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AP EAMCET202421 May 2024Evening ShiftMathematicsBinomial TheoremActual

If the ratio of the terms equidistant from the middle term in the expansion of (1+x)¹² is 1 256 (x N) then sum of all the terms of the expansion (1+x)¹² is

Options

  1. A4¹² or 6¹²
  2. B3¹² or 5¹²
  3. C6¹² or 7¹²
  4. D12¹²

Correct answer

B. 3¹² or 5¹²

Step-by-step solution

Middle term ( n 2 +1 )^ th term i.e., 7^ th term T₇= ¹² C₆ x^6 Now, ¹² C₈ x^4 ¹² C₄ x^8 = 1 256 x=4 and 12 10 x^2 ¹² C₂ x¹⁰ = 1 256 x=2 Sum of all term =(1+4)¹² or (1+2)¹²=5¹² or 3¹² .

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