निम्नलिखित में से कौन सी संख्या 412 + 413 + 414 + 415 को पूरी तरह से विभाजित करेगी?

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SSC Selection Post 2024 (Higher Secondary Level) Official Paper (Held On: 25 Jun, 2024 Shift 4)
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  1. 17
  2. 11
  3. 3
  4. 7

Answer (Detailed Solution Below)

Option 1 : 17
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दिया गया है:

 412 + 413 + 414 + 415

प्रयुक्त सूत्र:

समान पद 412 को व्यंजक से बाहर निकालें।

गणना:

412 + 413 + 414 + 415

⇒ 412 (1 + 4 + 42 + 43)

⇒ 412 (1 + 4 + 16 + 64)

⇒ 412 (85)

अब, हमें यह जांचना होगा कि दिए गए विकल्पों में से कौन सी संख्या 85 को पूरी तरह से विभाजित करती है।

85 = 5 × 17

इसलिए, वह संख्या जो 85 को पूरी तरह से विभाजित करती है, वह 17 है।

∴ सही उत्तर विकल्प (1) है।

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