Chapter 8 ka aakhri post, aur base method ka sabse mazedaar hissa! 🏆 Aaj 8.1–8.3 ka mix: do guna ek saath, ulta sawaal jisme udhaar ko ulta kholna padega, pattern (jawab 10000 se 1, 4, 9, 16 … kam), aur dhokhe jahan base method lagta hi nahi.
⏱ Before Timer: Pehle Purane Tareeke Se
Pehle seedha tareeka. Dono guna alag karo, phir jodo.
- 102 × 98: 102 ko 100 baar − 102 ko 2 baar = 10200 − 204 = 9996.
- 103 × 97: 97 ko 100 baar + 97 ko 3 baar = 9700 + 291 = 9991.
- Jodo: 9996 + 9991 = 19987.
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
102 × 98 + 103 × 97 = 19987
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: 8.1 (base 10, alag taraf), 8.2 (base 100, saikda udhaar), 8.3 (base 1000, kab nahi). Neeche boxes ek baar aur. Naye shabd:
📖 Shabd jo is post mein aayenge
- Udhaar ko ulta kholna: jawab 100 | 88 dikhe to socho: udhaar se pehle left 1 zyada tha (101), aur kona = 100 − 88 = 12.
- Barabar door: ek number base se jitna upar, doosra utna hi neeche (106 aur 94). Tab left = base, aur jawab = base × base − doori × doori.
- Pattern: ek niyam se badhte/ghatate jawab: 9999, 9996, 9991, 9984 …
- Dhokha: sawaal jo base method jaisa dikhe par shart (ek hi base, paas) poori na ho: 98 × 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.
✖️ 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.
➖ Minus wala right hissa aur udhaar (base 100)
Is chapter mein ek number base se upar hoga aur doosra neeche. Tab right hissa (kitna zyada × kitna kam) jodna nahi, ghatana hota hai. Ise hum − (minus) nishaan se dikhate hain. “−4” ko bolo “minus 4”, matlab “4 nikaalna hai”. Yeh koi naya number nahi, bas ek yaad-dilaane wala nishaan hai: “isko ghatana mat bhoolna!”
Udhaar ki yaad (Post 3.1): ghatane mein jab kisi jagah se kuch nikaalna ho aur wahan kam ho, to left wali jagah se 1 bundle udhaar lete hain. Jaise 1 dahai = 10 ikai, 1 saikda = 100.
Example: 100 | −09 (yeh 103 × 97 mein aayega). Pehle dhyaan: base 100 mein 2 zero, to right hissa do digit ka: 9 → 09. Matlab: 100 saikde mein se 9 nikaalo.
- Udhaar: 100 saikde mein se 1 saikda udhaar lo. Left mein 99 saikde bache.
- Woh 1 saikda = 100. Ab 100 − 09 nikaalo, Chapter 3 ki trick se: dahai 0 → 9 − 0 = 9, ikai 9 → 10 − 9 = 1. To 91.
- Jawab: 99 | 91 = 9991. Pakka: 9900 + 91 = 9991, aur 10000 − 9 = 9991 ✅.
Chhota yaad: minus wala right hissa ho to left mein se 1 ghatao, aur right ki jagah (100 − right) likho. Jaise 103 | −40 → 102 | 60 (yeh 108 × 95 mein aata hai).
🔁 Chhota sa warm-up
- 100 − 88 = ?
- 10000 − 36 = ?
- 9996 + 9991 = ?
Answers dekho
- 12
- 9964
- 19987
Tools tayyar! Ab tricky sawaal.
— 📌 charumam.com
🎬 Kahani: Quiz Ka Final: Chhupa Number
Kai schoolon ki quiz pratiyogita (competition) ka aakhri round. Board pe likha aaya: □ × 97 = 10088. “□ 100 se zyada hai. 15 second!”
Ek team ne 10088 ÷ 97 ka lamba bhaag (barabar hisson mein baantna) shuru kiya. Riya ne socha: “□ 100 se upar, 97 neeche: alag taraf, to kona minus tha aur udhaar hua hoga. 10088 = 100 | 88, yeh udhaar ke baad ka roop hai! Pehle 101 | −12 tha. 97 → 3 kam, to kona 12 = 3 × 4. □ 4 zyada: 104!”
Ghanti baji! Sahi jawab. Doosre round mein sawaal aaya 98 × 12, aur Riya muskurayi: “Yeh dhokha hai: alag base. Seedha karo: 1176.”
Aaj yahi sab: ulta kholna, pattern, aur dhokhe pehchanna. 🏆
— 📌 charumam.com
🪄 Trick Step by Step: Taraf Dekho, Kona Ka Nishaan Chuno, Udhaar, Check
💡 Is post ki ek badi baat: Har sawaal mein: (1) ek hi base? (2) ek taraf (kona +) ya alag taraf (kona −)? (3) khaane = zero; minus ho to left − 1 | base − kona. Ulta sawaal mein yahi kadam peeche ki taraf.
Step 1: Ek hi base?
102 aur 98 → 100. 98 aur 12 → alag (100 aur 10): seedha tod.
Step 2: Ek taraf ya alag taraf?
Dono kam/dono zyada → kona jodo. Ek upar ek neeche → kona ghatao.
Step 3: Khaane aur udhaar
Base 100 → 2 khaane. Minus kona → left − 1, right 100 − kona.
Step 4: Check
Alag taraf → jawab left ke saikde se thoda kam (104 × 97: left 101 saikde = 10100, jawab 10088). Ya seedha tod.
Yaad-patra
| Type | Example | Kya karo | Jawab |
|---|---|---|---|
| Base 10, alag taraf | 13 × 8 | 11 | −6 → 10 | 4 | 104 |
| Base 100, alag taraf | 104 × 97 | 101 | −12 → 100 | 88 | 10088 |
| Bada kona | 115 × 92 | 107 | −120 → 105 | 80 | 10580 |
| Base 1000, alag taraf | 1003 × 996 | 999 | −012 → 998 | 988 | 998988 |
| Barabar door | 106 × 94 | 10000 − 36 | 9964 |
| Ulta | □ × 97 = 10088 | 101 | −12, 12 = 3 × 4 | 104 |
Pattern: barabar door wale
101 × 99 = 9999, 102 × 98 = 9996, 103 × 97 = 9991, 104 × 96 = 9984, 105 × 95 = 9975. Har baar left 100, aur 10000 mein se doori × doori kam: 1, 4, 9, 16, 25. (Neeche patti chart.)
Ulta sawaal: □ × 97 = 10088, □ 100 se zyada
- Jawab ko todo (base 100, 2 khaane): 100 | 88.
- □ upar hai, 97 neeche → alag taraf → yeh udhaar ke baad ka roop hai. Ulta kholo: left + 1 = 101, kona = 100 − 88 = 12.
- 97 → 3 kam. Kona 12 bana 3 ko □ ke kitna zyada se guna karke. 3 ko 4 se guna karo to 12, to □ 4 zyada → □ = 104.
- Left se check: 104 − 3 = 101 ✅.
Dhokha: 98 × 12
98 base 100 ke paas, 12 base 10 ke paas: alag base. Seedha: 98 ko 12 baar = 98 ko 10 baar + 98 ko 2 baar = 980 + 196 = 1176. (Ya 12 ko 100 baar − 12 ko 2 baar = 1200 − 24 = 1176.)
🆘 Atak gaye? Aise socho
- Ulta sawaal alag taraf wala? Pehle udhaar ulta kholo: left + 1, kona = 100 − right.
- Barabar door? Seedha base × base − doori × doori: 106 × 94 = 10000 − 36.
- Do guna ka jod? Pehle dono guna, phir jod.
- Alag base? Seedha tod.
— 📌 charumam.com
🔍 Yeh Kaam Kyun Karta Hai?
Ulta kyun chalta hai? Seedha chalne mein kadam the: left nikaalo, kona nikaalo, udhaar (left − 1, 100 − kona). Har kadam ulta bhi ho sakta hai: 100 − kona ka ulta 100 − right, aur left − 1 ka ulta left + 1. Isliye jawab se kona aur left wapas mil jaate hain.
Barabar door wale kyun 10000 se kam? 106 × 94 ka chitra: patti kaat kar upar rakho to 100 × 100 ka dabba banta hai, par 6 × 6 ka kona khaali. Isliye 10000 − 36. Jitni doori badi, utna bada khaali kona: neeche ki pattiyan dekho, har baar kami 1, 4, 9, 16, 25.
— 📌 charumam.com
✏️ Solved Examples (Har Ek Normal Tareeke Se Check)
Example 1: 102 × 98 + 103 × 97 = ?
9996 + 9991 = 19987.
✔️ Normal tareeke se check: Seedha: 10200 − 204 = 9996, 9700 + 291 = 9991 (Before Timer). Jod 19987 ✅
Example 2: Do numbers 100 se barabar door (ek upar, ek neeche), guna 9964. Numbers?
10000 − 9964 = 36 = 6 × 6 → doori 6 → 106 aur 94.
✔️ Normal tareeke se check: 106 × 94: 100 | −36 → 99 | 64 → 9964 ✅
Example 3: □ × 97 = 10088, □ 100 se zyada. □ = ?
100 | 88 → ulta: 101 | −12. 12 = 3 × 4 → □ = 104.
✔️ Normal tareeke se check: 104 ko 100 baar − 104 ko 3 baar = 10400 − 312 = 10088 ✅
Example 4: 98 × 12 = ? (dhokha)
Alag base: seedha 98 ko 10 baar + 98 ko 2 baar = 980 + 196 = 1176.
✔️ Normal tareeke se check: 12 ko 100 baar − 12 ko 2 baar = 1200 − 24 = 1176 ✅
— 📌 charumam.com
🕉️ Vedic Maths Connection
Vedic Maths ki kitabon mein barabar door wale gunaon (jaise 106 × 94) ke liye alag niyam bhi bataye jaate hain. Humne dekha ki base method ka chitra (khaali kona) hi in sab ki wajah samjha deta hai: barabar door ho to left base hi aata hai, aur kona doori × doori.
— 📌 charumam.com
🧭 Kab Use Karein, Kab Nahi
| Situation | Trick use karein? | Kyun |
|---|---|---|
| Ek hi base, alag taraf (104 × 97) | ✅ Haan | Left − 1 | 100 − kona. |
| Barabar door (106 × 94) | ✅ Sabse tez | Base × base − doori × doori. |
| Ulta sawaal (□ × 97 = 10088) | ✅ Haan | Udhaar ulta kholo. |
| Ek taraf (96 × 97) | ➡️ Chapter 7 | Kona jodo. |
| Alag base (98 × 12, 13 × 97) | ❌ Nahi | Seedha tod. |
| Door numbers (56 × 43) | ❌ Nahi | Seedha tod. |
— 📌 charumam.com
❌→✅ Common Mistakes
Galti 1: Ulte sawaal mein udhaar nahi khola
Sawaal: □ × 97 = 10088
❌ Galat: right 88 ko hi kona maan liya, aur 3 se baant nahi paaye.
✅ Sahi: alag taraf → pehle ulta kholo: kona = 100 − 88 = 12 → □ = 104.
Galti 2: Barabar door mein kona jod diya
Sawaal: 106 × 94
❌ Galat: 10000 mein 36 jod ke 10036 likh diya.
✅ Sahi: alag taraf → ghatao: 9964.
Galti 3: Alag base pe trick
Sawaal: 98 × 12
❌ Galat: 98 − 2 jaisa kuch karke 96 | … likhna shuru.
✅ Sahi: seedha: 1176.
Galti 4: Jod pehle
Sawaal: 102 × 98 + 103 × 97
❌ Galat: beech ke 98 aur 103 pehle jod diye.
✅ Sahi: pehle dono guna, phir jod: 19987.
🧠 Rule of thumb: Ek hi base? Taraf? Khaane? Minus ho to udhaar. Ulta ho to udhaar ulta. Trick theek na baithe to seedha.
— 📌 charumam.com
🏃 Speed Drill: 15 Sawaal, Timer Ke Saath
Final mix drill! Pehle type pehchano. Target: 6 minute.
- 13 × 8 = ?
- 17 × 9 = ?
- 104 × 97 = ?
- 109 × 96 = ?
- 105 × 95 = ?
- 107 × 93 = ?
- 96 × 97 = ?
- 104 × 106 = ?
- 1003 × 996 = ?
- 1002 × 999 = ?
- Do numbers 100 se barabar door (ek upar, ek neeche), guna 9919. Bada number = ?
- □ × 98 = 10192, □ 100 se zyada. □ = ?
- 102 × 98 + 98 × 98 = ?
- 98 × 12 = ?
- 56 × 43 = ?
Mera time: ______ · Sahi: ____ / 15
Answers dekho (pehle khud karo!)
- 104
- 153
- 10088
- 10464
- 9975
- 9951
- 9312
- 11024
- 998988
- 1000998
- 109
- 104
- 19600
- 1176
- 2408
Kaise kiya (kuch): guna 9919: 10000 − 9919 = 81 = 9 × 9 → 109 aur 91. □ × 98 = 10192: 101 | 92 → ulta 102 | −08 → 8 = 2 × 4 → □ = 104. 102 × 98 + 98 × 98 = 9996 + 9604 = 19600.
— 📌 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 × 9 = ?
- 14 × 8 = ?
- 103 × 98 = ?
- 106 × 97 = ?
- 104 × 96 = ?
- 108 × 92 = ?
- 102 × 103 = ?
- 97 × 95 = ?
- 1004 × 996 = ?
- 1001 × 997 = ?
| 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
- 108
- 112
- 10094
- 10282
- 9984
- 9936
- 10506
- 9215
- 999984
- 997997
Dhyaan: 108 × 92: barabar door → 10000 − 64 = 9936. 1004 × 996: 1000000 − 16 = 999984.
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. 102 × 98 + 103 × 97 = ?
Jawab aur kaaran dekho
Sahi jawab: (d) 19987
- (a) galat ❌: 20013: dono kone jod diye: 100 | 04 → 10004 aur 100 | 09 → 10009; 10004 + 10009 = 20013.
- (b) galat ❌: 20187: udhaar ke baad left 1 kam nahi kiya: 100 | 96 → 10096 aur 100 | 91 → 10091; 10096 + 10091 = 20187.
- (c) galat ❌: 19813: udhaar ke baad right mein 100 − kona ki jagah kona hi likha: 99 | 04 → 9904 aur 99 | 09 → 9909; 9904 + 9909 = 19813.
- (d) sahi ✅: Pehle guna: 102 × 98 → 100 | −04 → 99 | 96 → 9996, aur 103 × 97 → 100 | −09 → 99 | 91 → 9991. Jod: 9996 + 9991 = 19987.
Q2. □ × 97 = 10088, □ 100 se zyada. □ = ?
Jawab aur kaaran dekho
Sahi jawab: (c) 104
- (a) galat ❌: 101 to udhaar se pehle ka left hai (101 | −12), □ nahi. 101 × 97 → 101 − 3 = 98 | −03 → 97 | 97 → 9797, 10088 nahi.
- (b) galat ❌: 12 to kona hai (3 × 4 = 12), □ nahi.
- (c) sahi ✅: 10088 → 100 | 88 → udhaar ulta kholo: 101 | −12. 97 → 3 kam; 3 × 4 = 12, to □ 4 zyada: 104. Check: 104 − 3 = 101 ✅
- (d) galat ❌: 103 hota to 103 − 3 = 100 | −09 → 99 | 91 → 9991, 10088 nahi.
Q3. Do numbers 100 se barabar door, guna 9964. Numbers?
Jawab aur kaaran dekho
Sahi jawab: (b) 106 aur 94
- (a) galat ❌: Doori 3: 10000 − 3 × 3 = 10000 − 9 = 9991, 9964 nahi.
- (b) sahi ✅: Doori 6: 10000 − 6 × 6 = 10000 − 36 = 9964.
- (c) galat ❌: Doori 4: 10000 − 4 × 4 = 10000 − 16 = 9984, 9964 nahi.
- (d) galat ❌: Doori 8: 10000 − 8 × 8 = 10000 − 64 = 9936, 9964 nahi.
Q4. 105 × 95 = ?
Jawab aur kaaran dekho
Sahi jawab: (a) 9975
- (a) sahi ✅: 5 zyada, 5 kam: 105 − 5 = 100 | −25 → udhaar: 99 | 75 → 9975 (yaani 10000 − 25).
- (b) galat ❌: 10025: kona jod diya: 100 | 25 → 10025.
- (c) galat ❌: 9925: udhaar ke baad right mein 100 − 25 ki jagah 25 hi likh diya: 99 | 25 → 9925.
- (d) galat ❌: 9990: kona mein guna ki jagah jod: 5 + 5 = 10 → 10000 − 10 = 9990.
Q5. 98 × 12 pe base method kyun nahi?
Jawab aur kaaran dekho
Sahi jawab: (d) 98 aur 12 alag base ke paas
- (a) galat ❌: Chhota hona wajah nahi; 12 × 8 mein bhi 12 hai aur trick chalti hai.
- (b) galat ❌: Aakhri digit se farq nahi padta; 998 × 996 mein bhi 8 hai aur trick chalti hai. Asli baat base ki hai.
- (c) galat ❌: Asli wajah: dono ek hi base ke paas nahi. 12 base 10 ke paas hai.
- (d) sahi ✅: 98 → base 100 ke paas, 12 → base 10 ke paas: alag base. Seedha: 98 ko 10 baar + 98 ko 2 baar = 980 + 196 = 1176.
Q6. 1003 × 996 = ?
Jawab aur kaaran dekho
Sahi jawab: (c) 998988
- (a) galat ❌: 998012: udhaar se left 998 kiya, par right mein 1000 − 012 ki jagah 012 hi likh diya: 998 | 012 → 998012.
- (b) galat ❌: 999988: right 1000 − 012 = 988 kiya par left 1 kam nahi kiya: 999 | 988 → 999988.
- (c) sahi ✅: 3 zyada, 4 kam: 1003 − 4 = 999 | −012 → 1 hazaar udhaar: 998 | 988 → 998988.
- (d) galat ❌: 999012: kona jod diya: 999 | 012 → 999012.
Q7. 100 | 88 alag-taraf wale guna ka jawab hai. Udhaar se pehle kya tha?
Jawab aur kaaran dekho
Sahi jawab: (b) 101 | −12
- (a) galat ❌: Left theek kiya, par kona 100 − 88 = 12 hai, 88 nahi. 101 | −88 → 100 | 12 → 10012 banta.
- (b) sahi ✅: Ulta kholo: left + 1 = 101, kona = 100 − 88 = 12. Check: 101 | −12 → 100 | 88 ✅
- (c) galat ❌: Left mein 1 ghata diya (100 − 1 = 99); ulta kholne mein 1 jodte hain. 99 | −12 → 98 | 88 → 9888 banta, 10088 nahi.
- (d) galat ❌: 88 ko hi kona maan liya; 100 | −88 → 99 | 12 → 9912 banta, 10088 nahi.
Q8. Kaun bada: 106 × 94 ya 105 × 95?
Jawab aur kaaran dekho
Sahi jawab: (a) 105 × 95, 11 se
- (a) sahi ✅: 105 × 95 = 10000 − 25 = 9975, 106 × 94 = 10000 − 36 = 9964; farq 36 − 25 = 11.
- (b) galat ❌: Ulta: 106 × 94 = 9964 chhota hai, bada nahi.
- (c) galat ❌: Kone alag hain (25 aur 36), isliye barabar nahi.
- (d) galat ❌: Farq 36 − 25 = 11 hai, 1 nahi.
Q9. 17 × 9 = ?
Jawab aur kaaran dekho
Sahi jawab: (d) 153
- (a) galat ❌: 163: right mein 10 − 7 = 3 kiya par left 1 kam nahi kiya: 16 | 3 → 163.
- (b) galat ❌: 167: kona ghatane ki jagah jod diya: 16 | 7 → 167.
- (c) galat ❌: 157: udhaar se left 15 kiya par right mein 10 − 7 ki jagah 7 hi likh diya: 15 | 7 → 157.
- (d) sahi ✅: 7 zyada, 1 kam: 17 − 1 = 16 | −7 → udhaar: 15 | 3 → 153.
Q10. 13 × 97 = ?
Jawab aur kaaran dekho
Sahi jawab: (c) 1261
- (a) galat ❌: 1339: ghatane ki jagah jod diya: 1300 + 39 = 1339.
- (b) galat ❌: 91: zabardasti base method: 13 − 3 = 10 | −9 → 9 | 1 → 91. Alag base pe trick galat jawab deti hai.
- (c) sahi ✅: Alag base, seedha: 13 ko 100 baar − 13 ko 3 baar = 1300 − 39 = 1261.
- (d) galat ❌: 1297: 13 × 3 = 39 ki jagah sirf 3 ghataya: 1300 − 3 = 1297.
— 📌 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. 104 × 104 aur 104 × 96: farq kitna?
Solution dekho
104 × 104: 108 | 16 → 10816. 104 × 96: 100 | −16 → 99 | 84 → 9984. Farq: 10816 − 9984 = 832.
Dekho: 104 × 104 matlab 104 ko 104 baar, aur 104 × 96 matlab 104 ko 96 baar. Farq: 104 ko (104 − 96 = 8) baar zyada liya, yaani 104 ko 8 baar = 100 ko 8 baar + 4 ko 8 baar = 800 + 32 = 832 ✅
Q2. 1004 cheezein, har ek ₹996. Kul?
Solution dekho
Barabar door (1000 se 4): 1000000 − 16 = ₹999984.
Check: 1004 ko 1000 baar − 1004 ko 4 baar = 1004000 − 4016 = 999984 ✅
Q3. 107 × 93 aur 103 × 97, kaun bada, aur kitne se?
Solution dekho
Dono sawaalon mein ek number 100 se upar, ek neeche, aur dono barabar door (107 = 100 + 7, 93 = 100 − 7; 103 = 100 + 3, 97 = 100 − 3). Barabar door ho to left 100 hi aata hai, aur jawab = 10000 − doori × doori (Post 8.2 ki HOTS): 107 × 93 = 10000 − 7 × 7 = 10000 − 49 = 9951. 103 × 97 = 10000 − 3 × 3 = 10000 − 9 = 9991. 103 × 97 bada, 9991 − 9951 = 40 se. Jitne paas, utna bada guna.
Check: 107 ko 93 baar = 107 ko 100 baar − 107 ko 7 baar = 10700 − 749 = 9951 ✅ (107 ko 7 baar = 100 ko 7 baar + 7 ko 7 baar = 700 + 49 = 749.)
Q4. 13 × 97 pe kaunsa tareeka?
Solution dekho
13 base 10 ke paas, 97 base 100 ke paas: alag base, base method nahi. Seedha: 13 ko 100 baar − 13 ko 3 baar = 1300 − 39 = 1261.
Check: 97 ko 13 baar = 97 ko 10 baar + 97 ko 3 baar = 970 + 291 = 1261 ✅
— 📌 charumam.com
🎯 Exam Mein Kahan Kaam Aayega?
| Exam | Kahan kaam aayega |
|---|---|
| School exam (Class 7–8) | Daam (cost), area aur do guna ke jod wale sawaal. |
| Maths Olympiad | Ulte sawaal, barabar door ka pattern, tulna (kaun bada). |
| NTSE / MAT | Dhokha pehchanna aur sahi tareeka chunna. |
| SSC / Bank (aage) | Simplification mein 104 × 96, 1004 × 996 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. Simplification = lambe hisaab ko chhota karke jawab nikaalna.
— 📌 charumam.com
👩🏫 CharuMam Ka Tip
Level 2 ke base method ka poora mantra: “ek base, taraf dekho, khaane gino, minus ho to udhaar, trick theek na baithe to seedha.” Shabaash, aapne Chapter 7 aur 8 poore kiye! 🏆
— 📌 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)
102 × 98: 100 | −04 → 9996. 103 × 97: 100 | −09 → 9991. Jodo: 9996 + 9991 = 19987 ✅ (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. 🚀
— 📌 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. Ulte sawaal mein kaise pata chale alag taraf hai?
Sawaal mein likha hota hai ki □ base se upar hai ya neeche. Doosra number dekho: agar ek upar aur ek neeche, to alag taraf.
2. Barabar door wala shortcut kab?
Jab ek base se jitna upar, doosra utna hi neeche (106 × 94). Tab seedha base × base − doori × doori.
3. Kya yeh sab exam mein likh sakte hain?
Kachchi copy (rough) mein trick lagao, answer sheet pe seedha tareeka likho; trick se check karo.
4. Agle chapter mein kya hai?
Speed Maths ke agle chapters jald aa rahe hain! Tab tak Chapter 7–8 ke drill roz karo, aur saare chapter Speed Maths page pe dekho.
— 📌 charumam.com
🟢 Recap: Aaj Kya Seekha
- Pehle: ek hi base? warna seedha tod.
- Alag taraf → kona minus, left − 1 | base − kona.
- Barabar door → base × base − doori × doori.
- Ulta (alag taraf) → left + 1, kona = base − right.
- Pehle guna, phir jod.
- Dhokhe: 98 × 12, 13 × 97, 56 × 43.
— charumam.com 🎯
👉 Aage Kya?
Chapter 7 aur 8 poore! 🎉 Speed Maths ka agla chapter jald aa raha hai. Tab tak roz 10 sawaal base method ke, aur saare chapter Speed Maths page pe dekho.
Koi doubt? CharuMam AI Tutor se poochho, ya comment mein likho! 💬
💛 Post Achha Laga? Like, Share, Subscribe, Follow!
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- 🌐 Website: charumam.com
- 🤖 AI Tutor (doubt poochho, 24×7): tutor.charumam.com
- ▶️ YouTube (subscribe): @charumamofficial
- 📸 Instagram (follow): @charumamofficial
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— 📌 charumam.com
