10 × 20 × 30 × ... × 1000 
में शून्य की संख्या ज्ञात कीजिए

  1. 100
  2. 124
  3. 120
  4. 150

Answer (Detailed Solution Below)

Option 2 : 124
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दिया है:

10 × 20 × 30 × ... × 1000

प्रयुक्त अवधारणा:

प्रत्येक में से 10 उभयनिष्ट लें।

n! में अनुगामी शून्य की संख्या = n को 5 से विभाजित करें, इस प्रक्रिया को तब तक जारी रखें जब तक हमें वह मान नहीं मिल जाता जो 5 से कम है। अब सभी भागफलों को जोड़ेंऔर परिणामी संख्या शून्यों की संख्या होगी।

गणना:

10 × 20 × 30 × ... × 1000

⇒ (10 × 1) × (10 × 2) × (10 × 3) × (10 × 4) ..........× (10 × 100)

⇒ 10100 × (1 × 2 × 3 × ... × 100)

⇒ 10100 × (100!)

शून्य की संख्या = 100 + {(100)/5 + (20)/5}

⇒ 100 + 20 + 4

⇒ 124

∴ 10 × 20 × 30 × ... × 1000 में अनुगामी शून्य की संख्या 124 है।

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