UPSC CAPF (AC) 2026 Paper I · Question 66

Question 66 of the UPSC CAPF (AC) 2026 Paper I (19 July 2026). Try it first, then open the answer and explanation.

1. CAPF 2026 · P-I · Q66 · General Mental Ability · Reasoning

   The smaller angle made by the hour and the minute hands is noted when it was 1:30 PM. In which of the following intervals of time will the smaller angle between these hands again be the same?

   1. 1:44 PM and 1:45 PM
   2. 1:45 PM and 1:46 PM
   3. 1:46 PM and 1:47 PM
   4. 1:47 PM and 1:48 PM

   घंटे और मिनट की सुइयों द्वारा बनाए गए लघुतर कोण को 1:30 PM पर देखा जाता है। निम्नलिखित में से समय के किस अंतराल में, इन सुइयों के बीच लघुतर कोण पुनः वही होगा?

   1. 1:44 PM और 1:45 PM
   2. 1:45 PM और 1:46 PM
   3. 1:46 PM और 1:47 PM
   4. 1:47 PM और 1:48 PM
   Show answer

   Answer: (3) 1:46 PM and 1:47 PM

   उत्तर: (3) 1:46 PM और 1:47 PM

   At m minutes past 1 the minute hand is 5.5m - 30 degrees ahead of the hour hand; at 1:30 this is 135°. The smaller angle is 135° again when 5.5m - 30 = 360 - 135 = 225, i.e. m = 255/5.5 ≈ 46.4, about 1:46:22 PM, which is between 1:46 and 1:47 PM.

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