Chapter 11 ka aakhri post! 🏆 Aaj 11.1–11.3 ka mix: ulte sawaal (jawab diya hai, number dhoondho), jodi banao (12 × 37 + 12 × 63), dhokhe jaise × 21 jo 12 jaisa dikhta hai, aur darjan-gross ki paheliyan. Har tareeka pehle seekhe hue auzaaron se hi banega.
⏱ Before Timer: Pehle Purane Tareeke Se
Pehle seedha tareeka. Dono guna alag karo, phir jodo.
- 12 × 37 = 37 × 12: 370 + 74 = 444.
- 12 × 63 = 63 × 12: 630 + 126 = 756.
- Jodo: 444 + 756 = 1200.
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
12 × 37 + 12 × 63 = 1200
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
Chahiye: × 12 aur × 11 niyam, andaaza aur ikai check (Post 11.3). Naye shabd:
📖 Shabd jo is post mein aayenge
- Juft aur taaq: juft (even) number woh hai jo 0, 2, 4, 6 ya 8 pe khatam ho; use do barabar hisson mein baant sakte hain. Taaq (odd) number 1, 3, 5, 7 ya 9 pe khatam hota hai. Jaise 6 toffee 2 dost mein barabar bant jaati hain (3-3), par 7 nahi (1 bach jaati hai).
- Ulta sawaal: jawab diya hai, number dhoondhna hai: □ × 12 = 696.
- □ (dabba): khaali jagah: jo number dhoondhna hai.
- Jodi banao: jab do guna mein ek hi number (12) ho, to doosre numbers pehle jod lo: 12 × 37 + 12 × 63 = 12 × 100.
- Dhokha: sawaal jo is chapter jaisa dikhe par niyam seedhe na lage (× 21).
- Darjan aur gross: 1 darjan = 12 cheezein. 1 gross = 12 darjan = 144 cheezein.
- Bracket ( ): bracket ke andar wala hissa pehle karo: (37 + 63) × 12 matlab pehle 37 + 63 = 100, phir 100 × 12.
📏 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.
✌️ Double karna kya hai?
Double matlab number ko do baar lena, yaani number mein wahi number jodna. 7 ka double: 7 + 7 = 14. Yahi 2 × 7 bhi hai (GUNA box: 2 × 7 matlab 7 ko 2 baar jodo).
| Digit | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
|---|---|---|---|---|---|---|---|---|---|---|
| Double | 0 | 2 | 4 | 6 | 8 | 10 | 12 | 14 | 16 | 18 |
(Table mein upar digit hai, neeche uska double. Jaise 6 ke neeche 12, kyunki 6 + 6 = 12.) Is chapter mein hum sirf ek digit (0 se 9) ka double karenge, to sabse bada double 18 hai.
🔁 Chhota sa warm-up
- 37 + 63 = ?
- 100 × 12 = ?
- Kaunse digit ka double 6 pe khatam hota hai?
Answers dekho
- 100
- 1200
- 3 aur 8 (3 + 3 = 6, 8 + 8 = 16)
Pehle do mila kar aaj ka Before Timer sawaal ho gaya!
— 📌 charumam.com
🎬 Kahani: Gayab Hua Number
Aarav ki copy pe syahi gir gayi. Bas itna dikh raha tha: □ × 12 = 696. “Ab number kaise pata karun?” woh pareshaan tha.
Riya boli: “Do sawaal poochho. Pehla: andaaza. 50 × 12 = 600 aur 60 × 12 = 720. 696 in dono ke beech, to number 50 aur 60 ke beech. Doosra: ikai. 696 ki ikai 6. Kaunse digit ka double 6 pe khatam? 3 ya 8. To number 53 ya 58.”
“58 try karo: 058 → 16 (6 likho, 1 carry), 10 + 8 + 1 = 19 (9, carry 1), 0 + 5 + 1 = 6. 696!” Aarav ne taali bajaayi. 🏆
— 📌 charumam.com
🪄 Trick Step by Step: Pehchano, Andaaza, Ikai, Phir Try
💡 Is post ki ek badi baat: Har tricky sawaal mein pehle pehchano (× 12 ya dhokha? jodi ban sakti hai?). Ulte sawaal mein: andaaze se number ki dahai pakdo, ikai check se number ki ikai ke 2 option, phir niyam se try karke pakka karo.
Step 1: Pehchano: kis type ka sawaal?
Same 12 do baar → jodi banao. □ hai → ulta sawaal. 21, 13 jaisa number → dhokha (12 ka niyam nahi). Darjan/gross → × 12 ya × 144.
Step 2: Ulta sawaal, kadam 1: andaaza (dahai)
□ × 12 = 696. 10 ke gunaj (10, 20, 30…) × 12 aasaan hain: peeche 0 (jaise 50 × 12: pehle 5 × 12 = 60, phir peeche 0 → 600). 50 × 12 = 600 aur 60 × 12 = 720. 696 beech mein hai, to □ 50 se 59 ke beech: dahai 5.
Step 3: Ulta sawaal, kadam 2: ikai check
696 ki ikai 6. Ikai ka padosi nahi hota, to jawab ki ikai = number ki ikai ka double ka aakhri digit. Double 6 pe khatam: 3 (3 + 3 = 6) ya 8 (8 + 8 = 16). To □ = 53 ya 58.
| Jawab ki ikai | 0 | 2 | 4 | 6 | 8 | 1, 3, 5, 7, 9 |
|---|---|---|---|---|---|---|
| Number ki ikai kya ho sakti hai | 0 ya 5 | 1 ya 6 | 2 ya 7 | 3 ya 8 | 4 ya 9 | koi nahi! |
(Kaise? Double table dekho: 3 + 3 = 6 aur 8 + 8 = 16, dono 6 pe khatam. Aur koi double taaq digit pe khatam nahi hota, kyunki double hamesha juft hota hai: 0, 2, 4, …, 18.)
Step 4: Ulta sawaal, kadam 3: try karke pakka
58 × 12 niyam se:
58 × 12: number ke aage 0 lagao → 058. Ab right se left (ikai se shuru) har digit pe niyam:
| Kadam | Jagah | Digit | Kaam | Likho | Carry aage |
|---|---|---|---|---|---|
| 1 | Ikai | 8 | 8 ka double: 8 + 8 = 16; padosi nahi (ikai ke right mein koi digit nahi). Kul: 16 | 6 | 1 |
| 2 | Dahai | 5 | 5 ka double: 5 + 5 = 10; padosi 8 jodo; haath ka carry 1. Jod: 10 + 8 + 1 = 19 | 9 | 1 |
| 3 | Saikda | 0 (aage wala) | aage wala 0: double 0 + 0 = 0; padosi 5 jodo; haath ka carry 1. Jod: 0 + 5 + 1 = 6 | 6 | — |
Ab “Likho” wale digit neeche se upar, yaani left se right padho: 6 | 9 | 6 → 696.
To □ = 58. (53 × 12 = 636 hota, 696 nahi.)
Step 5: Dhokha: × 21
21 ulta 12 jaisa dikhta hai, par 21 = 20 + 1. To 47 × 21 = 47 × 20 + 47 = 940 + 47 = 987. (47 × 20: 47 × 2 = 94, peeche 0 → 940.) 12 ka niyam yahan nahi!
Tricky sawaal ke type, ek nazar mein
| Type | Example | Kaise | Jawab |
|---|---|---|---|
| Jodi banao | 12 × 37 + 12 × 63 | 12 × 100 | 1200 |
| Ulta | □ × 12 = 696 | andaaza 50–59, ikai 3/8, try | 58 |
| Dhokha | 47 × 21 | 940 + 47 | 987 |
| Darjan | 4 darjan + 7 | 48 + 7 | 55 |
| Gross | 1 gross | 12 × 12 | 144 |
| Peeche 0 | 125 × 120 | 125 × 12 = 1500, phir 0 | 15000 |
🆘 Atak gaye? Aise socho
- Ulta sawaal mein dahai? 10, 20, 30 … × 12 karke dekho jawab kin do ke beech hai.
- Ikai ke 2 option: double table se (6 → 3 ya 8). Jawab ki ikai taaq ho to aisa number hai hi nahi.
- Dhokha pakdo: 12 ke alawa koi bhi number (21, 13, 22) ho to × 12 niyam mat lagao.
- Jodi: pehle bracket: (37 + 63) = 100, phir × 12.
— 📌 charumam.com
🔍 Yeh Kaam Kyun Karta Hai?
Ulta sawaal ka “ikai check” kyun chalta hai? Post 11.1 ka chitra yaad karo: ikai ke khaane mein sirf number ki ikai ka double aata hai, kyunki ikai ka koi padosi nahi (× 10 se ikai mein 0 aata hai). Isliye jawab ki ikai = (number ki ikai ka double) ka aakhri digit. Ulta chalo to double table se number ki ikai mil jaati hai.
Jodi kyun? 12 × 37 matlab 12 ko 37 baar, 12 × 63 matlab 12 ko 63 baar. Kul 37 + 63 = 100 baar. Neeche tricky sawaal ka poora naksha hai.
58 × 12 ke khaane
Ulte sawaal ka jawab 58 chitra mein bhi dekho: ikai ke khaane mein sirf 8 ka double 16, padosi nahi.
— 📌 charumam.com
✏️ Solved Examples (Har Ek Normal Tareeke Se Check)
Example 1: □ × 12 = 384. □ = ?
Andaaza: 30 × 12 = 360, 40 × 12 = 480 → □ 30 se 39 ke beech. Ikai: 384 ki ikai 4 → number ki ikai 2 ya 7. Try 32: 032 → 4; 6 + 2 = 8; 0 + 3 = 3 → 384 ✅. To □ = 32.
✔️ Normal tareeke se check: 32 × 10 = 320, 32 × 2 = 64, 320 + 64 = 384 ✅
Example 2: 47 × 21 = ? (dhokha)
21 = 20 + 1. 47 × 20 = 940 (47 × 2 = 94, peeche 0). Phir 47 ek baar aur: 940 + 47 = 987.
✔️ Normal tareeke se check: Column: 47 × 1 = 47, 47 × 20 = 940, 47 + 940 = 987 ✅
Example 3: Ek dukaan mein 1 gross pencil. 1 gross = 12 darjan. Kitni pencil? Aur 3 gross?
12 darjan = 12 × 12. 012 → 2 + 2 = 4; 1 + 1 = 2, padosi 2: 2 + 2 = 4; aage 0: padosi 1 → 1. To 144 pencil. 3 gross = 144 × 3 = 144 + 144 + 144 = 432.
✔️ Normal tareeke se check: 12 × 12 = 120 + 24 = 144 ✅; 144 + 144 = 288, 288 + 144 = 432 ✅
Example 4: 125 × 120 = ?
Peeche ka 0 alag: 125 × 12. 0125 → 10 (0, carry 1); 4 + 5 + 1 = 10 (0, carry 1); 2 + 2 + 1 = 5; 0 + 1 = 1 → 1500. Ab peeche 0: 15000.
✔️ Normal tareeke se check: 125 × 12 = 1250 + 250 = 1500, aur × 10 → 15000 ✅
— 📌 charumam.com
🕉️ Vedic Maths Connection
Vedic Maths mein ulte sawaal ke liye “Vilokanam” (dekh kar, yaani observation) ki soch hai: jawab ko dhyaan se dekho, uske aakhri digit aur size se number pehchano. Aaj humne bilkul yahi kiya: size se dahai (andaaza), aakhri digit se ikai. Aur jodi banana Vedic aur school dono mein ek hi niyam hai: same number ko bahar nikaal lo.
— 📌 charumam.com
🧭 Kab Use Karein, Kab Nahi
| Situation | Trick use karein? | Kyun |
|---|---|---|
| Same 12 do baar (12 × 37 + 12 × 63) | ✅ Jodi banao | 12 × 100. |
| □ × 12 = 696 | ✅ Ulta | Andaaza + ikai check + try. |
| × 21, × 22, × 13 | ⚠️ Dhokha | 12 ka niyam nahi; × 20 + × 1 jaisa tod. |
| Darjan / gross | ✅ Haan | Darjan = 12, gross = 144. |
| 125 × 120 | ✅ Haan | 125 × 12, phir peeche 0. |
| □ × 12 = 745 (taaq ikai) | ❌ Aisa number nahi | × 12 ka jawab hamesha juft. |
— 📌 charumam.com
❌→✅ Common Mistakes
Galti 1: Ulte sawaal mein ikai seedhi utha li
Sawaal: □ × 12 = 696
❌ Galat: “jawab 6 pe khatam, to number bhi 6 pe khatam: 56.” 56 × 12 = 672.
✅ Sahi: ikai ka double 6 pe khatam: 3 ya 8. Try: 58.
Galti 2: × 21 pe × 12 ka niyam
Sawaal: 47 × 21
❌ Galat: double + padosi → 564 (yeh to 47 × 12 hai).
✅ Sahi: 940 + 47 = 987.
Galti 3: Jodi mein 12 bhi jod diya
Sawaal: 12 × 37 + 12 × 63
❌ Galat: 12 + 37 + 12 + 63 = 124.
✅ Sahi: guna hai, jod nahi: 12 × (37 + 63) = 12 × 100 = 1200.
Galti 4: Peeche ka 0 bhool gaye
Sawaal: 125 × 120
❌ Galat: 1500.
✅ Sahi: 120 = 12 × 10, to 1500 ke peeche 0: 15000.
🧠 Rule of thumb: Pehchano (jodi, ulta, dhokha), ulte mein andaaza + ikai check + try, aur hamesha check.
— 📌 charumam.com
🏃 Speed Drill: 15 Sawaal, Timer Ke Saath
Timer lagao. 15 mix sawaal, kuch ulte bhi. Target: 7 minute.
- 12 × 25 = ?
- 12 × 50 = ?
- 16 × 12 = ?
- 12 × 75 = ?
- 250 × 12 = ?
- 144 × 12 = ?
- 12 × 12 × 10 = ?
- 99 × 12 = ?
- 47 × 21 = ?
- 23 × 21 = ?
- □ × 12 = 696. □ = ?
- □ × 12 = 1020. □ = ?
- □ × 12 = 540. □ = ?
- □ × 12 = 384. □ = ?
- □ × 12 = 276. □ = ?
Mera time: ______ · Sahi: ____ / 15
Answers dekho (pehle khud karo!)
- 300
- 600
- 192
- 900
- 3000
- 1728
- 1440
- 1188
- 987
- 483
- 58
- 85
- 45
- 32
- 23
Kaise kiya (kuch): 12 × 25 = 25 × 12 (jagah badlo): 025 → 10 (0, c1); 4 + 5 + 1 = 10 (0, c1); 0 + 2 + 1 = 3 → 300. 144 × 12: 0144 → 8; 8 + 4 = 12 (2, c1); 2 + 4 + 1 = 7; 0 + 1 = 1 → 1728. 23 × 21 = 460 + 23 = 483. □ × 12 = 1020: andaaza 80 × 12 = 960, 90 × 12 = 1080 → 80 se 89; ikai 0 → 0 ya 5 → 80 ya 85; 80 × 12 = 960, to 85.
— 📌 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.
- 12 × 10 = ?
- 12 × 20 = ?
- 12 × 30 = ?
- 12 × 11 = ?
- 12 × 13 = ?
- 12 × 15 = ?
- 12 × 40 = ?
- 12 × 100 = ?
- 11 × 12 + 12 = ?
- 12 × 9 + 12 = ?
| 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
- 120
- 240
- 360
- 132
- 156
- 180
- 480
- 1200
- 144
- 120
Dhyaan: 11 × 12 + 12: yeh 11 baar 12 aur ek 12 aur, yaani 12 baar 12, jo 144 hai. 12 × 9 + 12 = 12 × 10 = 120. 12 × 13 = 13 × 12: 013 → 6; 2 + 3 = 5; 0 + 1 = 1 → 156.
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. 12 × 37 + 12 × 63 = ?
Jawab aur kaaran dekho
Sahi jawab: (d) 1200
- (a) galat ❌: 124: guna ki jagah sab jod diya (12 + 37 + 12 + 63).
- (b) galat ❌: 1100: 37 + 63 = 100 ke baad 12 ki jagah 11 se guna kar diya.
- (c) galat ❌: 756: sirf 12 × 63 kiya, 12 × 37 bhool gaye.
- (d) sahi ✅: 12 × (37 + 63) = 12 × 100 = 1200.
Q2. □ × 12 = 696. □ = ?
Jawab aur kaaran dekho
Sahi jawab: (c) 58
- (a) galat ❌: 53: ikai check ka doosra option, par 53 × 12 = 636.
- (b) galat ❌: 696 to jawab hai, □ nahi.
- (c) sahi ✅: Andaaza 50–59, ikai check 3 ya 8, try: 58 × 12 = 696 ✅.
- (d) galat ❌: 56: jawab ki ikai 6 seedhi utha li; 56 × 12 = 672.
Q3. 47 × 21 = ?
Jawab aur kaaran dekho
Sahi jawab: (b) 987
- (a) galat ❌: 940: sirf 47 × 20, ek 47 aur jodna bhool gaye.
- (b) sahi ✅: 21 = 20 + 1: 940 + 47 = 987.
- (c) galat ❌: 564: × 12 ka niyam laga diya (dhokha!); yeh 47 × 12 hai.
- (d) galat ❌: 517: × 11 kar diya; yeh 47 × 11 hai.
Q4. 1 gross = 12 darjan. 1 gross mein kitni cheezein?
Jawab aur kaaran dekho
Sahi jawab: (a) 144
- (a) sahi ✅: 12 × 12: 012 → 4, 4, 1 → 144.
- (b) galat ❌: 24: 12 + 12 kar diya; guna chahiye tha.
- (c) galat ❌: 120: 12 × 10 kar diya; 12 × 12 chahiye.
- (d) galat ❌: 1212: 12 ke saath 12 likh diya, guna nahi kiya.
Q5. Kya □ × 12 = 745 ho sakta hai (□ poora number)?
Jawab aur kaaran dekho
Sahi jawab: (d) Nahi, × 12 ka jawab hamesha juft
- (a) galat ❌: 62 × 12 = 744, 745 nahi.
- (b) galat ❌: 745 × 12 to bahut bada (8940).
- (c) galat ❌: 65 × 12 = 780, 745 nahi.
- (d) sahi ✅: × 12 ki ikai = kisi digit ka double ka aakhri digit, jo hamesha juft (0, 2, 4, 6, 8). 745 taaq pe khatam, to nahi.
Q6. 125 × 120 = ?
Jawab aur kaaran dekho
Sahi jawab: (c) 15000
- (a) galat ❌: 150000: do 0 laga diye; 120 mein ek hi 0 hai.
- (b) galat ❌: 12500: 125 × 100 kar diya.
- (c) sahi ✅: 125 × 12 = 1500, phir peeche 0 → 15000.
- (d) galat ❌: 1500: peeche ka 0 bhool gaye; yeh 125 × 12 hai.
Q7. □ × 12 = 1020. □ = ?
Jawab aur kaaran dekho
Sahi jawab: (b) 85
- (a) galat ❌: 102: 1020 ka 0 hata diya; 102 × 12 = 1224.
- (b) sahi ✅: Andaaza 80–89; ikai 0 → 0 ya 5; 80 × 12 = 960, 85 × 12 = 1020 ✅.
- (c) galat ❌: 80 × 12 = 960, 1020 nahi.
- (d) galat ❌: 90 × 12 = 1080, 1020 nahi.
Q8. 4 darjan aur 7 kele = kitne kele?
Jawab aur kaaran dekho
Sahi jawab: (a) 55
- (a) sahi ✅: 4 darjan = 4 × 12 = 48, phir 48 + 7 = 55.
- (b) galat ❌: 47: 4 aur 7 ko saath likh diya.
- (c) galat ❌: 48: sirf 4 darjan gine, 7 bhool gaye.
- (d) galat ❌: 84: 7 darjan gin liye (7 × 12), 4 bhool gaye.
Q9. 12 × 9 + 12 = ?
Jawab aur kaaran dekho
Sahi jawab: (d) 120
- (a) galat ❌: 108: sirf 12 × 9, + 12 bhool gaye.
- (b) galat ❌: 121: 120 ke baad 1 aur jod diya.
- (c) galat ❌: 132: 12 × 11 kar diya.
- (d) sahi ✅: 12 baar 9 aur ek 12: 12 × 10 = 120. (108 + 12 = 120.)
Q10. Kaunse sawaal mein 12 ka niyam (double + padosi) sahi baithta hai?
Jawab aur kaaran dekho
Sahi jawab: (c) 16 × 12
- (a) galat ❌: 13 alag niyam: 16 × 13 = 160 + 48 = 208 (yahan 48 = 16 × 3).
- (b) galat ❌: 22 alag: 16 × 22 = 320 + 32 = 352 (yahan 320 = 16 × 20 aur 32 = 16 × 2).
- (c) sahi ✅: 016 → 12 (2, c1); 2 + 6 + 1 = 9; 0 + 1 = 1 → 192.
- (d) galat ❌: 21 dhokha: 16 × 21 = 320 + 16 = 336 (yahan 320 = 16 × 20).
— 📌 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. Ek dabbe mein 1 darjan ande. 47 dabbe aur 5 khule ande. Kul kitne ande?
Solution dekho
47 × 12 = 564 (Post 11.1), phir 564 + 5 = 569.
Check: 470 + 94 = 564, 564 + 5 = 569 ✅
Q2. Ek 2-digit number × 12 ka jawab 3-digit hai aur 8 pe khatam hota hai. Sabse chhota aisa number?
Solution dekho
Ikai: double 8 pe khatam → 4 (4 + 4 = 8) ya 9 (9 + 9 = 18). Sabse chhota 2-digit: 14. 14 × 12: 014 → 8; 2 + 4 = 6; 0 + 1 = 1 → 168 (3-digit ✅). Jawab 14.
Check: 140 + 28 = 168 ✅
Q3. 12 × 12 = 144, 12 × 12 × 12 = ?
Solution dekho
144 × 12: 0144 → 4 ka double 8; 4 ka double 8, padosi 4: 8 + 4 = 12 (2, carry 1); 1 ka double 2, padosi 4, carry 1: 2 + 4 + 1 = 7; aage 0: padosi 1 → 1. Jawab 1728.
Check: 1440 + 288 = 1728 ✅
Q4. Riya: “□ × 12 = 444, to □ = 37.” Aarav: “Nahi, 32.” Kaun sahi?
Solution dekho
Andaaza: 30 × 12 = 360, 40 × 12 = 480 → 30 se 39. Ikai: 444 ki ikai 4 → 2 ya 7. 32 × 12 = 384, aur 37 × 12: 037 → 14 (4, c1); 6 + 7 + 1 = 14 (4, c1); 0 + 3 + 1 = 4 → 444. Riya sahi: □ = 37.
Check: 370 + 74 = 444 ✅
— 📌 charumam.com
🎯 Exam Mein Kahan Kaam Aayega?
| Exam | Kahan kaam aayega |
|---|---|
| School exam (Class 6–8) | Darjan/gross ke word problem, jodi wale sawaal, guna check. |
| Maths Olympiad | Ulte sawaal, missing number, “kya aisa ho sakta hai?” wale sawaal. |
| NTSE / MAT | Mental maths, number series, pattern. |
| SSC / Bank (aage) | Simplification: 12 × 37 + 12 × 63 jaise. |
Shabdon ka matlab: Olympiad = school ke bachchon ki maths pratiyogita (competition). NTSE = Class 10 ke bachchon ka ek national scholarship (vazifa) exam. MAT = Mental Ability Test, yaani sochne-samajhne ki pariksha (NTSE ka ek hissa). SSC / Bank exam = badon ke sarkari naukri ke exam. Simplification = lambe hisaab ko chhota karke jawab nikaalna. Class 6–8 = school ki chhathi se aathvi kaksha.
— 📌 charumam.com
👩🏫 CharuMam Ka Tip
Mantra: “pehchano, andaaza, ikai, try.” Ulte sawaal mein ghabraao mat: do sawaal (dahai kitni? ikai kya?) aur ek try. Chapter 11 poora! Agle chapter mein Trachtenberg ke 6, 7, 8, 9 ke niyam: pahaade ke bina guna! 🏆
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⏱ 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)
Dono mein 12. 37 baar 12 aur 63 baar 12, yaani kul (37 + 63) baar 12 = 100 baar 12 = 1200 ✅ (Jodi banao, Chapter 10 jaisa!)
| 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. 🚀
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🤖 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:
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❓ FAQs (Bachchon Ke Asli Sawaal)
1. Ulte sawaal mein dono option galat nikle to?
To andaaza dobara dekho: shayad dahai galat pakdi. Ya jawab ki ikai taaq hai, to aisa poora number hai hi nahi.
2. 3-digit ulte sawaal (□ × 12 = 3036)?
Wahi soch: andaaza 250 × 12 = 3000 → □ 250 ke paas; ikai 6 → 3 ya 8; try 253: 3036 ✅. 258 kyun nahi? 258 × 12 = 3096, jo 3036 nahi hai.
3. Jodi kab banti hai?
Jab dono guna mein ek hi number ho (12). Tab doosre numbers pehle jodo.
4. Ab aage kya?
Chapter 12: Trachtenberg ke 6, 7, 8, 9 ke niyam (aadha padosi, taaq pe 5, 10 se ghatao).
— 📌 charumam.com
🟢 Recap: Aaj Kya Seekha
- Pehchano: jodi, ulta, dhokha, darjan.
- Ulta: andaaze se dahai, ikai check se 2 option, try.
- × 12 ka jawab hamesha juft.
- Jodi: 12 × 37 + 12 × 63 = 12 × 100.
- × 21 dhokha: × 20 + × 1.
- Darjan 12, gross 144.
— charumam.com 🎯
👉 Aage Kya?
Chapter 11 poora! 🎉 Ab Chapter 12 mein Trachtenberg ke 6, 7, 8 aur 9 ke niyam: Post 12.1 se shuru, × 6: aadha padosi aur taaq pe 5.
Koi doubt? CharuMam AI Tutor se poochho, ya comment mein likho! 💬
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- 🌐 Website: charumam.com
- 🤖 AI Tutor (doubt poochho, 24×7): tutor.charumam.com
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