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Parity Pehchaano

Class 7 Maths · Chapter 6: Number Play · NCERT Ganita Prakash section 6.2

Seekho

Kabir ke paas number cards 1, 3, 5, 7, 9, 11, 13 hain aur use 30 jodne wale 5 cards chahiye. Har chunaav aazmaane ki jagah jodiyon mein socho. Even number jodiyon mein bina bache baith jaata hai; odd mein hamesha ek bachta hai.

Even + even = even. Odd + odd = even: dono bache hue jodi bana lete hain! Par 3 odd ek bachaate hain: odd. To 5 odd numbers ka jod hamesha odd, aur 30 even: Kabir ki paheli asambhav. Even ya odd hona parity kehlaata hai.

odd + odd = even · 5 odds → odd

Meher Neel se theek ek saal badi hai, to unki umar lagaataar hai, ek even ek odd. Jod odd, to kabhi 112 nahi ho sakta. Aur r panktiyon, c stambhon ke grid mein r × c odd tabhi jab r aur c dono odd: 27 × 13 odd, 42 × 78 even.

even + odd = odd · odd × odd = odd

Expressions ki parity: 3n + 4 odd (n = 3 → 13) ya even (n = 8 → 28) ho sakta hai. Par 100p aur 48w − 2 hamesha even, aur 2m + 1 hamesha odd. nva even number 2n, aur nva odd ek kam: 2n − 1. To 100va odd number 199.

nth even = 2n · nth odd = 2n − 1

Explore: even ya odd?

  1. Har nateeje ko parity se sort karo.

Yaad rakho

  • Even numbers poori jodi banaate hain; odd mein ek bachta hai.
  • Odd numbers ki even ginti ka jod even; odd ginti ka odd. nva odd number 2n − 1.

Quick check

Gullak mein ₹1 ke odd, ₹5 ke odd aur ₹10 ke even sikke. Kya kul ₹205 ho sakta hai?

  1. Nahi: kul even hona chahiye
  2. Haan
  3. Sirf agar ₹10 ke sikke na hon
  4. Sirf har ek ka 1 sikka
Answer

Nahi: kul even hona chahiye. odd + odd + even = even, par 205 odd.

Socho

1 + 2 + 3 + … + 100 ka jod even hai ya odd?

Ek answer

1 se 100 tak 50 odd numbers hain. Odd ki even ginti ka jod even, aur even numbers ise nahi badalte: jod even (5050).

Practice

Teen levels (easy, medium, hard) ke naye sawaalon se practice karo, kuch hands-on, hints aur hal ke saath. Topic poora karne ke liye pichhle 5 mein se 4 sahi karo.