Dosto, is chapter mein teen chhote-chhote topics hain, aur har ek ke paas apna ek pakka formula hai:
1. Clock — ghadi ki suiyon ke beech ka kona. 2. Calendar — "us din kaunsa vaar tha?" 3. Mathematical Operations — jahan +, −, ×, ÷ ke matlab badal diye jate hain.
CET Group D mein in teeno se milake 1–2 questions aate hain. Teeno topics chhote hain — formula yaad hua to answer 20 second mein. Chalo shuru! 💪
1. ⭐ CLOCK — angle ka master formula
⭐ Angle = |30 × H − 5.5 × M|
H = ghanta, M = minute. Agar answer 180° se bada aaye to 360 − answer le lo (chhota kona chahiye).
Kyun? Ghanta-suee 1 ghante mein 30° chalti hai; minute-suee 1 minute mein 6°, par ghanta-suee bhi 0.5°/min khiskti hai → antar 5.5°/min.
Kyun? Ghanta-suee 1 ghante mein 30° chalti hai; minute-suee 1 minute mein 6°, par ghanta-suee bhi 0.5°/min khiskti hai → antar 5.5°/min.
✏️ Solved Examples
9:00 → |30×9 − 0| = 270° → 180 se bada, to 360 − 270 = 90° ✓
4:30 → |120 − 165| = 45° ✓ · 6:00 → |180 − 0| = 180° ✓ · 2:20 → |60 − 110| = 50° ✓
4:30 → |120 − 165| = 45° ✓ · 6:00 → |180 − 0| = 180° ✓ · 2:20 → |60 − 110| = 50° ✓
📌 Clock ke ratt-ne wale facts
12 ghante mein: suiyan 11 baar milti hain (coincide), 11 baar aamne-saamne (180°), aur 22 baar 90° banati hain.
Poore din (24 ghante) mein: 22 · 22 · 44 baar.
Poore din (24 ghante) mein: 22 · 22 · 44 baar.
✏️ "Kis samay suiyan milengi?" wala sawal
3 aur 4 ke beech suiyan kab milengi?
Step 1: Milne par angle = 0 → 30H = 5.5M
Step 2: M = (30 × 3)/5.5 = 90/5.5 = 180/11 = 16 4/11 minute
Answer: 3 baj kar 16 4/11 minute par ✓
Step 1: Milne par angle = 0 → 30H = 5.5M
Step 2: M = (30 × 3)/5.5 = 90/5.5 = 180/11 = 16 4/11 minute
Answer: 3 baj kar 16 4/11 minute par ✓
2. ⭐ CALENDAR — "odd days" ka khel
⭐ Odd days = 7 se bhaag dene par bacha hua
Hafte mein 7 din hote hain, isliye 7 ka har poora chakkar bekaar — sirf bacha hua (remainder) matter karta hai. Usi ko odd days kehte hain.
Saadharan saal (365 din) → 365 ÷ 7 = 52 hafte + 1 → 1 odd day
Leap saal (366 din) → 2 odd days
Saadharan saal (365 din) → 365 ÷ 7 = 52 hafte + 1 → 1 odd day
Leap saal (366 din) → 2 odd days
| Samay | Odd days |
|---|---|
| Saadharan saal | 1 |
| Leap saal | 2 |
| 100 saal | 5 |
| 200 saal | 3 |
| 300 saal | 1 |
| 400 saal | 0 |
⭐ Leap year ka niyam
Saal 4 se poora bat jaye → leap year. PAR agar saal 00 par khatam hota hai (century year) to use 400 se bhi katna chahiye.
2024 → 4 se kat gaya, century nahi → leap ✓
1900 → century hai par 400 se nahi kata → leap NAHI ✗
2000 → century hai aur 400 se kat gaya → leap ✓
2024 → 4 se kat gaya, century nahi → leap ✓
1900 → century hai par 400 se nahi kata → leap NAHI ✗
2000 → century hai aur 400 se kat gaya → leap ✓
✏️ Solved Example — "Aaj Monday hai, 45 din baad?"
Step 1: 45 ÷ 7 = 6 hafte + 3 bache
Step 2: Monday + 3 din = Thursday ✓
(Sirf bache hue din gino — poore hafte se vaar nahi badalta.)
Step 2: Monday + 3 din = Thursday ✓
(Sirf bache hue din gino — poore hafte se vaar nahi badalta.)
3. ⭐ MATHEMATICAL OPERATIONS — nishanon ka khel
⭐ Do step: (1) nishan badlo (2) BODMAS lagao
Sawal mein bataya jata hai ki + ka matlab × hai, − ka matlab + waghairah. Bas asli nishan likh ke, phir normal Maths ki tarah BODMAS se hal karo (Maths Ch 1 wala).
✏️ Solved Example 1
Agar + = ×, − = +, × = ÷, ÷ = − ho, to 8 + 4 − 6 × 3 ÷ 2 = ?
Step 1 (badlo): 8 × 4 + 6 ÷ 3 − 2
Step 2 (BODMAS): pehle × aur ÷ → 32 + 2 − 2
Step 3: = 32 ✓
Step 1 (badlo): 8 × 4 + 6 ÷ 3 − 2
Step 2 (BODMAS): pehle × aur ÷ → 32 + 2 − 2
Step 3: = 32 ✓
✏️ Solved Example 2 (akshar wale nishan)
Agar P = ÷, Q = ×, R = +, S = −, to 18 Q 12 P 4 R 5 S 6 = ?
Step 1: 18 × 12 ÷ 4 + 5 − 6
Step 2: × aur ÷ left-to-right → 216 ÷ 4 = 54 → 54 + 5 − 6
Step 3: = 53 ✓
Step 1: 18 × 12 ÷ 4 + 5 − 6
Step 2: × aur ÷ left-to-right → 216 ÷ 4 = 54 → 54 + 5 − 6
Step 3: = 53 ✓
📌 Ek aur roop — "nishan aapas mein badal do"
"Agar + aur − aapas mein badal diye jayein" — matlab jahan + likha hai wahan − karo aur jahan − hai wahan +. Phir wahi BODMAS. Sawal dhyan se padho ki kaunse do badle ja rahe hain.
✏️ Type 1 — "X:Y par kona kitna?"
Seedha |30H − 5.5M|. Answer 180 se bada aaye to 360 mein se ghata do.
✏️ Type 2 — "Suiyan kab milengi/90° banayengi?"
Milne ke liye 30H = 5.5M → M = 30H/5.5. 90° ke liye |30H − 5.5M| = 90 rakh ke M nikalo.
✏️ Type 3 — "Aaj X hai, N din baad kaunsa din?"
N ÷ 7 ka remainder nikalo aur utne din aage gino. Peeche wale sawal mein utne din peeche gino.
✏️ Type 4 — Leap year / odd days
Leap: 4 se kate (century ho to 400 se). Odd days table (1, 2, 5, 3, 1, 0) yaad rakho — seedha pucha jata hai.
✏️ Type 5 — Nishan badalna (math operations)
Pehle nishan badlo, phir BODMAS. Jaldbazi mein log left-to-right hi jod-ghata dete hain — wahi galti hai.
Trick 1: Clock ka ek hi formula
|30H − 5.5M|
Alag-alag case ratne ki zaroorat nahi — har angle sawal isi se banta hai. Bas 180 se bada aaye to 360 mein se ghata dena.
|30H − 5.5M|
Alag-alag case ratne ki zaroorat nahi — har angle sawal isi se banta hai. Bas 180 se bada aaye to 360 mein se ghata dena.
Trick 2: Ghanta-suee khiskti hai
0.5° har minute
3:30 par wo 3 par nahi, 3 aur 4 ke beech hoti hai. Isi wajah se answer 90° nahi, 75° hai.
0.5° har minute
3:30 par wo 3 par nahi, 3 aur 4 ke beech hoti hai. Isi wajah se answer 90° nahi, 75° hai.
Trick 3: Calendar mein sirf remainder
N ÷ 7 ka bacha hua
45 din = 6 hafte + 3 din → sirf 3 aage gino. 700 din baad bhi wahi din hoga (700 ÷ 7 = 0 bacha)!
N ÷ 7 ka bacha hua
45 din = 6 hafte + 3 din → sirf 3 aage gino. 700 din baad bhi wahi din hoga (700 ÷ 7 = 0 bacha)!
Trick 4: Leap year ka do-step test
4 se kate? century ho to 400 se?
1900 ✗, 2000 ✓, 2024 ✓, 2100 ✗. Century wale saal hi asli sawal hote hain.
4 se kate? century ho to 400 se?
1900 ✗, 2000 ✓, 2024 ✓, 2100 ✗. Century wale saal hi asli sawal hote hain.
Trick 5: Nishan badal ke pura expression LIKHO
Pehle likho, phir hal karo
Dimaag mein badalte hue hal karoge to gadbad pakki. Naya expression kagaz par likh lo — 5 second lagenge, galti zero.
Pehle likho, phir hal karo
Dimaag mein badalte hue hal karoge to gadbad pakki. Naya expression kagaz par likh lo — 5 second lagenge, galti zero.
❌ Galti 1: 3:30 ka answer 90° likh dena
Ghanta-suee 30 minute mein 15° aage khisak chuki hoti hai → sahi answer 75°. Formula lagao, aankhon se mat socho.
❌ Galti 2: 180° se bada kona wapas na karna
9:00 par formula 270° deta hai, par answer 90° hai (360 − 270). Chhota kona hi maanga jata hai.
❌ Galti 3: Century year ko leap maan lena
1900 leap nahi hai (400 se nahi katta), par 2000 hai. Ye sabse zyada poocha jane wala trap hai.
❌ Galti 4: Calendar mein poore din ginna
45 din aage matlab 45 baar ginna nahi — sirf remainder 3. Aur "pehle" pucha ho to peeche gino.
❌ Galti 5: Nishan badalne ke baad BODMAS bhoolna
8 × 4 + 6 ÷ 3 − 2 mein pehle × aur ÷ honge (32 aur 2), phir jod-ghatav. Left-to-right chalne par answer galat.
Clock angle ka formula?tap 👆
|30H − 5.5M|
Answer 180 se bada aaye to?tap 👆
360 − answer lo
3:30 par kona?tap 👆
75° (90° nahi!)
9:00 par kona?tap 👆
90° (270 → 360−270)
4:30 par kona?tap 👆
45°
Ghanta-suee 1 minute mein kitna chalti hai?tap 👆
0.5° (minute-suee 6°)
12 ghante mein suiyan kitni baar milti hain?tap 👆
11 baar (din bhar mein 22)
Ek din mein 90° kitni baar?tap 👆
44 baar (12 ghante mein 22)
3 aur 4 ke beech suiyan kab milengi?tap 👆
16 4/11 minute past 3
Saadharan saal mein odd days?tap 👆
1 (leap mein 2)
100 saal mein odd days?tap 👆
5 (200 → 3, 300 → 1, 400 → 0)
Leap year ka niyam?tap 👆
4 se kate; century ho to 400 se
1900 leap year hai?tap 👆
Nahi (2000 hai, 2024 hai)
Aaj Monday, 45 din baad?tap 👆
Thursday (45 mod 7 = 3)
700 din baad wahi din hoga?tap 👆
Haan (700 ÷ 7 = 0 bacha)
Nishan wale sawal ka tarika?tap 👆
Nishan badlo → BODMAS
BODMAS mein pehle kya?tap 👆
× aur ÷ (left-to-right), phir + −
Nishan badalte waqt sabse zaroori?tap 👆
Naya expression kagaz par likho
| Cheez | Formula / Value |
|---|---|
| Clock angle | |30H − 5.5M| (180 se bada → 360 − x) |
| 3:30 · 9:00 · 4:30 | 75° · 90° · 45° |
| Suiyon ki chaal | Minute 6°/min · Ghanta 0.5°/min |
| 12 ghante mein milan | 11 baar (din: 22) |
| 12 ghante mein 90° | 22 baar (din: 44) |
| Suiyan milne ka samay | M = 30H / 5.5 |
| Odd days: saadharan / leap | 1 / 2 |
| Odd days: 100/200/300/400 | 5 / 3 / 1 / 0 |
| Leap year | ÷4 (century ho to ÷400) |
| 1900 / 2000 / 2024 | ✗ / ✓ / ✓ |
| N din baad ka vaar | N ÷ 7 ka remainder aage gino |
| Symbol operations | Nishan badlo → BODMAS |
Practice (exam-style)
Q1. What is the angle between the hands of a clock at 3:30?
💡 |30×3 − 5.5×30| = |90 − 165| = 75° (ghanta-suee khisak chuki hoti hai).
Practice (exam-style)
Q2. What is the angle between the hands of a clock at 9:00?
💡 |270 − 0| = 270 → 180 se bada, isliye 360 − 270 = 90°.
Practice (exam-style)
Q3. What is the angle between the hands of a clock at 4:30?
💡 |30×4 − 5.5×30| = |120 − 165| = 45°.
Practice (exam-style)
Q4. How many times do the hands of a clock coincide in 12 hours?
💡 12 ghante mein 11 baar (poore din mein 22 baar).
Practice (exam-style)
Q5. How many times do the hands of a clock form a right angle in a day?
💡 12 ghante mein 22 baar → poore din 44 baar.
Practice (exam-style)
Q6. At what time between 3 and 4 o'clock will the hands of a clock coincide?
💡 30×3 = 5.5M → M = 90/5.5 = 180/11 = 16 4/11 minute.
Practice (exam-style)
Q7. How many odd days are there in an ordinary year?
💡 365 ÷ 7 = 52 hafte + 1 → 1 odd day (leap saal mein 2).
Practice (exam-style)
Q8. How many odd days are there in 100 years?
💡 100 saal → 5 odd days (200 → 3, 300 → 1, 400 → 0).
Practice (exam-style)
Q9. Which of the following is NOT a leap year?
💡 1900 century year hai par 400 se nahi katta → leap nahi (2000 katta hai → leap).
Practice (exam-style)
Q10. Is 2024 a leap year?
💡 2024 ÷ 4 poora katta hai aur century year nahi hai → leap ✓
Practice (exam-style)
Q11. If today is Monday, what day will it be after 45 days?
💡 45 ÷ 7 = 6 hafte + 3 → Monday + 3 = Thursday.
Practice (exam-style)
Q12. How many odd days are there in 400 years?
💡 400 saal mein 0 odd days — isliye calendar har 400 saal baad dohrata hai.
Practice (exam-style)
Q13. If '+' means '×', '−' means '+', '×' means '÷' and '÷' means '−', then 8 + 4 − 6 × 3 ÷ 2 = ?
💡 8 × 4 + 6 ÷ 3 − 2 = 32 + 2 − 2 = 32 (BODMAS!).
Practice (exam-style)
Q14. If P means ÷, Q means ×, R means + and S means −, then 18 Q 12 P 4 R 5 S 6 = ?
💡 18 × 12 ÷ 4 + 5 − 6 → 216 ÷ 4 = 54 → 54 + 5 − 6 = 53.
Teen topic, teen formule. Clock: angle = |30H − 5.5M|, aur 180 se bada aaye to 360 mein se ghatao — yaad rakho ghanta-suee khiskti hai (3:30 par 75°, 90° nahi). 12 ghante mein suiyan 11 baar milti hain aur 22 baar 90° banati hain. Calendar: sirf odd days (7 ka remainder) matter karte hain — saadharan saal 1, leap 2, aur 100/200/300/400 saal ke liye 5/3/1/0. Leap year = 4 se kate, century ho to 400 se (1900 ✗, 2000 ✓). Math operations: nishan badal ke naya expression likho, phir BODMAS — pehle × aur ÷, uske baad + aur −. 🚀