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BITSAT2023MathematicsBinomial TheoremActual

If x¹⁸ occurs in the rth term in the expansion of (x^4+ 1 x^3 )¹⁵ , then what is the value of r ?

Options

  1. A3
  2. B5
  3. C7
  4. D9

Correct answer

C. 7

Step-by-step solution

In the expansion of (x^4+ 1 x^3 )¹⁵ , let T_r is the r^ th term aligned T_r & = 15 r-1 (x^4 )^ 15-r+1 ( 1 x^3 )^ r-1 & = 15 r-1 x^ 64-4 r-3 r+3 =15_ C_ r-1 x^ 67-7 r aligned x ¹⁸ occurs in this term 18=67-7 r 7 r=49 r=7 .

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