Comprehensive study guide covering Clock for UPSSSC Lower Mains. UPSSSC लोअर मेन्स के लिए Clock को कवर करने वाली मार्गदर्शिका।
mindmap
root((Clock))
Basic_Geometry
Degrees
Divisions
Relative_Motion
Speed_Diff
Overlap
Angle_Calculation
Formula
Shortcuts
Time_Correction
Slow_Fast
Gain_Loss
Mirror_Water
Reflections
Inversion
A standard analog clock represents a circle of 360 degrees. The dial is divided into 12 hour-markings, each representing 30 degrees (360/12).एक मानक एनालॉग घड़ी 360 डिग्री के वृत्त का प्रतिनिधित्व करती है। डायल 12 घंटे के चिह्नों में विभाजित है, जिनमें से प्रत्येक 30 डिग्री (360/12) का प्रतिनिधित्व करता है।
The minute hand moves 360 degrees in 60 minutes (6° per minute), while the hour hand moves 360 degrees in 12 hours (0.5° per minute). This difference is the core of all calculations.मिनट की सुई 60 मिनट में 360 डिग्री (6° प्रति मिनट) चलती है, जबकि घंटे की सुई 12 घंटे में 360 डिग्री (0.5° प्रति मिनट) चलती है। यह अंतर सभी गणनाओं का आधार है।
| Parameter | Value (Minute Hand) | Value (Hour Hand) |
|---|---|---|
| Speed per minute | 6° | 0.5° |
| Speed per second | 0.1° | (1/120)° |
| Relative Speed | 5.5° per minute | - |
To calculate the angle (θ) between hands at time H:M, use the formula: θ = |30H - 5.5M|. This formula is derived from the relative positions of both hands from the 12 o'clock position.
Example: At 4:20, H=4, M=20. Angle = |30(4) - 5.5(20)| = |120 - 110| = 10°. This is a standard examination query format in UPSSSC exams.
| Event | Frequency (12 hrs) | Frequency (24 hrs) |
|---|---|---|
| Overlap (0°) | 11 times | 22 times |
| Opposite (180°) | 11 times | 22 times |
| Right Angle (90°) | 22 times | 44 times |
Note that the overlap does not happen exactly 12 times in 12 hours because the hands only overlap 11 times. The "missing" overlap occurs between 11:00 and 1:00.
For Mirror Images (Vertical), subtract the given time from 11:60 or 12:00. If the time is 8:40, the mirror image is 11:60 - 8:40 = 3:20.
For Water Images, subtract the time from 18:30. If the time is 4:40, subtract from 17:90 (to handle minutes > 30), resulting in 13:50 or 1:50.
Use the ratio method: (Gain/Total Time) * Time Elapsed = Total Gain. This is essential for questions involving faulty clocks in UPSSSC mains.
Mnemonic: "11-1-11". In 12 hours, hands overlap 11 times, are opposite 11 times, and at 90 degrees 22 times.
Shortcut for 0° (Overlap): Time = (60/11) * H. For example, at 3 o'clock, overlap is at (60/11)*3 = 180/11 = 16 4/11 minutes past 3.
When hands are given to be at a specific angle, use θ = |30H - 5.5M|. If the question asks for the time when hands are at 90°, set θ=90 and solve for M.
Remember: There are always two possible times for any angle except 0° and 180°, as the minute hand passes the hour hand twice in most hours.
| Concept | Formula/Logic |
|---|---|
| Angle | |30H - 5.5M| |
| Mirror | 11:60 - Time |
| Water | 18:30 - Time |
| Overlap | (60/11) * H |
Focus on time-saving. Memorize the 60/11 constant. Most UPSSSC questions involve calculating the exact minute for a given angle or finding the mirror image.
Practice at least 50 problems on faulty clocks to master the gain/loss logic, as these carry high weightage in the Mains paper.