Chapter 4 ka aakhri post! 4.1–4.3 mix, missing digits, jod-phir-guna jaise 25+48 phir ×11, aur dhokha sawaal jahaan ×11 trick nahi chalni.
⏱ Before Timer: Pehle Purane Tareeke Se
Do tareeke, ek jawab: 25×11 + 48×11, ya pehle 25+48=73 phir 73×11 — dono same.
73×11 check: 73×10 + 73 = 730 + 73 = 803.
Ikai 0+3=3; dahai 3+7=10 → 0 likho, 1 carry; saikda 7+1=8. Jawab 803.
Ab phone ya ghadi mein stopwatch (samay naapne wali ghadi) chalu kijiye. Neeche wala sawaal isi school wale tareeke (column method) se kijiye, copy-pencil ke saath. Column method na aata ho to ungliyon pe gin kar bhi kar sakte hain. Jaise hi jawab mil jaaye, stopwatch rok dijiye aur apna time likh lijiye.
Mera time: ______ second
Jawab dekho
73 × 11 = 803
Abhi trick nahi dekhni! Post ke end mein After Timer mein yahi sawaal trick se karenge aur dono time ki tulna karenge. 😊
— 📌 charumam.com
✅ Pehle Yeh Aata Hai
Tools: 2-digit rule, 3-digit pairs, ×10+number check, jod pe guna, aur ghatana pe guna.
📖 Shabd jo is post mein aayenge
- Jod pe guna: ×11 har hisse pe: 25×11 + 48×11 = 73×11, kyunki 25+48=73.
- Ghatana pe guna: 11 dabbe, har mein 312; har dabbe se 42 nikalo to har mein 270 bache → pehle 312 − 42 = 270, phir 270 × 11.
- Missing digit: jawab se number peeche se nikaalo; MCQ mein options try + check.
- Dhokha: ×12 / galat tool dikhaaya.
- Alag lambai: 2, 3, 4 digit ek drill mein.
- Carry dhoondho: jod 10 ya zyada dhoondho.
📏 Bade numbers padhna aur round number mein jodna
Har digit ki ek jagah (place) hoti hai. Right se gino: pehli jagah Ikai (ones, 1 wale), uske left mein Dahai (tens, 10 wale), phir Saikda (hundreds, 100 wale), phir Hazaar (thousands, 1000 wale).
10 ka bundle: 10 ikai = 1 dahai (10). 10 dahai = 1 saikda (100). 10 saikde = 1 hazaar (1000). Har jagah apne right wali jagah se 10 guna badi hai.
| Number | Kaise padhein | Kis cheez se bana |
|---|---|---|
| 98 | attaanve | 9 dahai (90) + 8 ikai |
| 165 | ek sau painsath | 1 saikda (100) + 6 dahai (60) + 5 ikai |
| 999 | nau sau ninyaanve | 9 saikde (900) + 9 dahai (90) + 9 ikai |
| 1011 | ek hazaar gyaarah | 1 hazaar (1000) + 0 saikda + 1 dahai (10) + 1 ikai |
Round number mein chhota number jodna (place box niyam): chhote number ko right se likho, yaani ikai ke neeche ikai, dahai ke neeche dahai. Phir har dabbe mein jo hai, woh jawab mein utaar do. Ek digit wala number sirf ikai ka zero badalta hai, do digit wala ikai aur dahai dono.
- 100 + 65: 65 mein do digit, to 6 dahai mein aur 5 ikai mein: 1|6|5 = 165.
- 100 + 2: 2 sirf ikai mein, dahai ka 0 waise hi rehta hai: 1|0|2 = 102 (12 nahi, 120 nahi!).
- 200 + 6: 6 sirf ikai mein: 2|0|6 = 206.
- 1000 + 11: 11 mein do digit, to 1 dahai mein aur 1 ikai mein: 1|0|1|1 = 1011.
✖️ Guna kya hai? (Multiplication)
Guna (nishaan ×) matlab ek hi number ko baar-baar jodna. “6 × 4” ko bolte hain “6 guna 4”, matlab 4 ko 6 baar jodo:
6 × 4 = 4 + 4 + 4 + 4 + 4 + 4 = 24
Isi tarah 6 × 7 matlab 7 ko 6 baar jodo. Running total (har baar ka naya jod) dekho: 7, 14, 21, 28, 35, 42. To 6 × 7 = 42.
10 dahai = 1 saikda: 10 dande (har danda 10) milkar 100 bante hain, yaani 1 saikda. Isliye 24 dahai = 20 dahai + 4 dahai = 2 saikde + 4 dahai = 240. (Aur 10 saikde milkar 1 hazaar, yaani 1000, bante hain.)
Tukdon mein guna kyun kar sakte hain? 47 = 4 dande (40) + 7 cube (7). 47 ko 6 baar lena matlab neeche jaisi 6 line. Dande alag gin lo, cube alag gin lo, kul utna hi rahega:
6 × 47: 6 baar 40 = 240, 6 baar 7 = 42, kul 240 + 42 = 282
Guna mein carry 1 se bada ho sakta hai: jod mein carry aksar 1 hota hai, par guna mein bada bhi aa sakta hai. Column mein 6 × 7 = 42 aaya, yaani 4 dahai aur 2 ikai. To ikai mein 2 likho aur 4 dahai carry karo (aage le jao). Phir dahai mein 6 × 4 = 24, usme carry ke 4 jodo: 24 + 4 = 28. Jawab 282.
Guna mein jagah badlo, jawab wahi: 16 × 4 aur 4 × 16 ek hi cheez hain. Neeche dots dekho: 4 line, har line mein 16 dots. Line se gino to 4 baar 16; khade column se gino to 16 baar 4. Dots wahi hain, to jawab bhi wahi: 64. Isliye jo aasaan lage, us tarah jodo.
Copy pe column mein (28 + 15 jaisa):
- Ikai: 6 × 7 = 42. Neeche ikai mein 2 likho. 42 ke 4 dahai carry hain: chhota 4 dahai wale digit (4) ke upar likho.
- Dahai: 6 × 4 = 24, usme upar likha carry 4 jodo: 24 + 4 = 28. Neeche 28 likho (8 dahai mein, 2 saikde mein).
- Jawab: 282.
10 se guna: 3 × 10 matlab 10 ko 3 baar jodna: 10 + 10 + 10 = 30. Kisi number ko 10 se guna karo to woh har digit ek jagah left khisak jaata hai aur ikai mein 0 aa jaata hai: 3 → 30, 30 → 300.
🔁 Chhota sa warm-up
- 25×11=?
- 48×11=?
- 275+528=?
Answers dekho
- 275
- 528
- 803
Jod-pe-guna check garam!
— 📌 charumam.com
🎬 Kahani: Do Groups, Ek Sawaal
Board: “25 + 48, phir pura × 11”.
Ek group: pehle jod 73, phir ×11 = 803. Doosra group: 25×11 aur 48×11 alag, phir jod — bhi 803!
CharuMam: “Dono sahi — jod pe guna. Aaj dhokha aur missing bhi!” 🧩
— 📌 charumam.com
🪄 Trick Step by Step: Pehle Socho, Phir Tool, Phir Check
💡 Is post ki ek badi baat: Tricky ×11: pehle poochho “kya sach mein ×11 hai?”. Phir lambai ke hisaab se rule. Jod pe guna se tod sakte ho. Hamesha ×10+number ya tukdon se check.
Step 1: Dhokha check
Pehle poochho: yeh ×11 hai ya ×12? Galat chapter mat kholo.
Step 2: Sawaal ka type pehchano — 2-digit, 3-digit, jod/ghatana, ya missing.
Jo type dikhe, usi ke hisaab se 4.1 / 4.2 / jod-pe-guna / peeche-se tool chuno.
Step 3: Rule lagaao aur carry ke saath jawab likho.
Chuna hua rule lagao; jod 10 ya zyada ho to carry sambhalo, phir digits likho.
Step 4: Check karo
×10+number se, ya tukdon ka jod karke, jawab pakka karo.
Yaad-patra
| Type | Kya karo |
|---|---|
| 2-digit × 11 | 4.1 left|sum|right |
| 3-digit × 11 | 4.2 padosi jod |
| 25+48 phir ×11 | pehle jod phir ×11, ya alag×11 phir jod |
| Missing | peeche se socho; MCQ mein options try + ×10+number |
| ×12 dhokha | ×11 ka rule mat lagao |
🆘 Atak gaye? Aise socho
- ×12 dikhe: ruk jao — yeh post ka dhokha.
- Missing: peeche se socho; MCQ mein options try karo, phir ×10+number se check.
- Bada jod: jod pe guna — pehle jod, phir ×11.
- Check: hamesha.
— 📌 charumam.com
🔍 Yeh Kaam Kyun Karta Hai?
Koi naya jaadu nahi — 4.1–4.3 + jod pe guna (guna jod pe fail nahi hoti).
25+48 phir ×11 matlab 25×11 + 48×11, kyunki 11 baar 25 aur 48 ka jod wahi hai jo 11 baar 25 plus 11 baar 48.
Ghatana pe guna: socho 11 dabbe, har dabbe mein 312 cheezein. Har dabbe se 42 nikaal do — har dabbe mein 270 bachti hain. To kul = 270 × 11. Matlab pehle 312 − 42 = 270, phir 270 × 11 = 2970. Check: 312×11 − 42×11 = 3432 − 462 = 2970 ✅
— 📌 charumam.com
✏️ Solved Examples (Har Ek Normal Tareeke Se Check)
Example 1: 25 + 48, phir × 11 = ?
73×11: 7+3=10 → 803.
✔️ Normal tareeke se check: 275+528=803 ✅
Example 2: □4 × 11 = 484. □?
Jawab 484: right digit = 4. Left digit bhi 4 hai aur beech 8 — matlab carry nahi tha, to number ka left bhi 4 (□=4). Check: 4+4=8 beech ✅ → 484. MCQ mein options try: 34×11=374, 44×11=484, 54×11=594.
✔️ Normal tareeke se check: 440+44=484 ✅
Example 3: 312×11 − 42×11 = ?
11 dabbe, har mein 312; har se 42 nikalo → har mein 270 → 270×11 = 2970. Digits: 2|9|7|0.
✔️ Normal tareeke se check: 3432−462=2970 ✅
Example 4: Dhokha: 42×12? (×11 mat)
×12 matlab ×10 aur ×2: 420+84=504. (×11 hota 462 — alag!)
✔️ Normal tareeke se check: 420+84=504 ✅
— 📌 charumam.com
🕉️ Vedic Maths Connection
Mix practice — jod pe guna har jagah kaam aata hai.
— 📌 charumam.com
🧭 Kab Use Karein, Kab Nahi
| Situation | Trick use karein? | Kyun |
|---|---|---|
| Mix ×11 puzzles | ✅ | Yahi post. |
| ×12 / ×9 | ❌ | Alag. |
| Exam answer sheet pe seedha | ❌ | Rough mein OK, sheet pe steps mat chhodo. |
| Carry se ghabrahat | ⚠️ | ×10+number backup. |
— 📌 charumam.com
❌→✅ Common Mistakes
Galti 1: Dhokha pe ×11 rule
42×12 ❌ 462. ✅ 504.
Galti 2: Jod pe guna bhool kar lambaa
Pehle jodna aksar chhota raasta hai.
Galti 3: Check nahi
Tricky mein check zaroori.
🧠 Rule of thumb: Pehle pakka karo ×11 hai; phir tool; phir check.
— 📌 charumam.com
🏃 Speed Drill: 15 Sawaal, Timer Ke Saath
15 sawaal, sab ×11, koi dhokha nahi. Target: 5 minute.
- 24 × 11 = ?
- 142 × 11 = ?
- 2142 × 11 = ?
- 53 × 11 = ?
- 305 × 11 = ?
- 18 + 19, phir × 11 = ?
- 66 × 11 = ?
- 707 × 11 = ?
- 36 × 11 = ?
- 129 × 11 = ?
- 88 × 11 = ?
- 450 × 11 = ?
- 17 × 11 = ?
- 226 × 11 = ?
- 1001 × 11 = ?
Mera time: ______ · Sahi: ____ / 15
Answers dekho (pehle khud karo!)
- 264
- 1562
- 23562
- 583
- 3355
- 407
- 726
- 7777
- 396
- 1419
- 968
- 4950
- 187
- 2486
- 11011
— 📌 charumam.com
⏰ One-Minute Challenge
Sirf 1 minute (60 second). Timer lagao, aur jitne ho sakein utne sawaal mann mein (bina copy ke) karo. Sirf jawab likhna hai.
- 31 × 11 = ?
- 131 × 11 = ?
- 45 × 11 = ?
- 154 × 11 = ?
- 62 × 11 = ?
- 71 × 11 = ?
- 80 × 11 = ?
- 91 × 11 = ?
- 108 × 11 = ?
- 200 × 11 = ?
| Rating | Kitne sahi, kitne time mein |
|---|---|
| 🌱 Beginner | 60 second mein 5 se 7 sahi. Badhiya shuruaat! |
| 🚀 Pro | 60 second mein 8 ya 9 sahi |
| 🏆 Champion | 10 mein 10 sahi, 60 second ke andar |
Answers dekho
- 341
- 1441
- 495
- 1694
- 682
- 781
- 880
- 1001
- 1188
- 2200
5 se kam sahi? Koi baat nahi! Trick wala section ek baar aur padho aur kal phir try karo. Har din thoda better, bas yahi chahiye. 💪
— 📌 charumam.com
📝 10 MCQs (Har Option Ka Kaaran)
MCQ matlab ek sawaal ke chaar jawab (options) diye hote hain, unme se ek sahi chunna hai.
Q1. 25 + 48, phir pura × 11 = ?
Jawab aur kaaran dekho
Sahi jawab: (d) 803
- (a) galat ❌: 275 sirf 25×11 hai — 48×11 bhi jodna tha (ya pehle 73×11).
- (b) galat ❌: 528 sirf 48×11 hai — dono hisse ×11 karke jodna tha.
- (c) galat ❌: 733: 73 likh kar chipka diya; ×11 bhi karna tha → 803.
- (d) sahi ✅: Pehle 25+48=73, phir 73×11=803.
Q2. □4×11=484. □?
Jawab aur kaaran dekho
Sahi jawab: (c) 4
- (a) galat ❌: 54×11=594, 484 nahi.
- (b) galat ❌: 84×11=924, 484 nahi.
- (c) sahi ✅: Jawab ka left 4, carry nahi → number ka left bhi 4; 4+4=8 beech ✅. MCQ: options try — 44×11=484.
- (d) galat ❌: 34×11=374, 484 nahi.
Q3. 42×12 (dhokha) = ?
Jawab aur kaaran dekho
Sahi jawab: (b) 504
- (a) galat ❌: 522 tab jab 42 × 2 = 84 ki jagah galat jod (102) laga diya: 420 + 102 = 522. Sahi 420 + 84 = 504.
- (b) sahi ✅: 42×12 = 42×10 + 42×2 = 420+84 = 504.
- (c) galat ❌: 462 woh ×11 ka jawab hai, yahan ×12.
- (d) galat ❌: 424: na ×10+×2, na ×11 — galat hisaab.
Q4. 312×11 − 42×11 = ?
Jawab aur kaaran dekho
Sahi jawab: (a) 2970
- (a) sahi ✅: 11 dabbe: pehle 312 − 42 = 270, phir 270 × 11 = 2970.
- (b) galat ❌: 3432 sirf 312×11 — 42×11 ghatana bhool.
- (c) galat ❌: 462 sirf 42×11 — 312 wala hisa bhool.
- (d) galat ❌: 2880: 270×10=2700 + kuch galat; sahi 270×11=2970.
Q5. 24×11=?
Jawab aur kaaran dekho
Sahi jawab: (d) 264
- (a) galat ❌: 244 bina beech jod (2+4=6 hona chahiye).
- (b) galat ❌: 224: beech mein 2 likha, 2+4=6 nahi kiya.
- (c) galat ❌: 274: beech 7 (galat jod); sahi 2+4=6 → 264.
- (d) sahi ✅: 2 | 2+4=6 | 4 → 264.
Q6. Jod pe guna / ghatana pe guna ka matlab?
Jawab aur kaaran dekho
Sahi jawab: (c) 25×11 + 48×11
- (a) galat ❌: Sirf jod bina ×11 adhoora — ×11 bhi lagaana zaroori hai.
- (b) galat ❌: Ghatana pe guna mein 312 − 42 = 270 ke baad ×11 zaroori; bina ×11 adhoora.
- (c) sahi ✅: 25+48 phir ×11 = 25×11 + 48×11 — jod pe guna.
- (d) galat ❌: 25+48+11 galat — har hisse pe ×11 chahiye, sirf +11 nahi.
Q7. 2142×11=?
Jawab aur kaaran dekho
Sahi jawab: (b) 23562
- (a) galat ❌: 23552: 4+2=6 ki jagah 5 — ek digit miss.
- (b) sahi ✅: 2 | 2+1=3 | 1+4=5 | 4+2=6 | 2 → 23562.
- (c) galat ❌: 21422: pairs skip, digits chipak.
- (d) galat ❌: 22142: padosi jodon ka order / jod galat.
Q8. Kab trick NA?
Jawab aur kaaran dekho
Sahi jawab: (a) ×12 sawaal
- (a) sahi ✅: ×12 pe yeh ×11 padosi-jod mat lagao.
- (b) galat ❌: 3-digit ×11 pe use karo — yahi chapter.
- (c) galat ❌: Rough andaaza OK, dhokha nahi.
- (d) galat ❌: Check hamesha OK — NA nahi.
Q9. 18 + 19, phir × 11 — pehle kya?
Jawab aur kaaran dekho
Sahi jawab: (d) 37×11
- (a) galat ❌: Sirf 18×11 adhoora — 19 bhi jodna tha.
- (b) galat ❌: Sirf 19 adhoora — pehle 18+19=37 karo.
- (c) galat ❌: Yahan ×12 nahi, ×11 hai.
- (d) sahi ✅: Pehle 18+19=37, phir ×11.
Q10. 18 + 19, phir × 11 = ?
Jawab aur kaaran dekho
Sahi jawab: (c) 407
- (a) galat ❌: 209 sirf 19×11.
- (b) galat ❌: 370 sirf 37×10; +37 bhi chahiye → 407.
- (c) sahi ✅: 37×11=407.
- (d) galat ❌: 198 sirf 18×11.
— 📌 charumam.com
🧠 Challenge: HOTS Aur Olympiad Style
HOTS matlab Higher Order Thinking Skills, yaani aise sawaal jinme sirf trick nahi, thoda dimaag bhi lagana padta hai. Olympiad ek maths competition (pratiyogita) hota hai.
Q1. Kaunsa 2-digit × 11 = 484?
Solution dekho
□4 × 11 = 484. Jawab ka left digit 4 hai aur carry nahi (beech 8, left 4 jaisa). To number ka left bhi 4 → □=4. Check: 4+4=8 beech ✅, jawab 484. MCQ ho to options try: 34×11=374, 44×11=484, 54×11=594. Number 44. Check: 440+44=484 ✅
Q2. 42×11 aur 11×42 same kyun?
Solution dekho
Guna mein jagah badlo, jawab wahi. 42 ko 11 baar jodna = 11 ko 42 baar jodna — same total.
Q3. Sabse chhota 3-digit jisme ×11 mein bilkul ek carry ho (ek pair 10 ya zyada, doosra nahi).
Solution dekho
Left+beech chhota rakhna hai (carry nahi), to carry sirf beech+right se aaye. Beech+right 10 ya zyada ka sabse chhota: beech 1, right 9 (1+9=10). Left bhi sabse chhota 1 (left+beech=1+1=2, carry nahi). To number 119. 119×11=1309. Check: 1190+119=1309 ✅. 118 mein 1+8=9 (carry nahi) — isliye 119 sabse chhota.
Q4. Olympiad: 11×11×11?
Solution dekho
Pehle 11×11: 1 | 1+1=2 | 1 → 121. Phir 121×11: 1|3|3|1 → 1331. Check: 1210+121=1331 ✅
— 📌 charumam.com
🎯 Exam Mein Kahan Kaam Aayega?
| Exam | Kahan kaam aayega |
|---|---|
| School | Mix ×11 mann mein. |
| Olympiad | Jod pe guna + digit tricks. |
| NTSE | Dhokha + mann mein tez. |
| SSC | Simplification ×11. |
Shabdon ka matlab: Olympiad = school ke bachchon ki maths pratiyogita (competition). NTSE = Class 10 ke bachchon ka ek national scholarship (vazifa) exam. SSC / Bank exam = badon ke sarkari naukri ke exam. Simplification = lambe hisaab ko chhota karke jawab nikaalna.
— 📌 charumam.com
👩🏫 CharuMam Ka Tip
Tricky pe 5 second: “×11 hai na?” Phir tool. Dhokha avoid karna bhi speed hai! 🧩
— 📌 charumam.com
⏱ After Timer: Ab Trick Se!
Wahi sawaal jo shuru mein kiya tha. Stopwatch phir chalu kijiye, aur is baar aaj ki trick se kijiye:
Trick se kaise karein (dekho)
Pehle 25+48=73. Phir 73×11: 7+3=10 → carry → 803. Check: 275+528=803 ✅
| Before time | After time | Kitna tez? |
|---|---|---|
| ____ second | ____ second | Before − After = ____ second bache! |
Pehli baar mein time zyada bhi lag sakta hai, ghabraiye nahi! Nayi trick ko 3 se 4 din ki practice chahiye. Phir yeh purane tareeke se kaafi tez ho jaati hai. 🚀
— 📌 charumam.com
🤖 Aur Practice: AI Tutor Se Poochho
Neeche wali line copy kijiye aur CharuMam AI Tutor (tutor.charumam.com) mein paste kar dijiye. Tutor aapko naye sawaal dega aur galti hone pe samjhayega:
— 📌 charumam.com
❓ FAQs (Bachchon Ke Asli Sawaal)
1. Chapter 4 khatam ho gaya?
Haan — Ch 4 ke chapter page pe saare 4 posts milenge.
2. 4.2 weak lage to?
Wapas 3-digit pairs + carry drill karo, phir mix.
3. Calculator kab use?
Check ke baad. Seekhte waqt pehle khud socho.
4. Chapter 5 kab?
Chapter 5 live hai: Multiply by 5, 25, 50 — Ch 5 ke saare posts.
— 📌 charumam.com
🟢 Recap: Aaj Kya Seekha
- 4.1–4.3 ke tools mix karo.
- Jod pe guna: 25×11 + 48×11 = 73×11.
- Dhokha: ×12 pe ×11 ka rule nahi chalta.
- Missing: peeche se socho / options try + check.
- Hamesha check karo.
- Pehle pakka karo ×11 hai.
— charumam.com 🎯
👉 Aage Kya?
Chapter 4 complete! Chapter page se revise karo. Ab Ch 5: Multiply by 5, 25 aur 50 live hai — chapter page se shuru karo.
Koi doubt? CharuMam AI Tutor se poochho, ya comment mein likho! 💬
💛 Post Achha Laga? Like, Share, Subscribe, Follow!
Agar aaj kuch naya samajh aaya, to post ko like kijiye, apne doston aur class ke group mein share kijiye, aur roz nayi trick ke liye humein subscribe aur follow kijiye! 🙏
- 🌐 Website: charumam.com
- 🤖 AI Tutor (doubt poochho, 24×7): tutor.charumam.com
- ▶️ YouTube (subscribe): @charumamofficial
- 📸 Instagram (follow): @charumamofficial
- ✈️ Telegram: t.me/charumam
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— 📌 charumam.com
