பின்வரும் எண்களில் எது \((49^{15} - 1) \) வின் வகுப்பான்?

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SSC CGL 2022 Tier-I Official Paper (Held On : 01 Dec 2022 Shift 1)
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  1. 46
  2. 14
  3. 8
  4. 50

Answer (Detailed Solution Below)

Option 3 : 8
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PYST 1: SSC CGL - English (Held On : 11 April 2022 Shift 1)
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Detailed Solution

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கொடுக்கப்பட்டது:

\((49^{15} - 1) \)

பயன்படுத்தப்பட்ட கருத்து:

an - bn ஆனது (a + b) ஆல் வகுபடும் போது n ஒரு இரட்டைப்படை மிகை முழுக்களாக இருக்கும்.

கணக்கீடு:

\((49^{15} - 1) \)

\(({(7^2)}^{15} - 1) \)

\((7^{30} - 1) \)

இங்கே, 30 என்பது மிகை முழு எண்.

கருத்தின்படி,

\((7^{30} - 1) \) (7 + 1) அதாவது 8 ஆல் வகுபடும்.

∴ 8 என்பது \((49^{15} - 1) \) வின் வகுப்பான்.

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