यदि  के प्रसार में अचर पद 405 है, तो k के मान क्या हो सकते हैं?

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NDA (Held On: 17 Nov 2019) Maths Previous Year paper
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  1. ±2
  2. ±3
  3. ±5
  4. ±9

Answer (Detailed Solution Below)

Option 2 : ±3
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संकल्पना:

(a + b)के द्विपद प्रसरण में वह पद जो किसी चर में शामिल नहीं है, उसे स्वतंत्र पद कहा जाता है।

(a + b)n के द्विपद प्रसरण में सामान्य पद निम्न द्वारा ज्ञात किया जाता है:

गणना:

दिया गया है:  के प्रसरण में स्थिरांक पद 405 है

अर्थात् का स्वतंत्र पद 405 है।

माना कि (r + 1)वां पद स्वतंत्र पद है।

∵ (r + 1)वां पद स्वतंत्र पद है।

⇒ k = ± 3

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