UPSC CAPF (AC) 2025 Paper I · Question 60

Question 60 of the UPSC CAPF (AC) 2025 Paper I (3 August 2025). Try it first, then open the answer and explanation.

1. CAPF 2025 · P-I · Q60 · General Mental Ability · Arithmetic

   Four cylindrical drums, each of radius 1 m, are placed such that each one touches other two drums. A sewer pipe is to be placed through the gap of these drums. What could be the maximum possible radius for this pipe?

   1. (√2 + 1) m
   2. (√2 - 1) m
   3. (π√2 - 1) m
   4. (π√2 + 1) m

   चार बेलनाकार ड्रम, जिनमें से प्रत्येक की त्रिज्या 1 m है, इस प्रकार रखे गए हैं कि प्रत्येक ड्रम अन्य दो ड्रमों को स्पर्श करता है। इन ड्रमों के बीच खाली स्थान से एक सीवर पाइप डाला जाना है। इस पाइप की अधिकतम संभावित त्रिज्या क्या हो सकती है?

   1. (√2 + 1) m
   2. (√2 - 1) m
   3. (π√2 - 1) m
   4. (π√2 + 1) m
   Show answer

   Answer: (2) (√2 - 1) m

   उत्तर: (2) (√2 - 1) m

   The centres of the four touching drums form a square of side 2 m, whose half-diagonal is √2 m. The largest pipe in the central gap reaches from the centre of the square to the drum surfaces, so its radius = √2 - 1 ≈ 0.41 m.

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