Math & Science with Arun Sir

Math & Science with Arun Sir Breaking down the mysteries of math and science for young minds. Lessons, tricks, and answers with Arun Sir. Your journey to A+ grades begins here!

đŸŒŧ āĻļ⧁āĻ­ āύāĻŦāĻŦāĻ°ā§āώ ā§§ā§Ēā§Šā§Š đŸŒŧāύāϤ⧁āύ āĻŦāĻ›āϰ āĻŽāĻžāύ⧇āχ āύāϤ⧁āύ āĻ¸ā§āĻŦāĻĒā§āύ, āύāϤ⧁āύ āĻļ⧁āϰ⧁â€Ļāφāϰ āϏ⧇āχ āĻ¸ā§āĻŦāĻĒā§āύāϗ⧁āϞ⧋āϕ⧇ āĻŦāĻžāĻ¸ā§āϤāĻŦ⧇ āϰ⧂āĻĒ āĻĻ⧇āĻ“ā§ŸāĻžāϰ āϜāĻ¨ā§āϝ āĻĻāϰāĻ•āĻžāϰāϏāĻ āĻŋāĻ• āĻĻāĻŋāĻļāĻž + āϧāĻž...
15/04/2026

đŸŒŧ āĻļ⧁āĻ­ āύāĻŦāĻŦāĻ°ā§āώ ā§§ā§Ēā§Šā§Š đŸŒŧ

āύāϤ⧁āύ āĻŦāĻ›āϰ āĻŽāĻžāύ⧇āχ āύāϤ⧁āύ āĻ¸ā§āĻŦāĻĒā§āύ, āύāϤ⧁āύ āĻļ⧁āϰ⧁â€Ļ
āφāϰ āϏ⧇āχ āĻ¸ā§āĻŦāĻĒā§āύāϗ⧁āϞ⧋āϕ⧇ āĻŦāĻžāĻ¸ā§āϤāĻŦ⧇ āϰ⧂āĻĒ āĻĻ⧇āĻ“ā§ŸāĻžāϰ āϜāĻ¨ā§āϝ āĻĻāϰāĻ•āĻžāϰ
āϏāĻ āĻŋāĻ• āĻĻāĻŋāĻļāĻž + āϧāĻžāϰāĻžāĻŦāĻžāĻšāĻŋāĻ• āĻĒāϰāĻŋāĻļā§āϰāĻŽ + āϏāĻ āĻŋāĻ• guidance đŸ’¯

Math & Science with Arun Sir āĻĒāϰāĻŋāĻŦāĻžāϰ⧇āϰ āĻĒāĻ•ā§āώ āĻĨ⧇āϕ⧇
āϏāĻŽāĻ¸ā§āϤ āĻ›āĻžāĻ¤ā§āϰ-āĻ›āĻžāĻ¤ā§āϰ⧀ āĻ“ āĻ…āĻ­āĻŋāĻ­āĻžāĻŦāĻ•āĻĻ⧇āϰ āϜāĻžāύāĻžāχ
āĻ…āĻ¨ā§āϤāϰ⧇āϰ āĻ—āĻ­ā§€āϰ āĻĨ⧇āϕ⧇ āĻ­āĻžāϞ⧋āĻŦāĻžāϏāĻž āĻ“ āĻļ⧁āϭ⧇āĻšā§āĻ›āĻž â¤ī¸

📚 āĻāχ āύāϤ⧁āύ āĻŦāĻ›āϰ⧇ āφāĻŽāĻžāĻĻ⧇āϰ āĻ…āĻ™ā§āĻ—ā§€āĻ•āĻžāĻ°â€”
āφāĻŽāϰāĻž āĻļ⧁āϧ⧁ āĻĒ⧜āĻžāĻŦā§‹ āύāĻž,
āϤ⧋āĻŽāĻžāĻĻ⧇āϰ āϚāĻŋāĻ¨ā§āϤāĻž āĻ•āϰāĻžāϰ āĻ•ā§āώāĻŽāϤāĻž (thinking power) āĻŦāĻžā§œāĻžāĻŦā§‹
āϭ⧟ āĻĻā§‚āϰ āĻ•āϰ⧇ āφāĻ¤ā§āĻŽāĻŦāĻŋāĻļā§āĻŦāĻžāϏ āϤ⧈āϰāĻŋ āĻ•āϰāĻŦā§‹
āĻāĻŦāĻ‚ āϤ⧋āĻŽāĻžāĻĻ⧇āϰ āĻĒāĻžāĻļ⧇ āĻĨāĻžāĻ•āĻŦā§‹ āĻļ⧇āώ āĻĒāĻ°ā§āϝāĻ¨ā§āϤ 🤝

đŸŽ¯ āĻŽāύ⧇ āϰ⧇āĻ–ā§‹â€”
Success āĻšāĻ āĻžā§Ž āĻ•āϰ⧇ āφāϏ⧇ āύāĻž,
Consistency + Smart Work = Result

🌟 ā§§ā§Ēā§Šā§Š āĻšā§‹āĻ• āϤ⧋āĻŽāĻžāϰ āĻœā§€āĻŦāύ⧇āϰ
āϏāĻŦāĻšā§‡ā§Ÿā§‡ productive āĻāĻŦāĻ‚ successful āĻŦāĻ›āϰ 🌟

✨ Stay Focused
✨ Stay Consistent
✨ Believe in Yourself

— Math & Science with Arun Sir





āφāϜ ā§¨ā§ŠāĻļ⧇ āϜāĻžāύ⧁āϝāĻŧāĻžāϰāĻŋ —āφāĻŽāĻžāĻĻ⧇āϰ āĻŽāĻšāĻžāύ āĻŦāĻŋāĻĒā§āϞāĻŦā§€, ****-āĻāϰ āϜāĻ¨ā§āĻŽāĻĻāĻŋāύ đŸ‡ŽđŸ‡ŗNetaji āĻļ⧁āϧ⧁ āĻāĻ•āϜāύ āĻ¸ā§āĻŦāĻžāϧ⧀āύāϤāĻž āϏāĻ‚āĻ—ā§āϰāĻžāĻŽā§€ āύāύ,āϤāĻŋāύāĻŋ āĻ›āĻŋāϞ⧇āύ āĻ…āϏ⧀āĻŽ āϏāĻžāĻšāϏ⧀, ...
23/01/2026

āφāϜ ā§¨ā§ŠāĻļ⧇ āϜāĻžāύ⧁āϝāĻŧāĻžāϰāĻŋ —
āφāĻŽāĻžāĻĻ⧇āϰ āĻŽāĻšāĻžāύ āĻŦāĻŋāĻĒā§āϞāĻŦā§€, ****-āĻāϰ āϜāĻ¨ā§āĻŽāĻĻāĻŋāύ đŸ‡ŽđŸ‡ŗ

Netaji āĻļ⧁āϧ⧁ āĻāĻ•āϜāύ āĻ¸ā§āĻŦāĻžāϧ⧀āύāϤāĻž āϏāĻ‚āĻ—ā§āϰāĻžāĻŽā§€ āύāύ,
āϤāĻŋāύāĻŋ āĻ›āĻŋāϞ⧇āύ āĻ…āϏ⧀āĻŽ āϏāĻžāĻšāϏ⧀, āĻ…āĻ¤ā§āϝāĻ¨ā§āϤ āĻŦ⧁āĻĻā§āϧāĻŋāĻŽāĻžāύ āĻāĻŦāĻ‚
āĻĻ⧇āĻļ⧇āϰ āϜāĻ¨ā§āϝ āύāĻŋāĻœā§‡āϰ āϏāĻŦāĻ•āĻŋāϛ⧁ āĻ‰ā§ŽāϏāĻ°ā§āĻ— āĻ•āϰāϤ⧇ āĻĒā§āϰāĻ¸ā§āϤ⧁āϤ āĻāĻ• āĻ…āύāĻ¨ā§āϝ āĻŽāĻžāύ⧁āώāĨ¤

āϤāĻŋāύāĻŋ āφāĻŽāĻžāĻĻ⧇āϰ āĻļāĻŋāĻ–āĻŋāϝāĻŧ⧇āϛ⧇āύ —
👉 Fearless mind āĻĨāĻžāĻ•āϞ⧇ āĻŦāĻĄāĻŧ āĻĒāϰāĻŋāĻŦāĻ°ā§āϤāύ āϏāĻŽā§āĻ­āĻŦ
👉 Sharp brain āĻĨāĻžāĻ•āϞ⧇ āĻ…āϏāĻŽā§āĻ­āĻŦāϕ⧇āĻ“ āϜāϝāĻŧ āĻ•āϰāĻž āϝāĻžāϝāĻŧ
👉 āφāϰ Deshoprem āĻĨāĻžāĻ•āϞ⧇ āύāĻŋāĻœā§‡āϰ āϜāĻ¨ā§āϝ āύāϝāĻŧ, āĻĻ⧇āĻļ⧇āϰ āϜāĻ¨ā§āϝ āĻŦāĻžāρāϚāĻž āϝāĻžāϝāĻŧ

āφāϜāϕ⧇āϰ āφāĻŽāĻžāϰ Math & Science with Arun Sir-āĻāϰ āĻ›āĻžāĻ¤ā§āϰāĻ›āĻžāĻ¤ā§āϰ⧀āĻĻ⧇āϰ āωāĻĻā§āĻĻ⧇āĻļā§āϝ⧇ āĻāĻ•āϟāĻžāχ āĻ•āĻĨāĻž —
📚 āĻĒāĻĄāĻŧāĻžāĻļā§‹āύāĻž āĻļ⧁āϧ⧁ āύāĻŽā§āĻŦāϰ āĻŦāĻž āϚāĻžāĻ•āϰāĻŋāϰ āϜāĻ¨ā§āϝ āύāϝāĻŧ,
āĻāϟāĻž āĻāĻŽāύ āĻāĻ• āĻļāĻ•ā§āϤāĻŋ,
āϝāĻž āĻĻāĻŋāϝāĻŧ⧇ āĻ­āĻŦāĻŋāĻˇā§āϝāϤ⧇ āϤ⧁āĻŽāĻŋ āĻĻ⧇āĻļ⧇āϰ āϏāĻŽāĻ¸ā§āϝāĻž āϏāĻŽāĻžāϧāĻžāύ āĻ•āϰāϤ⧇ āĻĒāĻžāϰāĻŦ⧇āĨ¤

đŸ”Ŧ Science āĻĻāĻŋāϝāĻŧ⧇ āύāϤ⧁āύ āφāĻŦāĻŋāĻˇā§āĻ•āĻžāϰ
📐 Math āĻĻāĻŋāϝāĻŧ⧇ āϏāĻ āĻŋāĻ• āϏāĻŋāĻĻā§āϧāĻžāĻ¨ā§āϤ
đŸ”Ĩ āφāϰ Netajir āĻŽāϤ⧋ āϏāĻžāĻšāϏ āύāĻŋāϝāĻŧ⧇ āĻĻ⧇āĻļ⧇āϰ āϜāĻ¨ā§āϝ āĻ•āĻŋāϛ⧁ āĻ•āϰāĻžāϰ āχāĻšā§āϛ⧇ —
āĻāχ āϤāĻŋāύāĻŸā§‡āχ āϤ⧋āĻŽāĻžāĻĻ⧇āϰ āĻ­āĻŋāϤāϰ⧇ āϤ⧈āϰāĻŋ āĻ•āϰāĻžāχ āφāĻŽāĻžāϰ āϞāĻ•ā§āĻˇā§āϝāĨ¤

👉 “Give me blood, and I shall give you freedom”
āĻāχ āĻ•āĻĨāĻžāϰ āĻŽāĻžāύ⧇ āφāϜāϕ⧇āϰ āĻĻāĻŋāύ⧇ —
Give your hard work, honesty and courage — and you will give India a better future.

đŸ‡ŽđŸ‡ŗ Netaji Subhas Chandra Bose-āϕ⧇ āĻļā§āϰāĻĻā§āϧāĻžāĻžā§āϜāϞāĻŋ đŸ‡ŽđŸ‡ŗ
āϚāϞ⧋, āφāĻŽāϰāĻžāĻ“ āϏāĻžāĻšāϏ⧀ āĻšāχ, āĻŦ⧁āĻĻā§āϧāĻŋāĻŽāĻžāύ āĻšāχ, āφāϰ āĻĻ⧇āĻļ⧇āϰ āϜāĻ¨ā§āϝ āĻ•āĻžāϜ āĻ•āϰāĻžāϰ āĻ¸ā§āĻŦāĻĒā§āύ āĻĻ⧇āĻ–āĻŋāĨ¤








New year āĻŽāĻžāύ⧇ perfect āĻšāĻ“āϝāĻŧāĻž āύāĻž,better āĻšāĻ“āϝāĻŧāĻžāϰ āĻāĻ•āϟāĻž āύāϤ⧁āύ āϏ⧁āϝ⧋āĻ—āĨ¤Effort + consistency = successLet’s make Math & Science fea...
31/12/2025

New year āĻŽāĻžāύ⧇ perfect āĻšāĻ“āϝāĻŧāĻž āύāĻž,
better āĻšāĻ“āϝāĻŧāĻžāϰ āĻāĻ•āϟāĻž āύāϤ⧁āύ āϏ⧁āϝ⧋āĻ—āĨ¤
Effort + consistency = success
Let’s make Math & Science fear-free together 📘✨
Happy New Year
— Arun Sir











#āĻļāĻŋāĻ•ā§āώāĻž

29/12/2025

āĻŽāĻžāĻ§ā§āϝāĻŽāĻŋāĻ• 2026-āĻāϰ āφāϗ⧇ āĻāχ āϏāϰāϞ āϏ⧁āĻĻ⧇āϰ āĻĒā§āϰāĻļā§āύāϟāĻž miss āĻ•āϰāϞ⧇ āĻ•āĻŋāĻ¨ā§āϤ⧁ āĻŦāĻŋāĻĒāĻĻ! âš ī¸
5% āϏ⧁āĻĻ⧇āϰ āĻŽāĻžāϏāĻŋāĻ• āĻšāĻŋāϏāĻžāĻŦ — āĻ…āύ⧇āϕ⧇āχ āĻāĻ–āĻžāύ⧇ āϭ⧁āϞ āĻ•āϰ⧇ ❌
āĻ­āĻŋāĻĄāĻŋāĻ“āϟāĻž āĻĻ⧇āϖ⧇ āύāĻžāĻ“ āĻāĻ–āύāχ 👇


⧁āĻĻ

26/12/2025

📌 āĻŽāĻžāĻ§ā§āϝāĻŽāĻŋāĻ• 2026 āĻĒāϰ⧀āĻ•ā§āώāĻžāĻ°ā§āĻĨā§€āĻĻ⧇āϰ āϜāĻ¨ā§āϝ āĻ…āĻ¤ā§āϝāĻ¨ā§āϤ āϗ⧁āϰ⧁āĻ¤ā§āĻŦāĻĒā§‚āĻ°ā§āĻŖ MCQ đŸ”Ĩ

āφāϏāϞ āĻ“ ā§Ģ āĻŦāĻ›āϰ⧇āϰ āϏāϰāϞ āϏ⧁āĻĻ⧇āϰ āĻ…āύ⧁āĻĒāĻžāϤ ā§§ā§Ļ : ā§Š āĻšāϞ⧇,
āĻŦāĻžāĻ°ā§āώāĻŋāĻ• āĻļāϤāĻ•āϰāĻž āϏāϰāϞ āϏ⧁āĻĻ⧇āϰ āĻšāĻžāϰ āĻ•āϤ?

āĻāχ āĻĒā§āϰāĻļā§āύāϟāĻŋ āϏāϰāϞ āϏ⧁āĻĻ chapter āĻĨ⧇āϕ⧇ āĻĒāϰ⧀āĻ•ā§āώāĻžāϝāĻŧ āφāϏāĻžāϰ āϖ⧁āĻŦāχ strong chance āφāϛ⧇āĨ¤

āĻāχ āĻ­āĻŋāĻĄāĻŋāĻ“āϤ⧇ āĻĻ⧇āĻ–āĻžāύ⧋ āĻšāϝāĻŧ⧇āĻ›ā§‡â€”
âœ”ī¸ MCQ solve āĻ•āϰāĻžāϰ smart method
âœ”ī¸ āϏāĻžāϧāĻžāϰāĻŖ āϭ⧁āϞ āϕ⧋āĻĨāĻžāϝāĻŧ āĻšāϝāĻŧ
âœ”ī¸ āĻ•āĻŽ āϏāĻŽāϝāĻŧ⧇ āϏāĻ āĻŋāĻ• āωāĻ¤ā§āϤāϰ āĻŦ⧇āϰ āĻ•āϰāĻžāϰ āĻ•ā§ŒāĻļāϞ

Class 10 WB Board āĻ›āĻžāĻ¤ā§āϰāĻ›āĻžāĻ¤ā§āϰ⧀āϰāĻž āĻ…āĻŦāĻļā§āϝāχ āĻĻ⧇āĻ–ā§‹ 👇




⧁āĻĻ



24/12/2025

āĻŽāĻžāĻ§ā§āϝāĻŽāĻŋāĻ• 2026-āĻāϰ āϜāĻ¨ā§āϝ
āĻ…āĻ‚āĻļā§€āĻĻāĻžāϰāĻŋ āĻ•āĻžāϰāĻŦāĻžāϰ⧇āϰ āϏāĻŦāĻšā§‡ā§Ÿā§‡ āϗ⧁āϰ⧁āĻ¤ā§āĻŦāĻĒā§‚āĻ°ā§āĻŖ
2 Marks āĻĒā§āϰāĻļā§āύ đŸ”Ĩ
Video āύāĻž āĻĻ⧇āĻ–āϞ⧇ miss āĻ•āϰāĻŦ⧇ ❌

#āĻ…āĻ‚āĻļā§€āĻĻāĻžāϰāĻŋ_āĻ•āĻžāϰāĻŦāĻžāϰ



23/12/2025

Math āϭ⧁āϞ āĻšāϝāĻŧ āĻšāĻŋāϏāĻžāĻŦ⧇āϰ āϜāĻ¨ā§āϝ āύāĻž,
āĻĒā§āϰāĻļā§āύ āĻ āĻŋāĻ•āĻŽāϤ⧋ āύāĻž āĻĒāĻĄāĻŧāĻžāϰ āϜāĻ¨ā§āϝāĨ¤ ❌

āĻāχ āĻ­āĻŋāĻĄāĻŋāĻ“āϤ⧇ āĻ…āĻ‚āĻļā§€āĻĻāĻžāϰāĻŋ āĻ•āĻžāϰāĻŦāĻžāϰ āĻ…āĻ§ā§āϝāĻžā§Ÿā§‡āϰ
āĻāĻ•āϟāĻŋ āĻ…āĻ¤ā§āϝāĻ¨ā§āϤ āϗ⧁āϰ⧁āĻ¤ā§āĻŦāĻĒā§‚āĻ°ā§āĻŖ 2 āύāĻŽā§āĻŦāϰ⧇āϰ āĻĒā§āϰāĻļā§āύ
āϏāĻšāϜāĻ­āĻžāĻŦ⧇ āĻŦ⧁āĻāĻŋā§Ÿā§‡ āĻĻ⧇āĻ“ā§ŸāĻž āĻšā§Ÿā§‡āϛ⧇āĨ¤

📌 Class 10 | WB Board
📌 Board exam oriented

Math & Science āϏāĻšāϜāĻ­āĻžāĻŦ⧇ āĻļāĻŋāĻ–āϤ⧇
Page follow āĻ•āϰ⧋ 👍



#āĻ…āĻ‚āĻļā§€āĻĻāĻžāϰāĻŋ_āĻ•āĻžāϰāĻŦāĻžāϰ


The Sum of First n Odd Numbers = n²—āĻāĻ•āϟāĻŋ āĻ…āϏāĻžāϧāĻžāϰāĻŖ āĻ—āĻŖāĻŋāϤ āĻĒā§āϝāĻžāϟāĻžāĻ°ā§āύ, āϝ⧇āĻ–āĻžāύ⧇ āĻĒā§āϰāĻĨāĻŽ n āϟāĻŋ āĻŦāĻŋāĻœā§‹āĻĄāĻŧ āϏāĻ‚āĻ–ā§āϝāĻž (Odd Numbers) āϝ⧋āĻ— āĻ•āϰāϞ⧇āχ...
22/11/2025

The Sum of First n Odd Numbers = n²—āĻāĻ•āϟāĻŋ āĻ…āϏāĻžāϧāĻžāϰāĻŖ āĻ—āĻŖāĻŋāϤ āĻĒā§āϝāĻžāϟāĻžāĻ°ā§āύ, āϝ⧇āĻ–āĻžāύ⧇ āĻĒā§āϰāĻĨāĻŽ n āϟāĻŋ āĻŦāĻŋāĻœā§‹āĻĄāĻŧ āϏāĻ‚āĻ–ā§āϝāĻž (Odd Numbers) āϝ⧋āĻ— āĻ•āϰāϞ⧇āχ āϤ⧈āϰāĻŋ āĻšāϝāĻŧ āĻāĻ•āϟāĻŋ Perfect Square (āĻĒā§‚āĻ°ā§āĻŖāĻŦāĻ°ā§āĻ— āϏāĻ‚āĻ–ā§āϝāĻž)āĨ¤
āĻāχ āϏ⧁āĻ¨ā§āĻĻāϰ āĻĒā§āϝāĻžāϟāĻžāĻ°ā§āύ Number Sense, Algebra, Logical Thinking—āϏāĻŦāĻ•āĻŋāϛ⧁āϤ⧇āχ āĻ­ā§€āώāĻŖ āϗ⧁āϰ⧁āĻ¤ā§āĻŦāĻĒā§‚āĻ°ā§āĻŖāĨ¤
āĻ›āĻžāĻ¤ā§āϰāĻĻ⧇āϰ āϜāĻ¨ā§āϝ āϝ⧇āĻŽāύ āĻŦā§‹āĻāĻž āϏāĻšāϜ, āϤ⧇āĻŽāύāĻŋ āĻĒā§āϰāϤāĻŋāĻĻāĻŋāύ⧇āϰ Math Practice-āĻāϰ āϜāĻ¨ā§āϝ āĻ…āĻ¤ā§āϝāĻ¨ā§āϤ āωāĻĒāĻ•āĻžāϰ⧀āĨ¤

👉 Key Idea:
1 + 3 + 5 + â€Ļ (n terms) = n²
👉 Perfect Square āĻ—āĻ āύ⧇āϰ āĻ­āĻŋāĻœā§āϝ⧁āϝāĻŧāĻžāϞ āĻĒā§āϝāĻžāϟāĻžāĻ°ā§āύ āĻŽāύ⧋āϝ⧋āĻ— āĻŦāĻžāĻĄāĻŧāĻžāϤ⧇ āϏāĻžāĻšāĻžāĻ¯ā§āϝ āĻ•āϰ⧇āĨ¤

āĻ—āĻŖāĻŋāϤāϕ⧇ āϏāĻšāϜ āĻ“ āĻŽāϜāĻžāϰ āĻ•āϰ⧇ āϤ⧁āϞāϤ⧇āχ āĻāχ āϏ⧁āĻ¨ā§āĻĻāϰ āĻĒā§āϝāĻžāϟāĻžāĻ°ā§āύāϟāĻŋ āϏāĻŦāĻžāϰ āϏāĻ™ā§āϗ⧇ āĻļ⧇āϝāĻŧāĻžāϰ āĻ•āϰāĻ›āĻŋāĨ¤

— Math and Science with Arun Sir










📘 ZERO IS EVEN!āĻ…āύ⧇āϕ⧇āχ āĻ­āĻžāĻŦ⧇ 0 āĻāĻ•āϟāĻž odd number — āĻ•āĻŋāĻ¨ā§āϤ⧁ āφāϏāϞ⧇ 0 āĻšāĻšā§āϛ⧇ āĻāĻ•āϟāĻŋ EVEN number!āĻ—āĻŖāĻŋāϤ⧇ Even Number (āĻœā§‹āĻĄāĻŧ āϏāĻ‚āĻ–ā§āϝāĻž) āĻŦāϞāϤ⧇...
21/11/2025

📘 ZERO IS EVEN!
āĻ…āύ⧇āϕ⧇āχ āĻ­āĻžāĻŦ⧇ 0 āĻāĻ•āϟāĻž odd number — āĻ•āĻŋāĻ¨ā§āϤ⧁ āφāϏāϞ⧇ 0 āĻšāĻšā§āϛ⧇ āĻāĻ•āϟāĻŋ EVEN number!

āĻ—āĻŖāĻŋāϤ⧇ Even Number (āĻœā§‹āĻĄāĻŧ āϏāĻ‚āĻ–ā§āϝāĻž) āĻŦāϞāϤ⧇ āĻŦā§‹āĻāĻžāϝāĻŧ:
āϝ⧇ āϏāĻ‚āĻ–ā§āϝāĻž 2 āĻĻāĻŋāϝāĻŧ⧇ āĻ­āĻžāĻ— āĻ•āϰāϞ⧇ (Ãˇ2) āϕ⧋āύ⧋ remainder āĻĨāĻžāϕ⧇ āύāĻžāĨ¤
āϏ⧇āχ āĻšāĻŋāϏāĻžāĻŦ⧇ → 0 Ãˇ 2 = 0, āĻ…āĻ°ā§āĻĨāĻžā§Ž āϏāĻŽā§āĻĒā§‚āĻ°ā§āĻŖ āĻāĻ•āϟāĻŋ āĻĒā§‚āĻ°ā§āĻŖāϏāĻ‚āĻ–ā§āϝāĻžāĨ¤

āϤāĻžāχ 0 āĻ āĻŋāĻ•āχ Even Number (āĻœā§‹āĻĄāĻŧ āϏāĻ‚āĻ–ā§āϝāĻž) — āĻāĻŦāĻ‚ even number sequence āĻāϰ āĻŽāĻžāĻāĻ–āĻžāύ⧇ āϏ⧁āĻ¨ā§āĻĻāϰāĻ­āĻžāĻŦ⧇ āĻŦāϏ⧇ āφāϛ⧇:
â€Ļ -4, -2, 0, 2, 4 â€Ļ

āĻ—āĻŖāĻŋāϤ āϝāϤ āĻ—āĻ­ā§€āϰ⧇ āϝāĻžāĻŦ⧇, āϤāϤ āĻŽāϜāĻžāϰ āϜāĻŋāύāĻŋāϏ āϏāĻžāĻŽāύ⧇ āφāϏāĻŦ⧇!
āφāϰ⧋ āĻāĻŽāύ math facts āϜāĻžāύāϤ⧇ āφāĻŽāĻžāϰ āĻĒ⧇āϜāϟāĻŋ āĻĢāϞ⧋ āĻ•āϰ⧋āĨ¤ â¤ī¸

– Math and Science with Arun Sir



āϜāϞ⧇āϰ āĻāĻ• āĻ…āϏāĻžāϧāĻžāϰāĻŖ āĻŦ⧈āĻļāĻŋāĻˇā§āĻŸā§āϝ āύāĻŋāϝāĻŧ⧇ āφāϜ āφāϞ⧋āϚāύāĻž āĻ•āϰāĻŦ! 🧊💧āφāĻŽāϰāĻž āϏāĻŦāĻžāχ āϜāĻžāύāĻŋ āϝ⧇ āĻŦāϰāĻĢ (ice) āϜāϞ⧇ (water) āĻ­āĻžāϏ⧇, āĻ•āĻŋāĻ¨ā§āϤ⧁ āĻāϰ āĻĒ⧇āĻ›āύ⧇āϰ āĻŦ⧈āĻœā§āĻžāĻžāύāĻŋ...
18/11/2025

āϜāϞ⧇āϰ āĻāĻ• āĻ…āϏāĻžāϧāĻžāϰāĻŖ āĻŦ⧈āĻļāĻŋāĻˇā§āĻŸā§āϝ āύāĻŋāϝāĻŧ⧇ āφāϜ āφāϞ⧋āϚāύāĻž āĻ•āϰāĻŦ! 🧊💧

āφāĻŽāϰāĻž āϏāĻŦāĻžāχ āϜāĻžāύāĻŋ āϝ⧇ āĻŦāϰāĻĢ (ice) āϜāϞ⧇ (water) āĻ­āĻžāϏ⧇, āĻ•āĻŋāĻ¨ā§āϤ⧁ āĻāϰ āĻĒ⧇āĻ›āύ⧇āϰ āĻŦ⧈āĻœā§āĻžāĻžāύāĻŋāĻ• āĻ•āĻžāϰāĻŖāϟāĻž āĻ•āĻŋ āϜāĻžāύ⧇āύ?

āϏāĻžāϧāĻžāϰāĻŖāϤ, āĻŦ⧇āĻļāĻŋāϰāĻ­āĻžāĻ— āĻĒāĻĻāĻžāĻ°ā§āĻĨāχ āϝāĻ–āύ āϤāϰāϞ (liquid) āĻĨ⧇āϕ⧇ āĻ•āĻ āĻŋāύ⧇ (solid) āϰ⧂āĻĒāĻžāĻ¨ā§āϤāϰāĻŋāϤ āĻšāϝāĻŧ, āϤāĻ–āύ āϏ⧇āϗ⧁āϞ⧋āϰ āϘāύāĻ¤ā§āĻŦ (density) āĻŦ⧇āĻĄāĻŧ⧇ āϝāĻžāϝāĻŧ āĻāĻŦāĻ‚ āφāϝāĻŧāϤāύ (volume) āĻ•āĻŽā§‡ āϝāĻžāϝāĻŧāĨ¤ āĻ•āĻŋāĻ¨ā§āϤ⧁ āϜāϞ āĻāχ āύāĻŋāϝāĻŧāĻŽā§‡āϰ āĻŦā§āϝāϤāĻŋāĻ•ā§āϰāĻŽ!
āĻŽāϜāĻžāϰ āϤāĻĨā§āϝ: āϜāϞ (water) āĻāĻ•āĻŽāĻžāĻ¤ā§āϰ āĻĒāĻĻāĻžāĻ°ā§āĻĨ āϝāĻž āĻŦāϰāĻĢ (ice) āĻ…āĻŦāĻ¸ā§āĻĨāĻžāϝāĻŧ āϤāϰāϞ (liquid) āĻ…āĻŦāĻ¸ā§āĻĨāĻžāϰ āϤ⧁āϞāύāĻžāϝāĻŧ āĻ•āĻŽ āϘāύ (less dense) āĻšāϝāĻŧāĨ¤

āĻāϰ āĻŽāĻžāύ⧇ āĻ•āĻŋ? āĻāϰ āĻŽāĻžāύ⧇ āĻšāϞ⧋, āϝāĻ–āύ āϜāϞ āϜāĻŽā§‡ āĻŦāϰāĻĢ āĻšāϝāĻŧ, āϤāĻ–āύ āϤāĻžāϰ āĻ…āϪ⧁āϗ⧁āϞ⧋ (molecules) āĻāĻ•āϟāĻŋ āύāĻŋāĻ°ā§āĻĻāĻŋāĻˇā§āϟ āώāĻĄāĻŧāϭ⧁āϜāĻžāĻ•āĻžāϰ (hexagonal) āĻ•āĻžāĻ āĻžāĻŽā§‹āϤ⧇ āϏāĻœā§āϜāĻŋāϤ āĻšāϝāĻŧāĨ¤ āĻāχ āĻ•āĻžāĻ āĻžāĻŽā§‹āϟāĻŋ āϤāϰāϞ āϜāϞ⧇āϰ āĻ…āϪ⧁āϗ⧁āϞāĻŋāϰ āĻšā§‡āϝāĻŧ⧇ āĻŦ⧇āĻļāĻŋ āĻĢāĻžāρāĻ•āĻž āϜāĻžāϝāĻŧāĻ—āĻž (empty space) āϤ⧈āϰāĻŋ āĻ•āϰ⧇āĨ¤ āĻĢāϞ⧇ āĻāĻ•āχ āĻĒāϰāĻŋāĻŽāĻžāĻŖ āϜāϞ⧇āϰ āĻšā§‡āϝāĻŧ⧇ āĻāĻ•āχ āĻĒāϰāĻŋāĻŽāĻžāĻŖ āĻŦāϰāĻĢ⧇āϰ āφāϝāĻŧāϤāύ (volume) āĻŦ⧇āĻļāĻŋ āĻšāϝāĻŧ, āĻ•āĻŋāĻ¨ā§āϤ⧁ āĻ­āϰ (mass) āĻāĻ•āχ āĻĨāĻžāϕ⧇āĨ¤

āϝ⧇āĻšā§‡āϤ⧁ āϘāύāĻ¤ā§āĻŦ (density) = āĻ­āϰ (mass) / āφāϝāĻŧāϤāύ (volume), āϤāĻžāχ āĻŦāϰāĻĢ⧇āϰ āϘāύāĻ¤ā§āĻŦ (density) āϤāϰāϞ āϜāϞ⧇āϰ āĻšā§‡āϝāĻŧ⧇ āĻ•āĻŽ āĻšāϝāĻŧāĨ¤ āφāϰ āĻ•āĻŽ āϘāύāĻ¤ā§āĻŦ⧇āϰ (less dense) āĻŦāĻ¸ā§āϤ⧁āχ āĻŦ⧇āĻļāĻŋ āϘāύāĻ¤ā§āĻŦ⧇āϰ (more dense) āĻŦāĻ¸ā§āϤ⧁āϰ āωāĻĒāϰ āĻ­āĻžāϏ⧇!

āĻāχ āĻ•āĻžāϰāϪ⧇āχ āĻŽā§‡āϰ⧁ āĻ…āĻžā§āϚāϞ⧇ (polar regions) āĻŦāĻž āĻļā§€āϤāĻĒā§āϰāϧāĻžāύ āĻĻ⧇āĻļ⧇ (cold countries) āĻšā§āϰāĻĻ (lakes) āĻāĻŦāĻ‚ āύāĻĻā§€āϰ (rivers) āωāĻĒāϰāĻŋāĻ­āĻžāĻ— āϜāĻŽā§‡ āϗ⧇āϞ⧇āĻ“ āϤāĻžāϰ āύāĻŋāĻšā§‡ āϜāϞ āϤāϰāϞāχ āĻĨāĻžāϕ⧇, āϝāĻž āϜāϞāϜ āĻĒā§āϰāĻžāĻŖā§€āĻĻ⧇āϰ (aquatic life) āĻŦ⧇āρāĻšā§‡ āĻĨāĻžāĻ•āϤ⧇ āϏāĻžāĻšāĻžāĻ¯ā§āϝ āĻ•āϰ⧇āĨ¤ āĻĒā§āϰāĻ•ā§ƒāϤāĻŋāϰ āĻāĻ• āϚāĻŽā§ŽāĻ•āĻžāϰ āĻ­āĻžāϰāϏāĻžāĻŽā§āϝ!
āĻāχ āĻŦ⧈āĻœā§āĻžāĻžāύāĻŋāĻ• āϧāĻžāϰāĻŖāĻžāϟāĻŋ āĻ•ā§āϞāĻžāϏ ā§Ģ āĻĨ⧇āϕ⧇ ā§§ā§Ļ-āĻāϰ āĻļāĻŋāĻ•ā§āώāĻžāĻ°ā§āĻĨā§€āĻĻ⧇āϰ āϜāĻ¨ā§āϝ āϖ⧁āĻŦāχ āϗ⧁āϰ⧁āĻ¤ā§āĻŦāĻĒā§‚āĻ°ā§āĻŖ āĻāĻŦāĻ‚ āϏāĻšāϜāĻŦā§‹āĻ§ā§āϝāĨ¤

#āϜāϞ #āĻŦāĻŋāĻœā§āĻžāĻžāύ #āϘāύāĻ¤ā§āĻŦ #āĻŦāϰāĻĢ

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