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AP EAMCET201726 Apr 2017Morning ShiftMathematicsBinomial TheoremActual

³⁷ C₄+ _ r=1 ^5(42-r)_ C_r =

Options

  1. A⁴¹ C₄
  2. B³⁹ C₄
  3. C³⁸ C₄
  4. D⁴² C₄

Correct answer

D. ⁴² C₄

Step-by-step solution

Given that, aligned & ³⁷ C₄+ _ r=1 ^5 ^ (42-r) C_r & = ³⁷ C₄+ ⁴¹ C₁+ ⁴⁰ C₂+ ³⁹ C₃+ ³⁸ C₃+ ³⁷ C₃ & = ³⁷ C₃+ ³⁷ C₄+ ³⁸ C₃+ ³⁹ C₃+ ⁴⁰ C₃+ ⁴¹ C₃ aligned As we know, aligned & ^n C_ r-1 + ^n C_r= ^ n+1 C_r & = ³⁸ C₄+ ³⁸ C₃+ ³⁹ C₃+ ⁴⁰ C₃+ ⁴¹ C₃ & = ³⁹ C₄+ ³⁹ C₃+ ⁴⁰ C₃+ ⁴¹ C₃ & = ⁴⁰ C₄+ ⁴⁰ C₃+ ⁴¹ C₃ & = ⁴¹ C₄+ ⁴¹ C₃= ⁴² C₄ aligned

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