻ‚āĻ–ā§āϝāĻž × āĻœā§‹āĻĄāĻŧ āϏāĻ‚āĻ–ā§āϝāĻž = āĻœā§‹āĻĄāĻŧ
āϏāĻ‚āĻ–ā§āϝāĻžāĨ¤
āϝ⧇āĻŽāύāσ 6 × 8 = 48.
đŸ—Ŗī¸5.āĻœā§‹āĻĄāĻŧ āϏāĻ‚āĻ–ā§āϝāĻž × āĻŦāĻŋāĻœā§‹āĻĄāĻŧ āϏāĻ‚āĻ–ā§āϝāĻž = āĻœā§‹āĻĄāĻŧ
āϏāĻ‚āĻ–ā§āϝāĻžāĨ¤
āϝ⧇āĻŽāύāσ 6 × 7 = 42
đŸ—Ŗī¸6.āĻŦāĻŋāĻœā§‹āĻĄāĻŧ āϏāĻ‚āĻ–ā§āϝāĻž × āĻŦāĻŋāĻœā§‹āĻĄāĻŧ āϏāĻ‚āĻ–ā§āϝāĻž =
āĻŦāĻŋāĻœā§‹āĻĄāĻŧ āϏāĻ‚āĻ–ā§āϝāĻžāĨ¤
āϝ⧇āĻŽāύāσ 3 × 9 = 27
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⭕👉āĻ•ā§āϝāĻžāϞāϕ⧁āϞ⧇āϟāϰ āĻ›āĻžāĻĄāĻŧāĻž āϝ⧇ āϕ⧋āύ āϏāĻ‚āĻ–ā§āϝāĻžāϕ⧇ āĻ­āĻžāĻ— āĻ•āϰāĻžāϰ āĻāĻ•āϟāĻŋ effective āĻŸā§‡āĻ•āύāĻŋāĻ•!
🌟 āĻ•ā§āϝāĻžāϞāϕ⧁āϞ⧇āϟāϰ āĻ›āĻžāĻĄāĻŧāĻž āϝ⧇ āϕ⧋āύ āϏāĻ‚āĻ–ā§āϝāĻžāϕ⧇ 5 āĻĻāĻŋāϝāĻŧ⧇ āĻ­āĻžāĻ— āĻ•āϰāĻžāϰ āĻāĻ•āϟāĻŋ effective āĻŸā§‡āĻ•āύāĻŋāĻ•
1.🚩 13/5= 2.6 (āĻ•ā§āϝāĻžāϞāϕ⧁āϞ⧇āϟāϰ āĻ›āĻžāĻĄāĻŧāĻž āĻŽāĻžāĻ¤ā§āϰ ā§Š āϏ⧇āϕ⧇āĻ¨ā§āĻĄā§‡ āĻāϟāĻŋ āϏāĻŽāĻžāϧāĻžāύ āĻ•āϰāĻž āϝāĻžāϝāĻŧ)
⭕★āĻŸā§‡āĻ•āύāĻŋāĻ•āσ
5 āĻĻāĻŋāϝāĻŧ⧇ āϝ⧇ āϏāĻ‚āĻ–ā§āϝāĻžāϕ⧇ āĻ­āĻžāĻ— āĻ•āϰāĻŦ⧇āύ āϤāĻžāϕ⧇ 2 āĻĻāĻŋāϝāĻŧ⧇ āϗ⧁āĻŖ āĻ•āϰ⧁āύ āϤāĻžāϰāĻĒāϰ āĻĄāĻžāύāĻĻāĻŋāĻ• āĻĨ⧇āϕ⧇ 1 āϘāϰ āφāϗ⧇ āĻĻāĻļāĻŽāĻŋāĻ• āĻŦāϏāĻŋāϝāĻŧ⧇ āĻĻāĻŋāύāĨ¤ āĻ•āĻžāϜ āĻļ⧇āώ!!! 13*2=26, āϤāĻžāϰāĻĒāϰ āĻĨ⧇āϕ⧇ 1 āϘāϰ āφāϗ⧇ āĻĻāĻļāĻŽāĻŋāĻ• āĻŦāϏāĻŋāϝāĻŧ⧇ āĻĻāĻŋāϞ⧇ 2.6 āĨ¤
2.🚩 213/5=42.6 (213*2=426)
0.03/5= 0.006 (0.03*2=0.06 āϝāĻžāϰ āĻāĻ•āϘāϰ āφāϗ⧇ āĻĻāĻļāĻŽāĻŋāĻ• āĻŦāϏāĻžāϞ⧇ āĻšāϝāĻŧ 0.006) 333,333,333/5= 66,666,666.6 (āĻāχ āϗ⧁āϞāĻž āĻ•āϰāϤ⧇ āφāĻŦāĻžāϰ āĻ•ā§āϝāĻžāϞāϕ⧁āϞ⧇āϟāϰ āϞāĻžāϗ⧇ āύāĻž āĻ•āĻŋ!)
3.🚩 12,121,212/5= 2,424,242.4
āĻāĻŦāĻžāϰ āύāĻŋāĻœā§‡ āχāĻšā§āϛ⧇āĻŽāϤ 5 āĻĻāĻŋāϝāĻŧ⧇ āϝ⧇ āϕ⧋āύ āϏāĻ‚āĻ–ā§āϝāĻžāϕ⧇ āĻ­āĻžāĻ— āĻ•āϰ⧇ āĻĻ⧇āϖ⧁āύ
🌟👉 āĻ•ā§āϝāĻžāϞāϕ⧁āϞ⧇āϟāϰ āĻ›āĻžāĻĄāĻŧāĻž āϝ⧇ āϕ⧋āύ āϏāĻ‚āĻ–ā§āϝāĻžāϕ⧇ 25 āĻĻāĻŋāϝāĻŧ⧇ āĻ­āĻžāĻ— āĻ•āϰāĻžāϰ āĻāĻ•āϟāĻŋ effective āĻŸā§‡āĻ•āύāĻŋāĻ•
1.🚩 13/25=0.52 (āĻ•ā§āϝāĻžāϞāϕ⧁āϞ⧇āϟāϰ āĻ›āĻžāĻĄāĻŧāĻž āĻāϟāĻŋāĻ“ āϏāĻŽāĻžāϧāĻžāύ āĻ•āϰāĻž āϝāĻžāϝāĻŧ)
⭕★āĻŸā§‡āĻ•āύāĻŋāĻ•āσ
25 āĻĻāĻŋāϝāĻŧ⧇ āϝ⧇ āϏāĻ‚āĻ–ā§āϝāĻžāϕ⧇ āĻ­āĻžāĻ— āĻ•āϰāĻŦ⧇āύ āϤāĻžāϕ⧇ 4 āĻĻāĻŋāϝāĻŧ⧇ āϗ⧁āĻŖ āĻ•āϰ⧁āύ āϤāĻžāϰāĻĒāϰ āĻĄāĻžāύāĻĻāĻŋāĻ• āĻĨ⧇āϕ⧇ 2 āϘāϰ āφāϗ⧇ āĻĻāĻļāĻŽāĻŋāĻ• āĻŦāϏāĻŋāϝāĻŧ⧇ āĻĻāĻŋāύāĨ¤ 13*4=52, āϤāĻžāϰāĻĒāϰ āĻĨ⧇āϕ⧇ 2 āϘāϰ āφāϗ⧇ āĻĻāĻļāĻŽāĻŋāĻ• āĻŦāϏāĻŋāϝāĻŧ⧇ āĻĻāĻŋāϞ⧇ 0.52 āĨ¤
02.🚩 210/25 = 8.40
03.🚩 0.03/25 = 0.0012
04.🚩 222,222/25 = 8,888.88
05🚩. 13,121,312/25 = 524,852.48
⭕👉 āĻ•ā§āϝāĻžāϞāϕ⧁āϞ⧇āϟāϰ āĻ›āĻžāĻĄāĻŧāĻž āϝ⧇ āϕ⧋āύ āϏāĻ‚āĻ–ā§āϝāĻžāϕ⧇ 125 āĻĻāĻŋāϝāĻŧ⧇ āĻ­āĻžāĻ— āĻ•āϰāĻžāϰ āĻāĻ•āϟāĻŋ effective āĻŸā§‡āĻ•āύāĻŋāĻ•
01.🚩 7/125 = 0.056
⭕★āĻŸā§‡āĻ•āύāĻŋāĻ•āσ
125 āĻĻāĻŋāϝāĻŧ⧇ āϝ⧇ āϏāĻ‚āĻ–ā§āϝāĻžāϕ⧇ āĻ­āĻžāĻ— āĻ•āϰāĻŦ⧇āύ āϤāĻžāϕ⧇ 8 āĻĻāĻŋāϝāĻŧ⧇ āϗ⧁āĻŖ āĻ•āϰ⧁āύ āϤāĻžāϰāĻĒāϰ āĻĄāĻžāύāĻĻāĻŋāĻ• āĻĨ⧇āϕ⧇ 3 āϘāϰ āφāϗ⧇ āĻĻāĻļāĻŽāĻŋāĻ• āĻŦāϏāĻŋāϝāĻŧ⧇ āĻĻāĻŋāύāĨ¤ āĻ•āĻžāϜ āĻļ⧇āώ! 7*8=56, āϤāĻžāϰāĻĒāϰ āĻĨ⧇āϕ⧇ 3 āϘāϰ āφāϗ⧇ āĻĻāĻļāĻŽāĻŋāĻ• āĻŦāϏāĻŋāϝāĻŧ⧇ āĻĻāĻŋāϞ⧇ 0.056 āĨ¤
02.🚩 111/125 = 0.888
03.🚩 600/125 = 4.800
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â­•đŸ—Ŗī¸đŸ‘‰āφāϏ⧁āύ āϏāĻšāĻœā§‡ āĻ•āϰāĻŋ
āϟāĻĒāĻŋāĻ•āσ 10 āϏ⧇āϕ⧇āĻ¨ā§āĻĄā§‡ āĻŦāĻ°ā§āĻ—āĻŽā§‚āϞ āύāĻŋāĻ°ā§āĻŖāϝāĻŧāĨ¤
āĻŦāĻŋāσāĻĻā§āϰāσ āϝ⧇ āϏāĻ‚āĻ–ā§āϝāĻžāϗ⧁āϞ⧋āϰ āĻŦāĻ°ā§āĻ—āĻŽā§‚āϞ 1 āĻĨ⧇āϕ⧇ 99 āĻāϰ āĻŽāĻ§ā§āϝ⧇ āĻāχ āĻĒāĻĻā§āϧāϤāĻŋāϤ⧇ āϤāĻžāĻĻ⧇āϰ āĻŦ⧇āϰ āĻ•āϰāĻž āϝāĻžāĻŦ⧇ āϖ⧁āĻŦ āϏāĻšāĻœā§‡āχāĨ¤ āĻĒā§āϰāĻļā§āύ⧇ āĻ…āĻŦāĻļā§āϝāχ āĻĒā§‚āĻ°ā§āĻŖāĻŦāĻ°ā§āĻ— āϏāĻ‚āĻ–ā§āϝāĻž āĻĨāĻžāĻ•āĻž āϞāĻžāĻ—āĻŦ⧇āĨ¤ āĻ…āĻ°ā§āĻĨāĻžā§Ž āωāĻ¤ā§āϤāϰ āϝāĻĻāĻŋ āĻĻāĻļāĻŽāĻŋāĻ• āĻ­āĻ—ā§āύāĻžāĻ‚āĻļ āφāϏ⧇ āϤāĻŦ⧇ āĻāχ āĻĒāĻĻā§āĻŦāϤāĻŋ āĻ•āĻžāĻœā§‡ āφāϏāĻŦ⧇āύāĻžāĨ¤
āĻ…āĻŦāĻļā§āϝāχ āĻŽāύ⧋āϝ⧋āĻ— āĻĻāĻŋāϝāĻŧ⧇ āĻĒāĻĄāĻŧāϤ⧇ āĻšāĻŦ⧇ āĻāĻŦāĻ‚ āĻĒā§āĻ°ā§āϝāĻžāĻ•āϟāĻŋāϏ āĻ•āϰāϤ⧇ āĻšāĻŦ⧇āĨ¤ āύāϝāĻŧāϤ āϭ⧁āϞ⧇ āϝāĻžāĻŦ⧇āύāĨ¤
āϤāĻŦ⧇ āφāϏ⧁āύ āĻļ⧁āϰ⧁ āĻ•āϰāĻž āϝāĻžāĻ•āĨ¤ āĻļ⧁āϰ⧁āϤ⧇ 1 āĻĨ⧇āϕ⧇ 9 āĻĒāĻ°ā§āϝāĻ¨ā§āϤ āϏāĻ‚āĻ–ā§āϝāĻžāϰ āĻŦāĻ°ā§āĻ— āĻŽā§āĻ–āĻ¸ā§āĻĨ āĻ•āϰ⧇ āύāĻŋāχāĨ¤ āφāĻļāĻž āĻ•āϰāĻŋ āĻāϗ⧁āϞ⧋ āϏāĻŦāĻžāχ āϜāĻžāύ⧇āύāĨ¤ āϏ⧁āĻŦāĻŋāϧāĻžāϰ āϜāĻ¨ā§āϝ⧇ āφāĻŽāĻŋ āύāĻŋāĻšā§‡ āϞāĻŋāϖ⧇ āĻĻāĻŋāĻšā§āĻ›āĻŋ-
1 square = 1, 2 square = 4
3 square = 9, 4 square = 16
5 square = 25, 6 square = 36
7 square = 49, 8 square = 64
9 square = 81
āĻāĻ–āĻžāύ⧇ āĻĒā§āϰāĻ¤ā§āϝ⧇āĻ•āϟāĻž āĻŦāĻ°ā§āĻ— āϏāĻ‚āĻ–ā§āϝāĻžāϰ āĻĻāĻŋāϕ⧇ āϖ⧇āϝāĻŧāĻžāϞ āĻ•āϰāϞ⧇ āĻĻ⧇āĻ–āĻŦ⧇āύ, āϏāĻŦāĻžāϰ āĻļ⧇āώ⧇āϰ āĻ…āĻ‚āĻ•āϟāĻŋāϰ āĻ•ā§āώ⧇āĻ¤ā§āϰ⧇ -
★1 āφāϰ 9 āĻāϰ āĻŦāĻ°ā§āϗ⧇āϰ āĻļ⧇āώ āĻ…āĻ‚āĻ• āĻŽāĻŋāϞ āφāϛ⧇ (1, 81)
★2 āφāϰ 8 āĻāϰ āĻŦāĻ°ā§āϗ⧇āϰ āĻļ⧇āώ āĻ…āĻ‚āĻ• āĻŽāĻŋāϞ āφāϛ⧇(4, 64)
★3 āφāϰ 7 āĻāϰ āĻŦāĻ°ā§āϗ⧇āϰ āĻļ⧇āώ āĻ…āĻ‚āĻ• āĻŽāĻŋāϞ āφāϛ⧇ (9, 49);
★4 āφāϰ 6 āĻāϰ āĻŦāĻ°ā§āϗ⧇āϰ āĻļ⧇āώ āĻ…āĻ‚āĻ• āĻŽāĻŋāϞ āφāϛ⧇(16, 36);
āĻāĻŦāĻ‚ 5 āĻāĻ•āĻž frown emoticon
āĻāĻĻā§āĻĻ⧁āϰ āĻĒāĻ°ā§āϝāĻ¨ā§āϤ āĻŦ⧁āĻāϤ⧇ āϝāĻĻāĻŋ āϕ⧋āύ āϏāĻŽāĻ¸ā§āϝāĻž āĻĨāĻžāϕ⧇ āϤāĻŦ⧇ āφāĻŦāĻžāϰ āĻĒāĻĄāĻŧ⧇ āύāĻŋāύāĨ¤
đŸ—Ŗī¸āωāĻĻāĻžāĻšāϰāĻŖ:- 576 āĻāϰ āĻŦāĻ°ā§āĻ—āĻŽā§‚āϞ āύāĻŋāĻ°ā§āĻŖāϝāĻŧ āĻ•āϰ⧁āύāĨ¤
👉āĻĒā§āϰāĻĨāĻŽ āϧāĻžāĻĒāσ āϝ⧇ āϏāĻ‚āĻ–ā§āϝāĻžāϰ āĻŦāĻ°ā§āĻ—āĻŽā§‚āϞ āύāĻŋāĻ°ā§āĻŖāϝāĻŧ āĻ•āϰāϤ⧇ āĻšāĻŦ⧇ āϤāĻžāϰ āĻāĻ•āϕ⧇āϰ āϘāϰ⧇āϰ āĻ…āĻ‚āĻ•āϟāĻŋ āĻĻ⧇āĻ–āĻŦ⧇āύāĨ¤ āĻāĻ•ā§āώ⧇āĻ¤ā§āϰ⧇ āϤāĻž āĻšāĻšā§āϛ⧇ '6' āĨ¤
👉 āĻĻā§āĻŦāĻŋāϤ⧀āϝāĻŧ āϧāĻžāĻĒāσ āωāĻĒāϰ⧇āϰ āϞāĻŋāĻ¸ā§āϟ āĻĨ⧇āϕ⧇ āϏ⧇ āϏāĻ‚āĻ–ā§āϝāĻžāϰ āĻŦāĻ°ā§āϗ⧇āϰ āĻļ⧇āώ āĻ…āĻ‚āĻ• 6 āϤāĻžāĻĻ⧇āϰ āύāĻŋāĻŦ⧇āύāĨ¤ āĻāĻ•ā§āώ⧇āĻ¤ā§āϰ⧇ 4 āĻāĻŦāĻ‚ 6 āĨ¤ āφāĻŦāĻžāϰ āĻŦāϞāĻŋ, āϖ⧇āϝāĻŧāĻžāϞ āĻ•āϰ⧁āύ- 4 āĻāĻŦāĻ‚ 6 āĻāϰ āĻŦāĻ°ā§āĻ— āϝāĻĨāĻžāĻ•ā§āϰāĻŽā§‡ 16 āĻāĻŦāĻ‚ 36; āϝāĻžāĻĻ⧇āϰ āĻāĻ•āϕ⧇āϰ āϘāϰ⧇āϰ āĻ…āĻ‚āĻ• āĻ•āĻŋāύāĻž '6' āĨ¤ āĻŦ⧁āĻāϤ⧇ āĻĒ⧇āϰ⧇āϛ⧇āύ? āύāĻž āĻŦ⧁āĻāϞ⧇ āφāĻŦāĻžāϰ āĻĒāĻĄāĻŧ⧇ āĻĻ⧇āϖ⧁āύāĨ¤
👉 āϤ⧃āϤ⧀āϝāĻŧ āϧāĻžāĻĒāσ 4 / 6 āϞāĻŋāϖ⧇ āϰāĻžāϖ⧁āύ āĻ–āĻžāϤāĻžāϝāĻŧāĨ¤ (āφāĻŽāϰāĻž āωāĻ¤ā§āϤāϰ⧇āϰ āĻāĻ•āϕ⧇āϰ āϘāϰ⧇āϰ āĻ…āĻ‚āĻ• āĻĒ⧇āϝāĻŧ⧇ āϗ⧇āĻ›āĻŋ, āϝāĻž āĻšāĻšā§āϛ⧇ 4 āĻ…āĻĨāĻŦāĻž 6; āĻ•āĻŋāĻ¨ā§āϤ⧁ āϕ⧋āύāϟāĻž? āĻāϰ āωāĻ¤ā§āϤāϰ āĻĒāĻžāĻŦ⧇āύ āĻ…āĻˇā§āϟāĻŽ āϧāĻžāĻĒ⧇, āĻĒāĻĄāĻŧāϤ⧇ āĻĨāĻžāϕ⧁āύ ...)
👉 āϚāϤ⧁āĻ°ā§āĻĨ āϧāĻžāĻĒāσ āĻĒā§āϰāĻļā§āύ⧇āϰ āĻāĻ•āĻ• āφāϰ āĻĻāĻļāϕ⧇āϰ āĻ…āĻ‚āĻ• āĻŦāĻžāĻĻ āĻĻāĻŋāϝāĻŧ⧇ āĻŦāĻžāĻ•āĻŋ āĻ…āĻ‚āϕ⧇āϰ āĻĻāĻŋāϕ⧇ āϤāĻžāĻ•āĻžāύāĨ¤ āĻāĻ•ā§āώ⧇āĻ¤ā§āϰ⧇ āĻāϟāĻŋ āĻšāĻšā§āϛ⧇ 5 āĨ¤
👉āĻĒāĻžā§āϚāĻŽ āϧāĻžāĻĒāσ āωāĻĒāϰ⧇āϰ āϞāĻŋāĻ¸ā§āϟ āĻĨ⧇āϕ⧇ 5 āĻāϰ āĻ•āĻžāĻ›āĻžāĻ•āĻžāĻ›āĻŋ āϝ⧇ āĻŦāĻ°ā§āĻ— āϏāĻ‚āĻ–ā§āϝāĻžāϟāĻŋ āφāϛ⧇ āϤāĻžāϰ āĻŦāĻ°ā§āĻ—āĻŽā§‚āϞāϟāĻž āύāĻŋāύāĨ¤ āĻāĻ•ā§āώ⧇āĻ¤ā§āϰ⧇ 4, āϝāĻž āĻ•āĻŋāύāĻž 2 āĻāϰ āĻŦāĻ°ā§āĻ—āĨ¤ (āφāĻŽāϰāĻž āωāĻ¤ā§āϤāϰ⧇āϰ āĻĻāĻļāϕ⧇āϰ āϘāϰ⧇āϰ āĻ…āĻ‚āĻ• āĻĒ⧇āϝāĻŧ⧇ āϗ⧇āĻ›āĻŋ, āϝāĻž āĻšāĻšā§āϛ⧇ 2 )
👉āώāĻˇā§āĻ  āϧāĻžāĻĒāσ 2 āĻāϰ āϏāĻžāĻĨ⧇ āϤāĻžāϰ āĻĒāϰ⧇āϰ āϏāĻ‚āĻ–ā§āϝāĻž āϗ⧁āύ āĻ•āϰ⧁āύāĨ¤ āĻ…āĻ°ā§āĻĨāĻžā§Ž 2*3=6
👉āϏāĻĒā§āϤāĻŽ āϧāĻžāĻĒāσ āϚāϤ⧁āĻ°ā§āĻĨ āϧāĻžāĻĒ⧇ āĻĒāĻžāĻ“āϝāĻŧāĻž āϏāĻ‚āĻ–ā§āϝāĻžāϟāĻž (5) āώāĻˇā§āĻ  āϧāĻžāĻĒ⧇ āĻĒāĻžāĻ“āϝāĻŧāĻž āϏāĻ‚āĻ–ā§āϝāĻžāϰ (6) āĻšā§‡āϝāĻŧ⧇ āϛ⧋āϟ āύāĻžāĻ•āĻŋ āĻŦāĻĄāĻŧ āĻĻ⧇āϖ⧁āύāĨ¤ āϛ⧋āϟ āĻšāϞ⧇ āϤ⧃āϤ⧀āϝāĻŧ āϧāĻžāĻĒ⧇ āĻĒāĻžāĻ“āϝāĻŧāĻž āϏāĻ‚āĻ–ā§āϝāĻžāϰ āϛ⧋āϟāϟāĻŋ āύ⧇āĻŦ, āĻŦāĻĄāĻŧ āĻšāϞ⧇ āĻŦāĻĄāĻŧāϟāĻŋāĨ¤ (āĻŦ⧁āĻāϤ⧇ āĻĒ⧇āϰ⧇āϛ⧇āύ? āύāϝāĻŧāϤ āφāĻŦāĻžāϰ āĻĒāĻĄāĻŧ⧁āύ)
👉āĻ…āĻˇā§āϟāĻŽ āϧāĻžāĻĒāσ āφāĻŽāĻžāĻĻ⧇āϰ āωāĻĻāĻžāĻšāϰāϪ⧇āϰ āĻ•ā§āώ⧇āĻ¤ā§āϰ⧇ 5 āĻšāĻšā§āϛ⧇ 6 āĻāϰ āϛ⧋āϟ, āϤāĻžāχ āφāĻŽāϰāĻž 4 / 6 āĻŽāĻ§ā§āϝ⧇ āϛ⧋āϟ āϏāĻ‚āĻ–ā§āϝāĻž āĻ…āĻ°ā§āĻĨāĻžā§Ž 4 āύ⧇āĻŦāĨ¤
👉āύāĻŦāĻŽ āϧāĻžāĻĒāσ āĻŽāύ⧇ āφāϛ⧇, āĻĒāĻžā§āϚāĻŽ āϧāĻžāĻĒ⧇ āĻĻāĻļāϕ⧇āϰ āϘāϰ⧇āϰ āĻ…āĻ‚āĻ• āĻĒ⧇āϝāĻŧ⧇āĻ›āĻŋāϞāĻžāĻŽ 2 āĻāĻŦāĻžāϰ āĻĒ⧇āϝāĻŧ⧇āĻ›āĻŋ āĻāĻ•āϕ⧇āϰ āϘāϰ⧇āϰ āĻ…āĻ‚āĻ• 4 āĨ¤ āϤāĻžāχ āωāĻ¤ā§āϤāϰ āĻšāĻŦ⧇ 24
āĻ•āĻ āĻŋāύ āĻŽāύ⧇ āĻšāĻšā§āϛ⧇? āĻāĻ•āĻĻāĻŽāχ āύāĻž, āĻ•āϝāĻŧ⧇āĻ•āϟāĻž āĻĒā§āĻ°ā§āϝāĻžāĻ•āϟāĻŋāϏ āĻ•āϰ⧇ āĻĻ⧇āϖ⧁āύāĨ¤ āφāĻŽāĻžāϰ āĻŽāϤ⧇ āϖ⧁āĻŦ āĻŦ⧇āĻļāĻŋ āϏāĻŽāϝāĻŧ āϞāĻžāĻ—āĻžāϰ āĻ•āĻĨāĻž āύāĻžāĨ¤
đŸ—Ŗī¸āωāĻĻāĻžāĻšāϰāĻŖ:- 4225 āĻāϰ āĻŦāĻ°ā§āĻ—āĻŽā§‚āϞ āĻŦ⧇āϰ āĻ•āϰ⧁āύāĨ¤
āĻŽāύ⧇ āφāϛ⧇ 5 āϝ⧇ āĻāĻ•āĻž āĻ›āĻŋāϞ? āϏ⧇ āĻāĻ•āĻž āĻĨāĻžāĻ•āĻžāϝāĻŧ āφāĻĒāύāĻžāϰ āĻ•āĻžāϜ āĻ•āĻŋāĻ¨ā§āϤ⧁ āĻ…āύ⧇āĻ• āϏ⧋āϜāĻž āĻšāϝāĻŧ⧇ āϗ⧇āϛ⧇āĨ¤ āĻĻ⧇āϖ⧁āύ āϕ⧇āύ⧋ āĻĒā§āϰāĻļā§āύ⧇āϰ āĻļ⧇āώ āĻ…āĻ‚āĻ• 5 āĻšāĻ“āϝāĻŧāĻžāϝāĻŧ āωāĻ¤ā§āϤāϰ⧇āϰ āĻāĻ•āϕ⧇āϰ āϘāϰ⧇āϰ āĻ…āĻ‚āĻ• āĻšāĻŦ⧇ āĻ…āĻŦāĻļā§āϝāχ 5 āĨ¤
- āĻĒā§āϰāĻļā§āύ⧇āϰ āĻāĻ•āĻ• āĻ“ āĻĻāĻļāϕ⧇āϰ āϘāϰ⧇āϰ āĻ…āĻ‚āĻ• āĻŦāĻžāĻĻ āĻĻāĻŋāϝāĻŧ⧇ āĻĻāĻŋāϞ⧇ āĻŦāĻžāĻ•āĻŋ āĻĨāĻžāϕ⧇ 42 āĨ¤
- 42 āĻāϰ āϏāĻŦāĻšā§‡āϝāĻŧ⧇ āĻ•āĻžāϛ⧇āϰ āĻĒā§‚āĻ°ā§āĻŖāĻŦāĻ°ā§āĻ— āϏāĻ‚āĻ–ā§āϝāĻž āĻšāĻšā§āϛ⧇ 36, āϝāĻžāϰ āĻŦāĻ°ā§āĻ—āĻŽā§‚āϞ āĻšāĻšā§āϛ⧇ 6 āĨ¤ āϤāĻžāχ āωāĻ¤ā§āϤāϰ āĻšāĻšā§āϛ⧇ 65
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â„šī¸1. āĻĒāĻžāρāϚ āĻ…āĻ™ā§āϕ⧇āϰ āĻ•ā§āώ⧁āĻĻā§āϰāϤāĻŽ āϏāĻ‚āĻ–ā§āϝāĻž āĻāĻŦāĻ‚ āϚāĻžāϰ āĻ…āĻ™ā§āϕ⧇āϰ āĻŦ⧃āĻšāĻ¤ā§āϤāĻŽ āϏāĻ‚āĻ–ā§āϝāĻžāϰ āĻ…āĻ¨ā§āϤāϰ āĻ•āϤ?
āωāσ ā§§āĨ¤(ā§§ā§Ļā§Ļā§Ļā§Ļ-⧝⧝⧝⧝)
â„šī¸2. ā§Ļ,ā§§,⧍ āĻāĻŦāĻ‚ ā§Š āĻĻā§āĻŦāĻžāϰāĻž āĻ—āĻ āĻŋāϤ āϚāĻžāϰ āĻ…āĻ™ā§āϕ⧇āϰ āĻŦ⧃āĻšāĻ¤ā§āϤāĻŽ āĻāĻŦāĻ‚ āĻ•ā§āώ⧁āĻĻā§āϰāϤāĻŽ āϏāĻ‚āĻ–ā§āϝāĻžāϰ āĻŦāĻŋāϝāĻŧā§‹āĻ—āĻĢāϞ-
āωāσ ā§¨ā§§ā§Žā§­āĨ¤(ā§Šā§¨ā§§ā§Ļ-ā§§ā§Ļā§¨ā§Š)
â„šī¸3.āϝāĻĻāĻŋ ā§§ āĻĨ⧇āϕ⧇ ā§§ā§Ļā§Ļ āĻĒāĻ°ā§āϝāĻ¨ā§āϤ āĻ—āĻŖāύāĻž āĻ•āϰāĻž āĻšāϝāĻŧ āϤāĻŦ⧇ āĻāϰ āĻŽāĻ§ā§āϝ⧇ āĻ•āϤāϟāĻŋ ā§Ģ āĻĒāĻžāĻŦā§‹āĨ¤
āωāσ ⧍ā§ĻāϟāĻŋāĨ¤
*ā§§āĻĨ⧇āϕ⧇ ā§§ā§Ļā§Ļ āĻĒāĻ°ā§āϝāĻ¨ā§āϤ ā§Ļ=ā§§ā§§āϟāĻŋ
ā§§ āĻĨ⧇āϕ⧇ ā§§ā§Ļā§Ļ āĻĒāĻ°ā§āϝāĻ¨ā§āϤ ā§§=⧍⧧āϟāĻŋ
ā§§ āĻĨ⧇āϕ⧇ ā§§ā§Ļā§Ļ āĻĒāĻ°ā§āϝāĻ¨ā§āϤ ⧍āĻĨ⧇āϕ⧇ ⧝ āĻĒāĻ°ā§āϝāĻ¨ā§āϤ āĻ…āĻ™ā§āĻ•āϗ⧁āϞ⧋ āĻĒāĻžāĻ“āϝāĻŧāĻž āϝāĻžāĻŦ⧇=⧍ā§ĻāϟāĻŋāĨ¤
â„šī¸4. ⧭⧍ āϏāĻ‚āĻ–ā§āϝāĻžāϟāĻŋāϰ āĻŽā§‹āϟ āĻ­āĻžāϜāĻ• ?
āωāσ ⧧⧍āϟāĻŋ
*⧭⧍=ā§§Ã—ā§­ā§¨=ā§¨Ã—ā§Šā§Ŧ=ā§ŠÃ—ā§¨ā§Ē=ā§ĒÃ—ā§§ā§Ž=ā§ŦÃ—ā§§ā§¨=ā§ŽÃ—ā§¯
⧭⧍ āϏāĻ‚āĻ–ā§āϝāĻžāϟāĻŋ āĻ­āĻžāϜāĻ•=ā§§,⧍,ā§Š,ā§Ē,ā§Ŧ,ā§Ž,⧝,⧧⧍,ā§§ā§Ž,⧍ā§Ē,ā§Šā§Ŧ,⧭⧍āĨ¤
â„šī¸5. ā§§ āĻĨ⧇āϕ⧇ ā§§ā§Ļā§Ļ āĻĒāĻ°ā§āϝāĻ¨ā§āϤ āĻŽā§ŒāϞāĻŋāĻ• āϏāĻ‚āĻ–ā§āϝāĻž āĻ•āϤāϟāĻŋ?
āωāσ ⧍ā§ĢāϟāĻŋāĨ¤
â„šī¸6. (ā§Ļ.ā§Ļā§§)^⧍ āĻāϰ āĻŽāĻžāύ āϕ⧋āύ āĻ­āĻ—ā§āύāĻžāĻ‚āĻļāϟāĻŋāϰ āϏāĻŽāĻžāύ
āωāσ ā§§/ā§§ā§Ļā§Ļā§Ļā§Ļ
*(ā§Ļ.ā§Ļā§§)^⧍=ā§Ļ.ā§Ļā§§Ã—ā§Ļ.ā§Ļā§§
=ā§Ļ.ā§Ļā§Ļā§Ļā§§
=ā§§/ā§§ā§Ļā§Ļā§Ļā§Ļ
â„šī¸7. āĻĻ⧁āχāϟāĻŋ āϏāĻ‚āĻ–ā§āϝāĻžāϰ āϏāĻŽāĻˇā§āϟāĻŋ ā§­ā§Ļ āĻāĻŦāĻ‚ āĻ…āĻ¨ā§āϤāϰāĻĢāϞ ā§§ā§Ļ āĻšāϞ⧇ āĻŦāĻĄāĻŧ āϏāĻ‚āĻ–ā§āϝāĻžāϟāĻŋ
āωāσ ā§Ēā§Ļ
*āĻŦāĻĄāĻŧ āϏāĻ‚āĻ–ā§āϝāĻžāϟāĻŋ=ā§­ā§Ļ+ā§§ā§Ļ
=ā§Žā§ĻÃˇā§¨
=ā§Ēā§Ļ
â„šī¸8. āĻāĻ•āϟāĻŋ āϏāĻ‚āĻ–ā§āϝāĻž ā§­ā§Ē⧍ āĻĨ⧇āϕ⧇ āϝāϤ āĻŦāĻĄāĻŧ ā§Žā§Šā§Ļ āĻĨ⧇āϕ⧇ āϤāϤ āϛ⧋āϟāĨ¤ āϏāĻ‚āĻ–ā§āϝāĻžāϟāĻŋ āĻ•āϤ?
āωāσ ā§­ā§Žā§Ŧ
*āύāĻŋāĻ°ā§āĻŖāϝāĻŧ⧇ āϏāĻ‚āĻ–ā§āϝāĻž=ā§­ā§Ē⧍+ā§Žā§Šā§Ļ
=ā§§ā§Ģā§­ā§¨Ãˇā§¨
=ā§­ā§Žā§Ŧ
â„šī¸9.āĻĻ⧁āχāϟāĻŋ āϏāĻ‚āĻ–ā§āϝāĻžāϰ āϗ⧁āĻŖāĻĢāϞ ā§§ā§Ģā§Šā§Ŧ āϏāĻ‚āĻ–ā§āϝāĻž āĻĻ⧁āϟāĻŋāϰ āϞ āϏāĻž āϗ⧁ ⧝ā§Ŧ āĻšāϞ⧇ āĻ— āϏāĻž āϗ⧁ āĻ•āϤ?
āωāσ ā§§ā§Ŧ
* āϞ āϏāĻž āϗ⧁ × āĻ— āϏāĻž āϗ⧁ = āϗ⧁āύāĻĢāϞ
⧝ā§Ŧ×āĻ— āϏāĻž āϗ⧁ = ā§§ā§Ģā§Šā§Ŧ
āĻ— āϏāĻž āϗ⧁ = ā§§ā§Ģā§Šā§ŦÃˇā§¯ā§Ŧ
=ā§§ā§Ŧ
â„šī¸10. āĻ…āύ⧁āĻĒāĻžāϤ āĻ•āĻŋ?
āωāσ āĻāĻ•āϟāĻŋ āĻ­āĻ—ā§āύāĻžāĻ‚āĻļ
â„šī¸11. ⧍ā§Ē āϕ⧇ ā§­:ā§Ŧ āĻ…āύ⧁āĻĒāĻžāϤ⧇ āĻŦ⧃āĻĻā§āϧāĻŋ āĻ•āϰāϞ⧇ āύāϤ⧁āύ āϏāĻ‚āĻ–ā§āϝāĻž āĻšāĻŦ⧇?
āωāσ ā§¨ā§Ž
*āύāϤ⧁āύ āϏāĻ‚āĻ–ā§āϝāĻžÃˇā§¨ā§Ē=ā§­/ā§Ŧ
āύāϤ⧁āύ āϏāĻ‚āĻ–ā§āϝāĻž =ā§­Ã—ā§¨ā§ĒÃˇā§Ŧ
=ā§­Ã—ā§Ē
=ā§¨ā§Ž
â„šī¸12. ā§§ āĻĨ⧇āϕ⧇ ā§Ē⧝ āĻĒāĻ°ā§āϝāĻ¨ā§āϤ āĻ•ā§āϰāĻŽāĻŋāĻ• āϏāĻ‚āĻ–ā§āϝāĻž āϗ⧁āϞ⧋āϰ āĻ—āĻĄāĻŧ āĻ•āϤ?
āωāσ ⧍ā§Ģ
*āύāĻŋāĻ°ā§āĻŖāϝāĻŧ⧇ āĻ—āĻĄāĻŧ=
āĻļ⧇āώāĻĒāĻĻ +āĻĒā§āϰāĻĨāĻŽ āĻĒāĻĻÃˇā§¨
ā§Ē⧝+ā§§=ā§Ģā§ĻÃˇā§¨=⧍ā§Ģ
â„šī¸13.ā§§ āĻĨ⧇āϕ⧇ ⧝⧝ āĻĒāĻ°ā§āϝāĻ¨ā§āϤ āϏāĻ‚āĻ–ā§āϝāĻžāϗ⧁āϞ⧋āϰ āϏāĻŽāĻˇā§āϟāĻŋ āĻ•āϤ?
āωāσ ā§Ē⧝ā§Ģā§Ļ
*āϏāĻŽāĻˇā§āϟāĻŋ=n(n+ā§§)Ãˇā§¨
=⧝⧝(⧝⧝+ā§§)Ãˇā§¨
=ā§¯ā§¯Ã—ā§§ā§Ļā§ĻÃˇā§¨
=ā§¯ā§¯Ã—ā§Ģā§Ļ
=ā§Ē⧝ā§Ģā§Ļ
-----------------------------------------------------
📚1 āĻĢ⧁āϟ = 12 āχāĻžā§āϚāĻŋ
1 āĻ—āϜ = 3 āĻĢ⧁āϟ
1 āĻŽāĻžāχāϞ = ā§§ā§­ā§Ŧā§Ļ āĻ—āϜ
1 āĻŽāĻžāχāϞ ≈ 1.61 āĻ•āĻŋāϞ⧋āĻŽāĻŋāϟāĻžāϰ
1 āχāĻžā§āϚāĻŋ = 2.54 āϏ⧇āĻ¨ā§āϟāĻŋāĻŽāĻŋāϟāĻžāϰ
1 āĻĢ⧁āϟ = 0.3048 āĻŽāĻŋāϟāĻžāϰ
1 āĻŽāĻŋāϟāĻžāϰ = 1,000 āĻŽāĻŋāϞāĻŋāĻŽāĻŋāϟāĻžāϰ
1 āĻŽāĻŋāϟāĻžāϰ = 100 āϏ⧇āĻ¨ā§āϟāĻŋāĻŽāĻŋāϟāĻžāϰ
1 āĻ•āĻŋāϞ⧋āĻŽāĻŋāϟāĻžāϰ = 1,000 āĻŽāĻŋāϟāĻžāϰ
1 āĻ•āĻŋāϞ⧋āĻŽāĻŋāϟāĻžāϰ ≈ 0.62 āĻŽāĻžāχāϞ
📝āĻ•ā§āώ⧇āĻ¤ā§āϰāσ
1 āĻŦāĻ°ā§āĻ— āĻĢ⧁āϟ = 144 āĻŦāĻ°ā§āĻ— āχāĻžā§āϚāĻŋ
1 āĻŦāĻ°ā§āĻ— āĻ—āϜ = 9 āĻŦāĻ°ā§āĻ— āĻĢ⧁āϟ
1 āĻāĻ•āϰ = 43560 āĻŦāĻ°ā§āĻ— āĻĢ⧁āϟ
📝 āφāϝāĻŧāϤāύāσ
1 āϞāĻŋāϟāĻžāϰ ≈ 0.264 āĻ—ā§āϝāĻžāϞāύ
1 āϘāύ āĻĢ⧁āϟ = 1.728 āϘāύ āχāĻžā§āϚāĻŋ
1 āϘāύ āĻ—āϜ = 27 āϘāύ āĻĢ⧁āϟ
📝 āĻ“āϜāύāσ
1 āφāωāĻ¨ā§āϏ ≈ 28.350 āĻ—ā§āϰāĻžāĻŽ
1 cvDÛ= 16 āφāωāĻ¨ā§āϏ
1 cvDÛ ≈ 453.592 āĻ—ā§āϰāĻžāĻŽ
1 āĻāĻ• āĻ—ā§āϰāĻžāĻŽā§‡āϰ āĻāĻ°ā§āĻ•āϏāĻšāĻ¸ā§āϰāĻžāĻ‚āĻļ = 0.001āĻ—ā§āϰāĻžāĻŽ
1 āĻ•āĻŋāϞ⧋āĻ—ā§āϰāĻžāĻŽ = 1,000 āĻ—ā§āϰāĻžāĻŽ
1 āĻ•āĻŋāϞ⧋āĻ—ā§āϰāĻžāĻŽ ≈ 2.2 āĻĒāĻžāωāĻ¨ā§āĻĄ
1 āϟāύ = 2,200 āĻĒāĻžāωāĻ¨ā§āĻĄ
📚 āĻŽāĻŋāϞāĻŋāϝāĻŧāύ, āĻŦāĻŋāϞāĻŋāϝāĻŧāύ, āĻŸā§āϰāĻŋāϞāĻŋāϝāĻŧāύ āĻšāĻŋāϏāĻžāĻŦ
ā§§ āĻŽāĻŋāϞāĻŋāϝāĻŧāύ=ā§§ā§Ļ āϞāĻ•ā§āώ
ā§§ā§Ļ āĻŽāĻŋāϞāĻŋāϝāĻŧāύ=ā§§ āϕ⧋āϟāĻŋ
ā§§ā§Ļā§Ļ āĻŽāĻŋāϞāĻŋāϝāĻŧāύ=ā§§ā§Ļ āϕ⧋āϟāĻŋ
ā§§,ā§Ļā§Ļā§Ļ āĻŽāĻŋāϞāĻŋāϝāĻŧāύ=ā§§ā§Ļā§Ļ āϕ⧋āϟāĻŋ
āφāĻŦāĻžāϰ,
ā§§,ā§Ļā§Ļā§Ļ āĻŽāĻŋāϞāĻŋāϝāĻŧāύ= ā§§ āĻŦāĻŋāϞāĻŋāϝāĻŧāύ
ā§§ āĻŦāĻŋāϞāĻŋāϝāĻŧāύ=ā§§ā§Ļā§Ļ āϕ⧋āϟāĻŋ
ā§§ā§Ļ āĻŦāĻŋāϞāĻŋāϝāĻŧāύ=ā§§,ā§Ļā§Ļā§Ļ āϕ⧋āϟāĻŋ
ā§§ā§Ļā§Ļ āĻŦāĻŋāϞāĻŋāϝāĻŧāύ=ā§§ā§Ļ,ā§Ļā§Ļā§Ļ āϕ⧋āϟāĻŋ
ā§§,ā§Ļā§Ļā§Ļ āĻŦāĻŋāϞāĻŋāϝāĻŧāύ=ā§§ āϞāĻ•ā§āώ āϕ⧋āϟāĻŋ
āφāĻŦāĻžāϰ,
ā§§,ā§Ļā§Ļā§Ļ āĻŦāĻŋāϞāĻŋāϝāĻŧāύ=ā§§ āĻŸā§āϰāĻŋāϞāĻŋāϝāĻŧāύ
ā§§ āĻŸā§āϰāĻŋāϞāĻŋāϝāĻŧāύ=ā§§ āϞāĻ•ā§āώ āϕ⧋āϟāĻŋ
ā§§ā§Ļ āĻŸā§āϰāĻŋāϞāĻŋāϝāĻŧāύ=ā§§ā§Ļ āϞāĻ•ā§āώ āϕ⧋āϟāĻŋ
ā§§ā§Ļā§Ļ āĻŸā§āϰāĻŋāϞāĻŋāϝāĻŧāύ=ā§§ā§Ļā§Ļ āϞāĻ•ā§āώ āϕ⧋āϟāĻŋ
ā§§,ā§Ļā§Ļā§Ļ āĻŸā§āϰāĻŋāϞāĻŋāϝāĻŧāύ=ā§§,ā§Ļā§Ļā§Ļ āϞāĻ•ā§āώ āϕ⧋āϟāĻŋāĨ¤
-----------------------------
ā§§ āϰāĻŋāĻŽ = ⧍ā§Ļ āĻĻāĻŋāĻ¸ā§āϤāĻž = ā§Ģā§Ļā§Ļ āϤāĻž
ā§§ āĻ­āϰāĻŋ = ā§§ā§Ŧ āφāύāĻž ;
ā§§ āφāύāĻž = ā§Ŧ āϰāϤāĻŋ
ā§§ āĻ—āϜ = ā§Š āĻĢ⧁āϟ = ⧍ āĻšāĻžāϤ
ā§§ āϕ⧇āϜāĻŋ = ā§§ā§Ļā§Ļā§Ļ āĻ—ā§āϰāĻžāĻŽ
ā§§ āϕ⧁āχāĻ¨ā§āϟāĻžāϞ = ā§§ā§Ļā§Ļ āϕ⧇āϜāĻŋ
ā§§ āĻŽā§‡āĻŸā§āϰāĻŋāĻ• āϟāύ = ā§§ā§Ļ āϕ⧁āχāĻ¨ā§āϟāĻžāϞ = ā§§ā§Ļā§Ļā§Ļ āϕ⧇āϜāĻŋ
ā§§ āϞāĻŋāϟāĻžāϰ = ā§§ā§Ļā§Ļā§Ļ āϏāĻŋāϏāĻŋ
ā§§ āĻŽāĻŖ = ā§Ēā§Ļ āϏ⧇āϰ
ā§§ āĻŦāĻŋāϘāĻž = ⧍ā§Ļ āĻ•āĻžāĻ āĻž( ā§Šā§Š āĻļāϤāĻžāĻ‚āĻļ) ;
ā§§ āĻ•āĻžāĻ āĻž = ⧭⧍ā§Ļ āĻŦāĻ°ā§āĻ—āĻĢ⧁āϟ (ā§Žā§Ļ āĻŦāĻ°ā§āĻ— āĻ—āϜ)
1 āĻŽāĻŋāϞāĻŋāϝāĻŧāύ = 10 āϞāĻ•ā§āώ
1 āĻŽāĻžāχāϞ = 1.61 āĻ•āĻŋ.āĻŽāĻŋ ;
1 āĻ•āĻŋ.āĻŽāĻŋ. = 0..62
1 āχāĻžā§āϚāĻŋ = 2.54 āϏ⧇.āĻŽāĻŋ ;
1 āĻŽāĻŋāϟāĻžāϰ = 39.37 āχāĻžā§āϚāĻŋ
1 āϕ⧇.āϜāĻŋ = 2.20 āĻĒāĻžāωāĻ¨ā§āĻĄ ;
1 āϏ⧇āϰ = 0.93 āĻ•āĻŋāϞ⧋āĻ—ā§āϰāĻžāĻŽ
1 āĻŽā§‡. āϟāύ = 1000 āĻ•āĻŋāϞ⧋āĻ—ā§āϰāĻžāĻŽ ;
1 āĻĒāĻžāωāĻ¨ā§āĻĄ = 16 āφāωāĻ¨ā§āϏ
1 āĻ—āϜ= 3 āĻĢ⧁āϟ ;
1 āĻāĻ•āϰ = 100 āĻļāϤāĻ•
1 āĻŦāĻ°ā§āĻ— āĻ•āĻŋ.āĻŽāĻŋ.= 247 āĻāĻ•āϰ
āĻĒā§āϰāĻļā§āύāσ ā§§ āĻ•āĻŋāĻŽāĻŋ āϏāĻŽāĻžāύ āĻ•āϤ āĻŽāĻžāχāϞ ?
āωāĻ¤ā§āϤāϰāσ ā§Ļ.ā§Ŧ⧍ āĻŽāĻžāχāϞāĨ¤
āĻĒā§āϰāĻļā§āύāσ ā§§ āύ⧇āϟāĻŋāĻ•ā§āϝāĻžāϞ āĻŽāĻžāχāϞ⧇ āĻ•āϤ āĻŽāĻŋāϟāĻžāϰ ?
āωāĻ¤ā§āϤāϰāσ ā§§ā§Žā§Ģā§Š.ā§¨ā§Ž āĻŽāĻŋāϟāĻžāϰāĨ¤
āĻĒā§āϰāĻļā§āύāσ āϏāĻŽā§āĻĻā§āϰ⧇āϰ āϜāϞ⧇āϰ āĻ—āĻ­ā§€āϰāϤāĻž āĻŽāĻžāĻĒāĻžāϰ
āĻāĻ•āĻ• ?
āωāĻ¤ā§āϤāϰāσ āĻĢā§āϝāĻžāĻĻāĻŽāĨ¤
āĻĒā§āϰāĻļā§āύāσ ā§§.ā§Ģ āχāĻžā§āϚāĻŋ ā§§ āĻĢ⧁āĻŸā§‡āϰ āĻ•āϤ āĻ…āĻ‚āĻļ?
āωāĻ¤ā§āϤāϰāσ ā§§/ā§Ž āĻ…āĻ‚āĻļāĨ¤
ā§§āĻŽāĻžāχāϞ =ā§§ā§­ā§Ŧā§Ļ āĻ—āϜāĨ¤]
āĻĒā§āϰāĻļā§āύāσ āĻāĻ• āĻŦāĻ°ā§āĻ— āĻ•āĻŋāϞ⧋āĻŽāĻŋāϟāĻžāϰ āĻ•āϤ āĻāĻ•āϰ?
āωāĻ¤ā§āϤāϰāσ ⧍ā§Ēā§­ āĻāĻ•āϰāĨ¤
āĻĒā§āϰāĻļā§āύāσ āĻāĻ•āϟāĻŋ āϜāĻŽāĻŋāϰ āĻĒāϰāĻŋāĻŽāĻžāύ ā§Ģ āĻ•āĻžāĻ āĻž āĻšāϞ⧇,
āϤāĻž āĻ•āϤ āĻŦāĻ°ā§āĻ—āĻĢ⧁āϟ āĻšāĻŦ⧇?
āωāĻ¤ā§āϤāϰāσ ā§Šā§Ŧā§Ļā§Ļ āĻŦāĻ°ā§āĻ—āĻĢ⧁āϟāĨ¤
āĻĒā§āϰāĻļā§āύāσ āĻāĻ• āĻŦāĻ°ā§āĻ— āχāĻžā§āϚāĻŋāϤ⧇ āĻ•āϤ āĻŦāĻ°ā§āĻ—
āϏ⧇āĻ¨ā§āϟāĻŋāĻŽāĻŋāϟāĻžāϰ?
āωāĻ¤ā§āϤāϰāσ ā§Ŧ.ā§Ēā§Ģ āϏ⧇āĻ¨ā§āϟāĻŋāĻŽāĻŋāϟāĻžāϰāĨ¤
āĻĒā§āϰāĻļā§āύāσ ā§§ āϘāύ āĻŽāĻŋāϟāĻžāϰ = āĻ•āϤ āϞāĻŋāϟāĻžāϰ?
āωāĻ¤ā§āϤāϰāσ ā§§ā§Ļā§Ļā§Ļ āϞāĻŋāϟāĻžāϰāĨ¤
āĻĒā§āϰāĻļā§āύāσ āĻāĻ• āĻ—ā§āϝāĻžāϞāύ⧇ āĻ•āϝāĻŧ āϞāĻŋāϟāĻžāϰ?
āωāĻ¤ā§āϤāϰāσ ā§Ē.ā§Ģā§Ģ āϞāĻŋāϟāĻžāϰāĨ¤
āĻĒā§āϰāĻļā§āύāσ ā§§ āϏ⧇āϰ āϏāĻŽāĻžāύ āĻ•āϤ āϕ⧇āϜāĻŋ?
āωāĻ¤ā§āϤāϰāσ ā§Ļ.ā§¯ā§Š āϕ⧇āϜāĻŋāĨ¤
āĻĒā§āϰāĻļā§āύāσ ā§§ āĻŽāϪ⧇ āĻ•āϤ āϕ⧇āϜāĻŋ?
āωāĻ¤ā§āϤāϰāσ ā§Šā§­.ā§Šā§¨ āϕ⧇āϜāĻŋāĨ¤
āĻĒā§āϰāĻļā§āύāσ ā§§ āϟāύ⧇ āĻ•āϤ āϕ⧇āϜāĻŋ?
āωāĻ¤ā§āϤāϰāσ ā§§ā§Ļā§Ļā§Ļ āϕ⧇āϜāĻŋāĨ¤
āĻĒā§āϰāĻļā§āύāσ ā§§ āϕ⧇āϜāĻŋāϤ⧇ āĻ•āϤ āĻĒāĻžāωāĻ¨ā§āĻĄ??
āωāĻ¤ā§āϤāϰāσ ⧍.⧍ā§Ļā§Ē āĻĒāĻžāωāĻ¨ā§āĻĄāĨ¤
āĻĒā§āϰāĻļā§āύāσ ā§§ āϕ⧁āχāĻ¨ā§āϟāĻžāϞ⧇ āĻ•āϤ āϕ⧇āϜāĻŋ?
āωāĻ¤ā§āϤāϰāσ ā§§ā§Ļā§Ļāϕ⧇āϜāĻŋāĨ¤
--------------------------------
📑British & U.S British U.S
1 gallons = 4.5434 litres = 4.404
litres
2 gallons = 1 peck = 9.8070 litres
= 8.810 litres
-----------------------------------------
📝āĻ•ā§āϝāĻžāϰ⧇āϟ āĻ•āĻŋ?.
āωāĻ¤ā§āϤāϰāσ āĻŽā§‚āĻ˛ā§āϝāĻŦāĻžāύ āĻĒāĻžāĻĨāϰ āĻ“ āϧāĻžāϤ⧁āϏāĻžāĻŽāĻ—ā§āϰ⧀
āĻĒāϰāĻŋāĻŽāĻžāĻĒ⧇āϰ āĻāĻ•āĻ• āĻ•ā§āϝāĻžāϰ⧇āϟ āĨ¤
1 āĻ•ā§āϝāĻžāϰ⧇āϟ =0 .2 āĻ—ā§āϰāĻžāĻŽ
📝āĻŦ⧇āϞ āĻ•āĻŋ?
āωāĻ¤ā§āϤāϰāσ āĻĒāĻžāϟ āĻŦāĻž āϤ⧁āϞāĻž āĻĒāϰāĻŋāĻŽāĻžāĻĒ⧇āϰ āϏāĻŽāϝāĻŧ ‘āĻŦ⧇āĻ˛â€™
āĻāĻ•āĻ• āĻšāĻŋāϏāĻžāĻŦ⧇ āĻŦā§āϝāĻŦāĻšā§ƒāϤ āĻšāϝāĻŧ āĨ¤
1 āĻŦ⧇āϞ = 3.5 āĻŽāĻŖ (āĻĒā§āϰāĻžāϝāĻŧ) āĨ¤

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