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Calendar

Lesson 17 of 113

1. Ye topic hai kya?

Kaun sa vaar — aaj se 61 din, 15 August agle saal, do saal ka same calendar. Clock ka angle yahan nahi (Clocks).

Paper kya maangta

Leap ya nahi, N din baad ka din, ek date se doosri, 31-din month mein kitne Sunday, kab 53 Sunday.

Yahan code

Sun=0 Mon=1 Tue=2 Wed=3 Thu=4 Fri=5 Sat=6. Kuch kitab Sun=1 rakhti — pehle 0 lock karo, last pe naam.

2. Odd days — poora topic yahi hai

Hafte 7 din. Extra din jo 7 se divide karke bachen = odd days. Wahi weekday aage badhta hai.

Odd days = (kul din) ÷ 7 ka remainder
365 = 52×7 + 1 → ordinary year = 1 odd
366 = 52×7 + 2 → leap year = 2 odd
7 odd = 0 (puri hafte, din nahi badla)
BlockOdd days
1 ordinary year1
1 leap year2
100 saal (xx00 leap nahi, jaise 1900)5
400 saal (2000 type)0

Mahine ke odd (non-leap): 31→3, 30→2, Feb 28→0. Leap Feb→1.

JanFebMarAprMayJunJulAugSepOctNovDec
30 / 13232332323

3. Leap year

4 se kat’ta → leap, lekin
100 se kat’ta → leap nahi, lekin
400 se kat’ta → leap (2000 haan, 1900 / 2100 nahi)
Feb 29: do dates ke beech odd nikaalte waqt leap tabhi jodo jab wo 29 Feb us gap mein aaye. 15 Aug 2024 → 15 Aug 2025: 2025 leap nahi, 29 Feb 2024 peeche reh gaya — 1 odd, 2 nahi.
Basic · leap

Q1. Kaun leap hai? 1900, 2000, 2012, 2100.

Solution shuru

  1. Step 1

    1900: 100 se, 400 se nahi → nahi. 2100 same.

  2. Step 2

    2000: 400 se. 2012: 4 se, century nahi. Dono leap.

Final answer — yahan khatam2000 aur 2012

4. Aaj se N din baad

“Aaj Monday, 61 din baad?” Remainder 7 se, utna aage weekday.

Basic · +N

Q2. Aaj Monday. 61 din baad kaun sa din?

Solution shuru

  1. Step 1

    61 ÷ 7 = 8 hafte + 5. Odd = 5.

  2. Step 2

    Mon=1, +5 → 6 = Saturday.

Final answer — yahan khatamSaturday
Basic · month

Q3. 31-din ka mahina, 1 tarikh Sunday. Last din kaun sa? Kitne Sunday?

Solution shuru

  1. Step 1 — last

    31st = 1st se 30 din baad. 30 = 4 odd. Sun+4 = Thursday.

  2. Step 2 — Sundays

    1, 8, 15, 22, 29 — paanch. 36 nahi hota.

Final answer — yahan khatamLast = Thursday; 5 Sundays

5. Do dates — beech ke odd

Same date agle saal: ordinary gap = 1 odd, agar 29 Feb beech mein girta hai to 2.

1 Jan se koi date: pehle ke mahine ke odd + (date − 1), phir 7 se remainder, 1 Jan ke weekday pe jodo.

Medium · next year

Q4. 15 August 2024 Thursday tha. 15 August 2025 kaun sa din?

Solution shuru

  1. Step 1

    2025 leap nahi. 15 Aug→15 Aug mein 29 Feb 2025 nahi aata (aur 2024 ka 29 Feb pehle nikal chuka). 365 din = 1 odd.

  2. Step 2

    Thu+1 = Friday.

Final answer — yahan khatamFriday
Medium · Feb 29 beech

Q5. 26 January 2020 Sunday. 26 January 2021?

Solution shuru

  1. Step 1

    2020 leap. 26 Jan 2020 se 26 Jan 2021 ke beech 29 Feb 2020 aata hai. 366 din = 2 odd.

  2. Step 2

    Sun+2 = Tuesday.

Final answer — yahan khatamTuesday
Medium · 1 Jan se

Q6. Non-leap saal, 1 January Thursday. 15 August kaun sa din?

Solution shuru

  1. Step 1 — mahine pehle

    Jan 3 + Feb 0 + Mar 3 + Apr 2 + May 3 + Jun 2 + Jul 3 = 16. 16 ÷ 7 remainder 2.

  2. Step 2 — date

    15 Aug = 1 Aug se 14 din. 2 + 14 = 16, remainder 2.

  3. Step 3

    Thu+2 = Saturday.

Final answer — yahan khatamSaturday
Medium · do mahine

Q7. Non-leap. 1 April jo din, 1 July wahi hai kya?

Solution shuru

  1. Step 1

    April+May+June = 30+31+30 = 91. 91 ÷ 7 = 13 exact. Odd = 0.

  2. Step 2

    Wahi weekday. Haan.

Final answer — yahan khatamHaan, same day

6. Same calendar

Do saal ka calendar tab same jab: (1) dono leap ya dono ordinary, (2) 1 Jan se 1 Jan odd days = 0.

1 Jan same ho, ek leap ek nahi — Feb ke baad calendar toot jaata. Sirf 1 Jan same kaafi nahi.
Pro · same year

Q8. 2013 aur 2019 ka calendar same hai kya?

Solution shuru

  1. Step 1 — saal beech

    2013, 14, 15, 16, 17, 18 poore hone ke baad 2019 start. Leap inmein: 2016 (2 odd). Baaki 5 ordinary (1-1). Kul 2+5=7 = 0 odd.

  2. Step 2 — type

    2013 ordinary, 2019 ordinary. 1 Jan same + same type. Haan.

Final answer — yahan khatamHaan

7. 53 Sundays / 100–400 saal

Ordinary saal 365 din = ek weekday 53 baar (jo 1 Jan ka din hai; 31 Dec bhi wahi).

Leap 366 = do weekdays 53 baar: 1 Jan ka din, aur uska agla (31 Dec = 1 Jan + 1).

53 Sundays:
Ordinary → 1 Jan Sunday
Leap → 1 Jan Saturday ya Sunday
Basic · 100 saal

Q9. 100 saal (jaise 1801–1900) mein kitne odd days? 400 saal?

Solution shuru

  1. Step 1

    100 saal: 24 leap + 76 ordinary (1900 leap nahi). 24×2 + 76 = 124. 124 ÷ 7 remainder 5.

  2. Step 2

    400 saal: 0 odd — calendar 400 ke baad 1 Jan wapas same pattern.

Final answer — yahan khatam5; 0
Pro · 53

Q10. Leap year, 1 January Saturday. Us saal 53 Sundays honge kya?

Solution shuru

  1. Step 1

    Leap: 53 baar 1 Jan wala din + agla = Saturday aur Sunday.

  2. Step 2

    Sunday aata hai. Haan, 53 Sundays.

Final answer — yahan khatamHaan

8. Pro checklist

  1. Odd = remainder 7. 7 = 0.
  2. Leap: 4 haan, 100 nahi, 400 haan.
  3. 29 Feb gap mein girta hai tabhi +2 odd year-to-year.
  4. Aaj + N: N mod 7 aage.
  5. Same calendar: 0 odd + same leap/ordinary.
  6. 53 Sunday: ordinary 1 Jan Sun; leap 1 Jan Sat/Sun.
  7. 31-din month 1=Sun → Sundays 1,8,15,22,29.

9. Practice

Pehle khud socho, phir neeche solution kholo. Q1–Q10 yahan nahi dohraaye.

Basic

Practice 1. 2016 leap hai kya? 1900?

Solution shuru

  1. Step 1

    2016 ÷ 4 = 504, century nahi → leap. 1900 ÷ 400 nahi → nahi.

Final answer — yahan khatam2016 haan; 1900 nahi
Basic

Practice 2. Aaj Wednesday. 100 din baad?

Solution shuru

  1. Step 1

    100 = 14×7 + 2. Wed+2 = Friday.

Final answer — yahan khatamFriday
Basic

Practice 3. Kisi din se 28 din baad wahi weekday hoga kya?

Solution shuru

  1. Step 1

    28 = 4×7. Odd 0. Hamesha wahi din.

Final answer — yahan khatamHaan
Basic

Practice 4. 1 February 2019 Friday. 1 March 2019?

Solution shuru

  1. Step 1

    2019 leap nahi, Feb 28 din. 1 Feb → 1 Mar = 28 din = 0 odd. Friday.

Final answer — yahan khatamFriday
Medium

Practice 5. 15 August 2023 Tuesday. 15 August 2024?

Solution shuru

  1. Step 1

    2024 leap. 15 Aug 23 → 15 Aug 24 ke beech 29 Feb 2024 aata. 2 odd. Tue+2 = Thursday.

Final answer — yahan khatamThursday
Medium

Practice 6. 31-din month, 1 tarikh Wednesday. 31 tarikh?

Solution shuru

  1. Step 1

    +30 din, 30=4 odd. Wed+4 = Sunday.

Final answer — yahan khatamSunday
Medium

Practice 7. 2012 aur 2013 ka calendar same?

Solution shuru

  1. Step 1

    2012 leap → agla saal 2 odd aage. Type bhi alag (leap vs ordinary). Nahi.

Final answer — yahan khatamNahi
Pro

Practice 8. 2014 aur 2020: 1 Jan same weekday ho sakta, poora calendar same?

Solution shuru

  1. Step 1

    2014–19: leap 2016 (2) + 5 ordinary = 7 = 0 odd. 1 Jan same.

  2. Step 2

    2014 ordinary, 2020 leap. Feb ke baad alag. Poora calendar nahi.

Final answer — yahan khatam1 Jan same ho sakta; poora calendar nahi
Basic

Practice 9. Ordinary year, 1 January Friday. 31 December?

Solution shuru

  1. Step 1

    31 Dec = saal ka 365waan din = 1 Jan se 364 din baad. 364=52×7. Same = Friday.

Final answer — yahan khatamFriday
Pro

Practice 10. Ordinary year, 1 January Monday. 53 Sundays?

Solution shuru

  1. Step 1

    Ordinary: 53 baar sirf 1 Jan wala din = Monday. Sunday 52. Nahi.

Final answer — yahan khatamNahi (53 Mondays)

10. Itna kaafi hai kya?

Agar odd days, leap 4/100/400, 29 Feb gap-check, +N, 1 Jan se month-odd, same-calendar (0 odd + same type), aur 53 Sunday wala Sat/Sun lock kar sako — to JA/CA-II ke calendar basic se pro tak attempt ho sakte hain.

Agle topic: Age.

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