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AP EAMCET2009MathematicsBinomial Theorem

The coefficient of x²⁴ in the expansion of (1+x^2 )¹² (1+x¹² ) (1+x²⁴ ) is

Options

  1. A¹² C₆
  2. B¹² C₆+2
  3. C¹² C₆+4
  4. D¹² C₆+6

Correct answer

B. ¹² C₆+2

Step-by-step solution

aligned & Now, (1+x^2 )¹² (1+x¹²+x²⁴+x³⁶ ) & array r = [1+ ¹² C₁ (x^2 )+ ¹² C₂ (x^2 )^2+ ¹² C₃ (x^2 )^3 . + ¹² C₄ (x^2 )^4+ ¹² C₅ (x^2 )^5+ ¹² C₆ (x^2 )^6 .+ + 12 12 (x^2 )¹² ] (1+x¹²+x²⁴+x³⁶ ) Coefficient of x²⁴= ¹² C₆+ 12 12 +1 = ¹² C₆+2 array aligned

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