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MHT CET202124 Sep 2021Morning ShiftMathematicsBinomial TheoremActual

If ¹¹ C ₄+ ¹¹ C ₅+ ¹² C ₆+ ¹³ C ₇= ¹⁴ C _ r , then value of r is

Options

  1. A11
  2. B14
  3. C7
  4. D3

Correct answer

C. 7

Step-by-step solution

¹¹ C ₄+ ¹¹ C ₅+ ¹² C ₆+ ¹³ C ₇= ¹⁴ C _ r We know that ^n C_r+ ^n C_ r-1 = ^ n+1 C_r aligned & ¹⁴ C _ r = ( ¹¹ C ₄+ ¹¹ C ₅ )+ ¹² C ₆+ ¹³ C ₇ & = ( ¹² C ₅+ ¹² C ₆ )+ ¹³ C ₇ & = ¹³ C ₆+ ¹³ C ₇= ¹⁴ C ₇ & r =7 aligned

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