300 और 1000 के बीच कुल कितनी संख्याएँ 7 से विभाज्य हैं?

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  1. 101
  2. 301
  3. 994
  4. 100

Answer (Detailed Solution Below)

Option 4 : 100
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दिया गया प्रतिबंध: 

300 और 1000 के बीच की संख्याएँ 7 से विभाज्य हैं।

अवधारणा:

समान्तर श्रेणी

an = a + (n - 1)d 

गणना:

7 (300 - 1000) से विभाज्य होने वाली पहली संख्या = 301 

इसी प्रकार: 301, 308, 315, 322...........994 

उपरोक्त श्रृंखला एक समान्तर श्रेणी बनाती है,

जहाँ a = 301, सार्व अंतर d = 308 - 301 = 7 तथा अंतिम पद (an) = 994

⇒ an = a + (n - 1)d

⇒ 994 = 301 + (n - 1)7 

⇒ (994 - 301)/7 = n - 1 

⇒ 693/7 + 1 = n 

⇒ 99 + 1 = n 

⇒ n = 100 

∴ यहाँ 300 और 1000 के बीच 100 संख्याएँ हैं जो 7 से विभाज्य हैं।

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