Lagnever AI English

Class 7 Maths Chapter 6: Number Play (Hinglish Notes)

Ye chapter 5 lines mein

Number Play aisi paheliyon ka chapter hai jinke peeche patterns chhupe hain. Line mein khade bachche batate hain ki unke aage kitne lambe bachche khade hain. Parity, yaani odd ya even hona, har case jaanche bina paheliyan hal kar deti hai. Grid ke jod magic squares tak le jaate hain jinka magic sum 15 hai, kavita ki rhythms se Virahanka numbers 1, 2, 3, 5, 8, … bante hain, aur cryptarithms mein letters ke peeche digits chhupe hote hain.

Chapter 6 ka mind map: kuch batate numbers, parity, parity ke niyam, grids aur magic squares, Virahanka numbers aur cryptarithms
Poora chapter ek page pe

Ye chapter kis baare mein hai?

Number Play paheliyon ka chapter hai. Har paheli khel jaisi lagti hai, par uske peeche aisa pattern hota hai jo har sambhaavna aazmaaye bina jawaab de deta hai. Chapter line mein numbers bolte bachchon se shuru hokar odd aur even numbers, grids ke jod aur magic squares, Bhartiya kavita mein pehli baar dikhe ek mashhoor sequence, aur aakhir mein aise jodon tak jaata hai jinmein letters ke peeche digits chhupe hain.

Kuch batate numbers

Saat bachche ek line mein khade hain, aur sab ek-ek number bolte hain. Niyam ye nikalta hai: batao ki tumhare aage kitne bachche tumse lambe hain. Pehle bachche ka number hamesha 0 hota hai, kyunki uske aage koi nahi, aur sabse lambe bachche ka number bhi 0 hota hai. Ye numbers kisi ki asli lambaai bataaye bina line ki banaavat bata dete hain. 8 logon ke group mein sabse bada sambhav number 7 hai, jo aakhir mein khade sabse chhote bachche ka hota hai.

Line mein saat bachche, aage ka hissa baayein taraf, bata rahe hain ki unke aage kitne lambe bachche hain: 0, 0, 1, 0, 3, 0, 3
Aage khade lambe bachchon ki ginti

Parity chunna

Koi number odd hai ya even, ise uski parity kehte hain. Even numbers bina kuch bachaaye jodon mein bant jaate hain; odd numbers mein hamesha ek bach jaata hai. Dots ke chitra niyam saabit karte hain: even + even = even; do odd numbers mein ek-ek dot bachta hai, aur ve do bache dots aapas mein jodi bana lete hain, isliye odd + odd = even; aur even + odd = odd. Isliye Kishor paanch odd number cards se 30 nahi bana sakta, kyunki paanch odd numbers ka jod odd hota hai. Martin aur Maria ke janm mein ek saal ka fark hai, to unki umar lagaataar numbers hain, ek odd aur ek even, isliye unka jod kabhi 112 nahi ho sakta. Padho parity: odd aur even.

Even numbers jodon mein, odd numbers mein ek dot bacha hua, aur do odd numbers jinke bache dots milkar even jod banaate hain
Even aur odd numbers jodon ke roop mein

Guna aur expressions ki parity

3 rows aur 3 columns waale grid mein 9 chhote squares hain, odd; 3 rows aur 4 columns waale mein 12, even. Squares ki ginti tabhi odd hai jab dono taraf odd hon. Expressions ki bhi parity hoti hai: 100p hamesha even hai, 2n + 1 hamesha odd, aur 3n + 4 n ke hisaab se kuch bhi ho sakta hai. 2, 4, 6, … ko 1, 3, 5, … se jagah-jagah milaane par dikhta hai ki nth even number 2n hai aur nth odd number 2n − 1; isliye 100th odd number 199 hai.

Position 1 se 6 aur 100 par even numbers 2n aur odd numbers 2n − 1; 100th odd number 199 hai
nth even aur odd numbers

Grids aur magic squares

3 × 3 grid ko 1 se 9 tak ke numbers se, har ek ko ek baar, bharo, aur har row aur column ka jod bahar likho. Teeno rows ke jod ka total hamesha 45 hota hai, aur teeno columns ka bhi, kyunki dono milkar 1 + 2 + … + 9 jodte hain. Isse turant pata chalta hai ki kuch paheliyan namumkin hain: 1 se 9 ke teen alag numbers ka jod kabhi 6 se kam ya 24 se zyaada nahi ho sakta. Magic square mein aur bhi khaas baat hai: har row, column aur diagonal ka jod ek hi hota hai, jise magic sum kehte hain. 1 se 9 ke saath magic sum 45 ÷ 3 = 15 hi hoga, beech mein 5 hi hoga, aur 1 aur 9 kone mein nahi aa sakte. Padho magic square kya hai.

1–9 magic square banaana: magic sum 15, beech mein 5, aur 1 aur 9 aamne-saamne ki edges ke beech mein, jisse 8 3 4, 1 5 9, 6 7 2 banta hai
1–9 magic square banaana

Magic squares aam roop mein aur itihaas mein

Beech ke number ko letter-number m maanein to baaki khaane m + 3, m − 4, m + 1, m − 2, m + 2, m − 1, m + 4 aur m − 3 bante hain, aur har line ka jod 3m hota hai; m = 25 par magic sum 75 hai. Har khaane mein ek hi number jodna, ya har khaane ko doguna karna, square ko magic hi rakhta hai. Sabse pehla darj 4 × 4 magic square, Chautisa Yantra, Khajuraho ke Parshvanath Jain mandir ke 10th century ke shilalekh mein khuda hai; iski saari lines ka jod 34 hai. Magic squares China ke Lo Shu square mein, Tamil Nadu ke Palani mein 8th century ke mandir ke khambhe par, aur gharon aur dukaanon ke yantron mein bhi milte hain.

Beech mein m waala generalised 3 × 3 magic square, aur beech mein 25 aur 20 waale udaaharan
Generalised magic square

Virahanka–Fibonacci numbers

Prakrit, Sanskrit, Marathi, Malayalam, Tamil, Telugu aur doosri Bhartiya bhaashaaon ki kavita mein chhota syllable ek beat aur lamba syllable do beat ka hota hai. Kisi tay beats ko kitni rhythms bhar sakti hain? 1, 2, 3, 4 aur 5 beats ke liye 1, 2, 3, 5 aur 8 rhythms hain. Lagbhag 700 CE mein Prakrit vidwaan Virahanka ne iski wajah samjhaayi: har rhythm chhote ya lambe syllable se shuru hoti hai, isliye n beats ki ginti = n − 1 beats ki ginti + n − 2 beats ki ginti. Isse 1, 2, 3, 5, 8, 13, 21, 34, 55, … bante hain, Virahanka numbers, jinhe pashchim mein ek Italian ganitagya ke naam par Fibonacci numbers kehte hain, jinhone 1202 CE mein inke baare mein likha. Inki parity odd, even, odd, odd, even, odd, … chalti hai, aur ye prakriti mein bhi milte hain, jaise 13, 21 ya 34 pankhudiyon waale daisy phool. Padho Virahanka numbers kya hain.

1 se 5 beats ke liye chhote aur lambe beats ki rhythms: 1, 2, 3, 5 aur 8 tareeke
Chhote aur lambe beats ki rhythms

Bhes badle digits

Cryptarithm, yaani alphametic, mein har letter 0 se 9 ke kisi digit ki jagah hota hai. T + T + T = UT mein, teen baar joda gaya digit apne hi digit par khatam ho, aisa sirf T = 5 par hota hai: 5 + 5 + 5 = 15. K2 + K2 = HMM mein ikaai ka digit 2 + 2 = 4 hai, to M = 4, aur K + K ko 14 hona chahiye, to K = 7 aur 72 + 72 = 144. Haasil, jawaab ka size aur parity sabse bade suraag hain.

Hal kiye cryptarithms, T + T + T = UT (5 + 5 + 5 = 15) se UT + TA = TAT (91 + 10 = 101) tak
Hal kiye cryptarithms

Saar mein

Line ke numbers lambaai bataaye bina line ka haal batate hain; parity kai paheliyan ek nazar mein hal karti hai; 1 se 9 ke grid ke jod hamesha 45 hote hain, jo magic sum 15 aur beech mein 5 waale 1–9 magic square tak le jaate hain; Virahanka ka niyam 1, 2, 3, 5, 8, … banaata hai; aur cryptarithms jaasoosi ki tarah hal hote hain. Har sawaal ke jawaab Chapter 6 ke NCERT solutions mein hain.

Key terms (zaroori shabd)

TermMatlab
ParityKoi number odd hai ya even. Jaise, do lagaataar numbers ke jod ki parity odd hoti hai.
Even numberAisa number jo bina kuch bachaaye jodon mein bant jaaye, jaise 6 ya 10; isme 2 ek factor hai. nth even number 2n hai.
Odd numberAisa number jo jodon mein baantne par ek bacha deta hai, jaise 7 ya 11; ye kisi even number se ek zyaada ya ek kam hota hai. nth odd number 2n − 1 hai.
Lagaataar numbersEk ke baad ek aane waale ginti ke numbers, jaise 51 aur 52. Do lagaataar numbers mein ek hamesha odd aur doosra even hota hai.
Magic squareNumbers ka aisa square grid jismein har row, har column aur dono diagonals ka jod ek hi number hota hai.
Magic sumMagic square ki har row, column aur diagonal ka saajha jod. 1 se 9 tak ke numbers se ye 15 hi ho sakta hai.
Generalised magic square3 × 3 magic square jiske beech mein letter-number m ho: m + 3, m − 4, m + 1; m − 2, m, m + 2; m − 1, m + 4, m − 3. Har line ka jod 3m hota hai.
Chautisa YantraSabse pehla darj kiya gaya 4 × 4 magic square, Khajuraho ke Parshvanath Jain mandir ke 10th century ke shilalekh mein; iski har row, column aur diagonal ka jod 34 hai.
Chhote aur lambe syllablesKai Bhartiya bhaashaaon ki kavita mein chhota syllable ek beat aur lamba syllable do beat ka hota hai; inki rhythms ginne se Virahanka numbers milte hain.
Virahanka numbersNumbers 1, 2, 3, 5, 8, 13, 21, 34, …, jinmein har number apne pichhle do numbers ka jod hai. Pashchim mein inhe Fibonacci numbers kehte hain.
CryptarithmAisa jod jismein har letter kisi digit ki jagah hai, jise alphametic bhi kehte hain, jaise T + T + T = UT, jahan T = 5 aur U = 1.
Chitra se proofAisi daleel jo dikhaaye ki koi baat hamesha sach hai, jaise do odd numbers ko jodon mein banaakar dekhna: bache hue do dots aapas mein jodi bana lete hain, isliye jod even hai.

Is chapter ke topics

Is chapter ke NCERT solutions Chapter ke saare exercise questions, step-by-step jawab ke saath.

Practice karo

  1. 5 odd numbers ka jod odd hota hai ya even?

    1. (a) Even
    2. (b) Odd
    3. (c) Numbers par nirbhar
    4. (d) Dono nahi
    Jawab dekho

    Jawab: (b) Odd

  2. 50th odd number kya hai?

    1. (a) 49
    2. (b) 99
    3. (c) 100
    4. (d) 101
    Jawab dekho

    Jawab: (b) 99

  3. 1 se 9 tak ke numbers se bane magic square ka magic sum kya hai?

    1. (a) 9
    2. (b) 12
    3. (c) 15
    4. (d) 45
    Jawab dekho

    Jawab: (c) 15

  4. 1–9 waale magic square ke beech mein kaunsa number hona chahiye?

    1. (a) 1
    2. (b) 5
    3. (c) 9
    4. (d) Koi bhi
    Jawab dekho

    Jawab: (b) 5

  5. 1, 2, 3, 5, 8, 13, 21, … ke baad kya aata hai?

    1. (a) 29
    2. (b) 34
    3. (c) 26
    4. (d) 42
    Jawab dekho

    Jawab: (b) 34

  6. Cryptarithm T + T + T = UT mein T kya hai?

    1. (a) 3
    2. (b) 5
    3. (c) 7
    4. (d) 9
    Jawab dekho

    Jawab: (b) 5

Students ke sawal

Class 7 Maths Chapter 6 ke mukhya topics kya hain?

Line mein khade bachchon ka ye batana ki unke aage kitne lambe bachche hain; parity, yaani odd aur even numbers, jod, ghataav, guna, grids aur 2n aur 2n − 1 ke formulas ke saath; grids mein rows aur columns ke jod aur magic squares, generalised 3 × 3 square aur Chautisa Yantra samet; Bhartiya kavita se aaye Virahanka–Fibonacci numbers; aur cryptarithms.

Kya Number Play nayi NCERT Class 7 Maths ki kitaab mein hai?

Haan. Ye Ganita Prakash, yaani Class 7 Maths ki kitaab Part 1 (Reprint 2026-27), ka Chapter 6 hai, pages 127 se 145 tak. Ye Parallel and Intersecting Lines ke baad aur A Tale of Three Intersecting Lines se pehle aata hai.

Parity paheliyan jaldi kaise hal karti hai?

Parity se hum har case jaanche bina jawaab rad kar sakte hain. Paanch odd cards kabhi 30 nahi bana sakte, kyunki paanch odd numbers ka jod odd hota hai; ek saal ke fark waali umar ka jod kabhi 112 nahi ho sakta, kyunki lagaataar numbers ka jod odd hota hai. Odd ya even par ek nazar sawaal hal kar deti hai.

Inhe Virahanka–Fibonacci numbers kyun kehte hain?

Prakrit vidwaan Virahanka ne lagbhag 700 CE mein kavita ki rhythms ginte hue in numbers ka niyam diya, Pingala ke pehle ke kaam ke baad; Gopala aur Hemachandra ne 12th century mein inke baare mein likha. Fibonacci ne Italy mein 1202 CE mein, Virahanka ke lagbhag 500 saal baad, inke baare mein likha, isliye ye saajha naam saaf karta hai ki pehle kaun aaya.

Koi sawal atak gaya?

Photo lo, Lagnever AI step-by-step samjhayega. 7 din ka trial sirf ₹2.

Google Play se app lo Browser mein kholo

Parents ke liye: trial ke baad plan har mahine UPI ya card autopay se renew hota hai. App mein kabhi bhi cancel kar sakte hain.