Chapter 7 ka aakhri post! Aaj 7.1–7.3 ka mix: do guna ek saath, ulta sawaal (jawab diya hai, number dhoondo), base 1000 ki pehli jhalak (999 × 998) aur dhokhe jahan base method seedha nahi lagta. Har sawaal mein: base pehchano, kam ya zyada dekho, khaane gino, phir check.
⏱ Before Timer: Pehle Purane Tareeke Se
Pehle seedha tareeka. 98 × 97 aur 103 × 102 alag-alag lamba guna karke jodo.
- 98 × 97: 97 ko 100 baar = 9700, usme se 97 ko 2 baar (194) ghatao: 9700 − 194 = 9506.
- 103 × 102: 103 ko 100 baar = 10300, plus 103 ko 2 baar (206): 10300 + 206 = 10506.
- Jodo: 9506 + 10506 = 20012.
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
98 × 97 + 103 × 102 = 20012
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
Aaj ke tools: 7.1 (base 10), 7.2 (100 se kam), 7.3 (100 se zyada), aur “Pehle guna, phir jod” wala niyam (PAD box mein). Neeche boxes ek baar aur. Naye shabd:
📖 Shabd jo is post mein aayenge
- Ulta sawaal: jawab diya hai, ek number chhupa hai (□). Right hisse se □ ka kitna kam/zyada nikaalo.
- □ (dabba): chhupa hua number jo dhoondhna hai.
- Base 1000: 1000 ke paas wale numbers (991 se 999, 1001 se 1009) ka base. 3 zero → right ko 3 khaane.
- Dhokha: sawaal jo trick jaisa dikhe par aaj wali shart (dono kam ya dono zyada) poori na ho, jaise 12 × 8.
- Pehle guna, phir jod: 98 × 97 + 103 × 102 mein pehle dono guna, phir unka jod. Kabhi bhi 97 + 103 pehle nahi.
📏 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.
💯 100 se guna = peeche do 0 lagao
100 = 10 × 10 (10 ko 10 baar jodo: 10, 20, 30, … 100). Isliye 100 se guna karna matlab do baar 10 se guna. Har baar 10 se guna pe peeche ek 0 lagta hai (upar wala box), to 100 se guna pe do 0:
36 → (× 10) 360 → (× 10) 3600
Place value se: 36 × 100 matlab 36 saikde (36 sau). 36 sau = 3600 (padho: teen hazaar chhe sau).
| Number | × 100 |
|---|---|
| 7 | 700 |
| 36 | 3600 |
| 37 | 3700 |
| 124 | 12400 (padho: barah hazaar chaar sau) |
Bade number padhna: 12400 mein right se paanchvi jagah Das hazaar (10000 wale) hai. 12400 = 1 das hazaar + 2 hazaar + 4 saikde, yaani 10000 + 2000 + 400.
🎯 Base kya hai? (Paas wala round number)
Round number woh hai jiske peeche (right mein) sirf zero hon: 10, 100, 1000. Aaj ki trick mein inhe base kehte hain. Base matlab “ghar” ya “nishaana”: woh round number jiske paas hamare dono numbers baithe hain.
- 8 aur 7: dono 10 ke paas hain (10 se thoda kam). Base = 10.
- 12 aur 13: dono 10 ke paas hain (10 se thoda zyada). Base = 10.
- 97 aur 96: dono 100 ke paas. Base = 100.
- 104 aur 107: dono 100 ke paas (thoda zyada). Base = 100.
- 997 aur 996: dono 1000 ke paas. Base = 1000.
Base kaise chunein? Number ko dekho aur socho: “Yeh 10, 100 ya 1000 mein se kiske sabse paas hai?” 8 to 10 se sirf 2 door hai, isliye 10. 97 to 100 se sirf 3 door, isliye 100. Dono numbers ka base ek hi hona chahiye.
| Base | Base mein kitne zero | Jawab ka left hissa kya ginta hai |
|---|---|---|
| 10 | 1 zero | kitne dahai (10 wale) |
| 100 | 2 zero | kitne saikde (100 wale) |
| 1000 | 3 zero | kitne hazaar (1000 wale) |
“Base mein kitne zero” wali baat yaad rakhna. Aage “right hissa kitne digit ka” isi se tay hoga.
📏 Base 100 se kitna kam, kitna zyada?
Har number ke liye ek chhota sawaal: “Base tak pahunchne mein kitna bacha?” ya “Base se kitna aage nikal gaya?”
- Kitna kam (number base se chhota ho) = base − number. Matlab number ko base banne ke liye kitna aur chahiye.
- Kitna zyada (number base se bada ho) = number − base. Matlab number base se kitna aage hai.
100 se kitna kam? Chapter 3 wali trick: Post 3.1 mein seekha tha ki 100 se ghatane ke liye dahai digit ko 9 se poora karo aur ikai digit ko 10 se poora karo. 100 − 97: dahai 9 → 9 − 9 = 0, ikai 7 → 10 − 7 = 3. Jawab 03, yaani 3. Ulti ginti se bhi: 97 se 98, 99, 100: teen kadam.
| Number | Base 100 se | Kaise nikala |
|---|---|---|
| 99 | 1 kam | 100 − 99 = 1 |
| 97 | 3 kam | 9 − 9 = 0, 10 − 7 = 3 → 03 |
| 96 | 4 kam | 100 − 96 = 4 |
| 92 | 8 kam | 100 − 92 = 8 |
| 88 | 12 kam | 9 − 8 = 1, 10 − 8 = 2 → 12 |
| 104 | 4 zyada | 104 − 100 = 4 |
| 112 | 12 zyada | 112 − 100 = 12 |
Chhota raasta: 100 se zyada wale (101 se 120 jaise) ka “kitna zyada” bas uske aakhri do digit hain: 107 → 07 = 7, 112 → 12. Kyunki 112 = 100 + 12.
🧱 Deewar ( | ), right hisse ke digit, aur carry
Is trick mein jawab do hisson mein banta hai: left hissa | right hissa. Beech ki khadi lakeer ( | ) ko “deewar” samjho. Yeh sirf hamare samjhne ke liye hai; asli jawab mein deewar nahi likhte, dono hisse saath-saath likh dete hain.
Base 100 mein 2 zero hain. Isliye left hissa kitne saikde ginta hai, aur right hisse ko jawab mein do khaane milte hain. Niyam:
Right hisse mein digit = base ke zero (2)
- Right chhota pade (kam digit) → aage 0 bharo.
- Right bada pade (zyada digit) → sabse left wala extra hissa left hisse mein jodo (carry).
- 93 | 12: 12 mein pehle se do digit hain. 93 saikde + 12 = 9300 + 12 = 9312.
- 95 | 6: 6 sirf ek digit hai. Use 06 likho: 0 dahai mein, 6 ikai mein. 95 saikde + 6 = 9500 + 6 = 9506. Agar 0 bhool gaye to “956” ban jaata, jo 9506 se bahut chhota hai (galat!). Yeh bilkul Post 6.3 wala 09 hai.
- Carry: 77 | 132: 132 mein teen digit, par jagah sirf do. 132 = 1 saikda + 32. Woh 1 saikda left ke saikdon mein jaata hai: 77 + 1 = 78 → 78 | 32 = 7832. Pakka: 7700 + 132 = 7832 ✅.
Pehle guna, phir jod (zaroori niyam): jab ek hi line mein × aur + dono hon, to pehle × (guna) karo, phir + (jod). Jaise 5 × 10 + 6: pehle 5 × 10 = 50, phir 50 + 6 = 56. (Agar pehle 10 + 6 = 16 karke 5 × 16 karte to 80 aata, jo galat hai.) Is post mein “left × base + right” isi niyam se padhna.
🔁 Chhota sa warm-up
- 100 − 98 = ?
- 2 × 3 = ? (2 khaane mein)
- 9506 + 10506 = ?
Answers dekho
- 2
- 06
- 20012
Tools tayyar! Ab tricky sawaal.
— 📌 charumam.com
🎬 Kahani: Dabbe Wala Ulta Sawaal
Olympiad practice mein sawaal aaya: □ × 98 = 9506. “□ kya hai? □ 100 se kam hai.”
Aarav ne 9506 ko 98 se bhaag dene ki koshish ki (bhaag = ÷, yaani barabar hisson mein baantna, jaise Ch 5 mein aadha kiya tha)… lamba bhaag, aur time khatam hone laga.
Sana ne socha: “9506 matlab 95 | 06. Right 06, yaani 2 ko kisi se guna kiya. 98 to 2 kam hai, to doosra 3 kam hoga. □ = 97!” Check: 98 − 3 = 95 ✅.
CharuMam: “Base method ulta bhi chalta hai! Aaj ulte sawaal, bade base, aur woh dhokhe jahan trick chupke se fail hoti hai.” 🧠
— 📌 charumam.com
🪄 Trick Step by Step: Base Pehchano, Kam/Zyada, Khaane Gino, Check
💡 Is post ki ek badi baat: Har base method sawaal mein: (1) base chuno (10, 100, 1000), (2) dono kam ya dono zyada? (3) left: tirchha ghatao ya jodo, (4) right: guna, utne khaane jitne base mein zero, (5) check andaaze se.
Step 1: Base pehchano
Dono numbers kis round number ke paas? 8, 7 → 10. 97, 103 → 100. 998 → 1000.
Step 2: Dono kam ya dono zyada?
Dono kam (97 × 96) → ghatao. Dono zyada (104 × 107) → jodo. Ek kam ek zyada (12 × 8) → abhi ruko, yeh Chapter 8 ka type hai.
Step 3: Right ke khaane gino
Base 10 → 1 khaana, 100 → 2, 1000 → 3. Kam pade to aage 0, zyada ho to carry.
Step 4: Check
Andaaza: 98 × 97 to 10000 se thoda kam; 103 × 102 thoda zyada. Ya seedha tareeka.
Yaad-patra
| Type | Example | Kya karo | Jawab |
|---|---|---|---|
| Base 10, dono kam | 8 × 7 | 8 − 3 | 2 × 3 | 56 |
| Base 10, dono zyada | 12 × 13 | 12 + 3 | 2 × 3 | 156 |
| Base 100, dono kam | 98 × 97 | 98 − 3 | 06 | 9506 |
| Base 100, dono zyada | 104 × 107 | 104 + 7 | 28 | 11128 |
| Base 1000, dono kam | 999 × 998 | 999 − 2 | 002 | 997002 |
| Ulta | □ × 98 = 9506 | 06: 2 ko 3 se guna → □ 3 kam | 97 |
Ulta sawaal kaise? (□ × 98 = 9506, □ 100 se kam)
- Jawab ko deewar se todo: base 100, to aakhri 2 digit right: 95 | 06.
- 98 ka kitna kam = 2. Right 06 (yaani 6) bana 2 ko □ ke kitna kam se guna karke. 2 ko 3 se guna karo to 6. To □ ka kitna kam = 3.
- □ = 100 − 3 = 97.
- Left se check: 98 − 3 = 95 ✅. Pakka.
Base 1000: 999 × 998
Dono 1000 ke paas. 1000 mein 3 zero → right ko 3 khaane. 999 → 1 kam, 998 → 2 kam. Left: 999 − 2 = 997. Right: 1 × 2 = 2 → 3 khaane: 002. Jawab 997 | 002 = 997002.
Left 997 asal mein 997 hazaar (997000) hai, plus 2 = 997002 ✅. (Post 8.3 mein base 1000 aur detail mein.)
Dhokha 1: 12 × 8
12 to 10 se 2 zyada, aur 8, 10 se 2 kam. Ek upar, ek neeche! Aaj wali shart (dono kam ya dono zyada) toot gayi. Agar galti se aaj wala tareeka laga do (left: 12 + 2 = 14, right: 2 × 2 = 4), to 14 | 4 = 144 aayega, jo galat hai. Seedha socho: 12 ko 8 baar = 10 ko 8 baar + 2 ko 8 baar = 80 + 16 = 96. (Iska apna base method Chapter 8 mein!)
Dhokha 2: 12 × 104
12, 10 ke paas hai aur 104, 100 ke paas. Alag base! Aaj ki trick ek hi base ke liye hai. Seedha: 104 ko 12 baar = 104 ko 10 baar + 104 ko 2 baar = 1040 + 208 = 1248.
🆘 Atak gaye? Aise socho
- Ulta sawaal? Pehle jawab ko deewar se todo (base 100 → aakhri 2 digit), phir right se □ ka kam/zyada.
- Base 1000? 3 khaane: 2 → 002.
- Ek upar ek neeche? Aaj ki trick nahi; seedha karo ya Chapter 8 dekho.
- Do alag base? Trick nahi; seedha tareeka.
— 📌 charumam.com
🔍 Yeh Kaam Kyun Karta Hai?
Ulta kyun chalta hai? Seedha chalne pe right hissa = do dooriyon ka guna, aur left = ek number − doosre ki doori. Jab jawab aur ek number pata ho, to ek doori pata hai (98 → 2). Right hissa batata hai doosri doori (6 = 2 × 3). Ek hi raasta, ulti disha.
Base 1000 mein 3 khaane kyun? Left hissa ab hazaar ginta hai (997 → 997000), to jo right bacha woh 1000 se chhota, yaani 3 digit (000 se 999).
12 × 8 pe kyun nahi? Chitra socho: 8 wala hissa 10 se chhota (patti kaatni padegi), 12 wala bada (patti judegi). Kona ab jodna nahi, ghatana padta hai. Woh Chapter 8 ki kahani hai. Neeche kadmon ka naksha (flow chart): har sawaal se pehle yeh sawaal poochho.
— 📌 charumam.com
✏️ Solved Examples (Har Ek Normal Tareeke Se Check)
Example 1: 98 × 97 + 103 × 102 = ?
Pehle guna: 9506 aur 10506. Phir jod: 20012.
✔️ Normal tareeke se check: Seedha: 9700 − 194 = 9506, 10300 + 206 = 10506 (Before Timer). 9506 + 10506 = 20012 ✅
Example 2: □ × 98 = 9506, □ 100 se kam. □ = ?
95 | 06. 98 → 2 kam. 2 ko 3 se guna karo to 6, to □ 3 kam → 97.
✔️ Normal tareeke se check: 97 × 98: 95 | 06 → 9506 ✅
Example 3: 999 × 998 = ?
Base 1000, 3 khaane. 1 kam, 2 kam. 997 | 002 → 997002.
✔️ Normal tareeke se check: 999 ko 1000 baar − 999 ko 2 baar. 1000 = 10 × 100, to 1000 baar matlab peeche teen 0: 999000. 999 ko 2 baar = 1000 ko 2 baar (2000) se 2 kam = 1998. Ab 999000 − 1998: pehle 999000 − 2000 = 997000; par humne 2 zyada ghataye, to 2 wapas jodo: 997002 ✅
Example 4: 12 × 8 = ? (dhokha)
Ek upar ek neeche: aaj ki trick nahi. Seedha: 80 + 16 = 96.
✔️ Normal tareeke se check: 8 ko 12 baar: 8 ko 10 baar = 80, 8 ko 2 baar = 16 → 96 ✅
— 📌 charumam.com
🕉️ Vedic Maths Connection
Vedic Maths ki kitabon mein Nikhilam ke saath base 1000, 10000 tak ke examples milte hain, aur “jitne zero, utne digit” wala niyam har jagah same. Kitabein ulte sawaalon ke liye alag sutra bhi batati hain, par humne dekha ki base method ko ulti disha mein chalaana hi kaafi hai.
— 📌 charumam.com
🧭 Kab Use Karein, Kab Nahi
| Situation | Trick use karein? | Kyun |
|---|---|---|
| Ek base, dono kam ya dono zyada | ✅ Haan | 7.1–7.3 wali trick. |
| Ulta sawaal (□ × 98 = 9506) | ✅ Haan | Right se doori, left se check. |
| Base 1000 (999 × 998) | ✅ Haan | 3 khaane. |
| Ek upar ek neeche (12 × 8, 103 × 97) | ➡️ Chapter 8 | Kona ghatana padta hai. |
| Alag base (12 × 104) | ❌ Nahi | Seedha todo: 1040 + 208. |
| Base se bahut door (63 × 71) | ❌ Nahi | Right bahut bada. |
— 📌 charumam.com
❌→✅ Common Mistakes
Galti 1: Jod pehle kar diya
Sawaal: 98 × 97 + 103 × 102
❌ Galat: pehle 97 + 103 jod diya, phir aage guna.
✅ Sahi: pehle dono guna (9506, 10506), phir jod: 20012.
Galti 2: Ulte sawaal mein deewar galat jagah
Sawaal: □ × 98 = 9506
❌ Galat: 950 | 6 todkar socha.
✅ Sahi: base 100 → aakhri 2 digit right: 95 | 06 → □ = 97.
Galti 3: Base 1000 mein 2 hi khaane
Sawaal: 999 × 998
❌ Galat: 997 | 02 → 99702.
✅ Sahi: 3 zero → 3 khaane: 002 → 997002. Andaaza: jawab 1000 × 1000 = 1000000 se thoda kam, yaani 6 digit ka; 99702 sirf 5 digit ka hai.
Galti 4: Ek upar ek neeche pe aaj ki trick
Sawaal: 12 × 8
❌ Galat: left 12 + 2 = 14, right 2 × 2 = 4 → 144.
✅ Sahi: yeh dhokha hai. Seedha: 80 + 16 = 96. Andaaza: 12 × 8 to 12 × 10 = 120 se kam.
🧠 Rule of thumb: Pehle shart: ek base, aur dono kam ya dono zyada. Phir khaane = zero. Phir check.
— 📌 charumam.com
🏃 Speed Drill: 15 Sawaal, Timer Ke Saath
Mix drill! Pehle type pehchano, phir karo. Target: 5 minute.
- 9 × 7 = ?
- 13 × 15 = ?
- 96 × 97 = ?
- 99 × 94 = ?
- 103 × 106 = ?
- 108 × 104 = ?
- 89 × 97 = ?
- 113 × 112 = ?
- □ × 97 = 9409, □ 100 se kam. □ = ?
- □ × 104 = 11024, □ 100 se zyada. □ = ?
- 999 × 997 = ?
- 98 × 98 + 102 × 102 = ?
- 12 × 8 = ?
- 11 × 104 = ?
- 96 × 104 = ?
Mera time: ______ · Sahi: ____ / 15
Answers dekho (pehle khud karo!)
- 63
- 195
- 9312
- 9306
- 10918
- 11232
- 8633
- 12656
- 97
- 106
- 996003
- 20008
- 96
- 1144
- 9984
Kaise kiya (kuch): □ × 104 = 11024: 110 | 24, 4 ko 6 se guna karo to 24 → □ = 106. 98 × 98 + 102 × 102 = 9604 + 10404 = 20008. 11 × 104 aur 96 × 104 dhokhe hain: 11 × 104 = 1144 (Ch 4 ki × 11 trick: 1, 1 + 0, 0 + 4, 4), 96 × 104 = Chapter 8 ka type (seedha: 96 ko 100 baar (9600) + 96 ko 4 baar (384) = 9984).
— 📌 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.
- 8 × 9 = ?
- 12 × 14 = ?
- 97 × 98 = ?
- 95 × 96 = ?
- 102 × 107 = ?
- 105 × 109 = ?
- 99 × 99 = ?
- 111 × 104 = ?
- 998 × 997 = ?
- 14 × 16 = ?
| 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
- 72
- 168
- 9506
- 9120
- 10914
- 11445
- 9801
- 11544
- 995006
- 224
Dhyaan: 998 × 997 → 995 | 006 → 995006 (3 khaane). 14 × 16 → 20 | 24 → 22 | 4 → 224.
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. 98 × 97 + 103 × 102 = ?
Jawab aur kaaran dekho
Sahi jawab: (d) 20012
- (a) galat ❌: 2012: dono mein 0 bhool gaye: 95 | 6 → 956 aur 105 | 6 → 1056; 956 + 1056 = 2012.
- (b) galat ❌: 19612: 103 × 102 mein bhi ghata diya: 103 − 2 = 101 | 06 → 10106; 9506 + 10106 = 19612.
- (c) galat ❌: 20120: dono mein 6 ko dahai ke khaane mein likha: 95 | 60 → 9560 aur 105 | 60 → 10560; 9560 + 10560 = 20120.
- (d) sahi ✅: Pehle guna: 98 × 97 → 95 | 06 → 9506, aur 103 × 102 → 105 | 06 → 10506. Phir jod: 9506 + 10506 = 20012.
Q2. □ × 98 = 9506, □ 100 se kam. □ = ?
Jawab aur kaaran dekho
Sahi jawab: (c) 97
- (a) galat ❌: 95 to left hissa hai (95 | 06), □ nahi. 95 × 98 → 95 − 2 = 93 | 5 × 2 = 10 → 9310, 9506 nahi.
- (b) galat ❌: 3 to □ ka kitna kam hai, □ nahi: □ = 100 − 3 = 97.
- (c) sahi ✅: 9506 → 95 | 06. 98 → 2 kam. 2 × 3 = 6, to □ 3 kam: 100 − 3 = 97. Check: 98 − 3 = 95 ✅
- (d) galat ❌: 96 hota to 4 kam: 98 − 4 = 94 | 2 × 4 = 8 → 94 | 08 → 9408, 9506 nahi.
Q3. 999 × 998 = ?
Jawab aur kaaran dekho
Sahi jawab: (b) 997002
- (a) galat ❌: 998002: 999 mein se apna hi kitna kam ghata diya: 999 − 1 = 998 | 002 → 998002.
- (b) sahi ✅: 1 kam, 2 kam: 999 − 2 = 997 | 1 × 2 = 2 → 3 khaane: 997 | 002 → 997002.
- (c) galat ❌: 99702: 2 ko 3 ki jagah 2 hi khaane diye: 997 | 02 → 99702.
- (d) galat ❌: 997020: 2 ko dahai wale khaane mein likha: 997 | 020 → 997020.
Q4. Base 1000 mein right ke kitne khaane?
Jawab aur kaaran dekho
Sahi jawab: (a) 3
- (a) sahi ✅: 1000 mein 3 zero, to 3 khaane (jaise 002).
- (b) galat ❌: 2 khaane base 100 mein hote hain (100 mein 2 zero).
- (c) galat ❌: 1 khaana base 10 mein hota hai (10 mein 1 zero).
- (d) galat ❌: 4 khaane base 10000 mein hote (10000 mein 4 zero).
Q5. 12 × 8 pe aaj wali (dono kam ya dono zyada) trick kyun nahi?
Jawab aur kaaran dekho
Sahi jawab: (d) 12 upar hai, 8 neeche (ek zyada, ek kam)
- (a) galat ❌: 12 bada nahi, base 10 se sirf 2 zyada hai.
- (b) galat ❌: 8 chhota nahi, base 10 se sirf 2 kam hai.
- (c) galat ❌: Base 10 hi hai; dikkat yeh hai ki numbers base ke alag-alag taraf hain.
- (d) sahi ✅: Shart: dono ek taraf hon. Yahan 12 → 2 zyada, 8 → 2 kam: alag taraf. Yeh Chapter 8 ka type hai.
Q6. 12 × 104 = ?
Jawab aur kaaran dekho
Sahi jawab: (c) 1248
- (a) galat ❌: 1040: sirf 104 ko 10 baar kiya: 104 × 10 = 1040; 104 ko 2 baar (208) jodna bhool gaye.
- (b) galat ❌: 1208: 104 ko 10 baar ki jagah 100 ko 10 baar le liya: 1000 + 208 = 1208.
- (c) sahi ✅: Alag base, seedha: 104 ko 10 baar = 1040, 104 ko 2 baar = 208; 1040 + 208 = 1248.
- (d) galat ❌: 168: zabardasti base method: 12 + 4 = 16 | 2 × 4 = 8 → 168. Alag base pe trick galat jawab deti hai.
Q7. □ × 104 = 11024, □ 100 se zyada. □ = ?
Jawab aur kaaran dekho
Sahi jawab: (b) 106
- (a) galat ❌: 6 to □ ka kitna zyada hai, □ nahi: □ = 100 + 6 = 106.
- (b) sahi ✅: 11024 → 110 | 24. 104 → 4 zyada. 4 × 6 = 24, to □ 6 zyada: 100 + 6 = 106. Check: 104 + 6 = 110 ✅
- (c) galat ❌: 104 hota to 104 + 4 = 108 | 4 × 4 = 16 → 108 | 16 → 10816, 11024 nahi.
- (d) galat ❌: 110 to left hissa hai (110 | 24), □ nahi. 110 × 104 → 110 + 4 = 114 | 10 × 4 = 40 → 11440, 11024 nahi.
Q8. Kaunsa sawaal dhokha hai (aaj ki trick nahi)?
Jawab aur kaaran dekho
Sahi jawab: (a) 96 × 104
- (a) sahi ✅: 96 neeche (4 kam), 104 upar (4 zyada): alag taraf, yeh Chapter 8 ka type hai.
- (b) galat ❌: 96 × 97 dono kam: 96 − 3 = 93 | 4 × 3 = 12 → 9312. Aaj ki trick chalti hai.
- (c) galat ❌: 104 × 103 dono zyada: 104 + 3 = 107 | 4 × 3 = 12 → 10712. Aaj ki trick chalti hai.
- (d) galat ❌: 9 × 8 dono kam: 9 − 2 = 7 | 1 × 2 = 2 → 72. Aaj ki trick chalti hai.
Q9. 98 × 98 + 102 × 102 = ?
Jawab aur kaaran dekho
Sahi jawab: (d) 20008
- (a) galat ❌: 20000: dono kone (04) bhool gaye: 9600 + 10400 = 20000.
- (b) galat ❌: 20080: dono mein 4 ko dahai ke khaane mein likha: 96 | 40 → 9640 aur 104 | 40 → 10440; 9640 + 10440 = 20080.
- (c) galat ❌: 2008: dono mein 0 bhool gaye: 96 | 4 → 964 aur 104 | 4 → 1044; 964 + 1044 = 2008.
- (d) sahi ✅: 98 × 98 → 96 | 04 → 9604, aur 102 × 102 → 104 | 04 → 10404. Jod: 9604 + 10404 = 20008.
Q10. 998 × 997 = ?
Jawab aur kaaran dekho
Sahi jawab: (c) 995006
- (a) galat ❌: 995060: 6 ko dahai wale khaane mein likha: 995 | 060 → 995060.
- (b) galat ❌: 996006: 998 mein se apna hi kitna kam ghata diya: 998 − 2 = 996 | 006 → 996006.
- (c) sahi ✅: 2 kam, 3 kam: 998 − 3 = 995 | 2 × 3 = 6 → 3 khaane: 995 | 006 → 995006.
- (d) galat ❌: 99506: 6 ko 2 hi khaane diye: 995 | 06 → 99506.
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🧠 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. 101 × 101 − 99 × 99 = ?
Solution dekho
101 × 101: 1 zyada, 1 zyada → 102 | 01 → 10201. 99 × 99: 1 kam, 1 kam → 98 | 01 → 9801. Farq: 10201 − 9801 = 400.
Dekho: dono kone (01) same the, to sirf left ka farq: 102 − 98 = 4 saikde = 400. ✅
Q2. 98 × 97 aur 102 × 103: dono ke kone same kyun?
Solution dekho
98 × 97 mein 2 kam, 3 kam → kona 2 × 3 = 06. 102 × 103 mein 2 zyada, 3 zyada → kona 2 × 3 = 06. Dooriyan same, to kona same! Left alag: 95 aur 105. Jawab 9506 aur 10506. Farq bhi 1000 (10 saikde).
Check: 10506 − 9506 = 1000 ✅
Q3. Ek bade stadium (khel ka maidan) mein 104 qataar (line) hain, har qataar mein 106 kursiyan. 100 kursiyan toot gayin. Kitni bachi?
Solution dekho
Pehle guna: 104 × 106 → 110 | 24 → 11024. Phir ghatao: 11024 − 100 = 10924 kursiyan.
Check: 104 ko 100 baar + 104 ko 6 baar = 10400 + 624 = 11024 ✅
Q4. 9□ × 9□ = 9025 (dono □ same digit). □ = ?
Solution dekho
9□ matlab do digit ka number: dahai mein 9, ikai mein □. 90 | 25: right 25 = kitna kam × kitna kam, to kitna kam 5 (5 × 5 = 25). Number = 100 − 5 = 95, to □ = 5. Left check: 95 − 5 = 90 ✅.
Check: 95 × 95 = 9025 ✅ (Post 6.1: 9 × 10 = 90, peeche 25)
— 📌 charumam.com
🎯 Exam Mein Kahan Kaam Aayega?
| Exam | Kahan kaam aayega |
|---|---|
| School exam (Class 7–8) | Do guna ka jod/ghatana, area aur kursiyon/dabbon wale word problems. |
| Maths Olympiad | Ulte sawaal (□ × 98 = 9506), kone ka pattern, 101 × 101 − 99 × 99. |
| NTSE / MAT | Dhokha pehchanna: kab trick, kab seedha. |
| SSC / Bank (aage) | 999 × 998 jaise bade guna seconds mein. |
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.
— 📌 charumam.com
👩🏫 CharuMam Ka Tip
Chapter 7 ka mantra: “base pehchano, taraf dekho, khaane gino.” Agle chapter mein woh type jo aaj dhokha tha: ek upar, ek neeche (12 × 8, 103 × 97). 🧠
— 📌 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)
98 × 97: 95 | 06 → 9506. 103 × 102: 105 | 06 → 10506. Jodo: 9506 + 10506 = 20012 ✅. (Pehle guna, phir jod.)
| 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 deewar kahan lagaun?
Right se utne digit jitne base mein zero: base 100 → aakhri 2 digit, base 1000 → aakhri 3.
2. Kya 9999 × 9998 bhi ho sakta hai?
Haan! Base 10000, 4 khaane: 9997 | 0002 → 99970002.
3. 12 × 8 ka base method kab?
Chapter 8.1 mein: ek upar, ek neeche, jahan kona ghatana padta hai.
4. Agle post mein kya hai?
Chapter 8 shuru: Post 8.1, ek upar ek neeche (12 × 8 = 96) ka base method.
— 📌 charumam.com
🟢 Recap: Aaj Kya Seekha
- Shart: ek base, dono kam ya dono zyada.
- Ulta sawaal: right se doori, left se check.
- Base 1000 → 3 khaane (999 × 998 = 997002).
- Pehle guna, phir jod.
- Dhokhe: ek upar ek neeche (12 × 8), alag base (12 × 104).
- Check: andaaza ya seedha tareeka.
— charumam.com 🎯
👉 Aage Kya?
Chapter 7 poora! 🎉 Ab Chapter 8: Above and Below Base, jahan ek number base se upar aur ek neeche hoga: 12 × 8, 103 × 97. Kona ghatana padega, aur ek naya kadam aayega: udhaar!
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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