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JEE Main2018MathematicsBinomial TheoremActual

If n is the degree of the polynomial, 2 5 x 3 + 1 - 5 x 3 - 1 8 + 2 5 x 3 + 1 + 5 x 3 - 1 8 and m is the coefficient of x n in it, then the ordered pair n , m is equal to

Options

  1. A8 ,   5 10 4
  2. B12 ,   8 10 4
  3. C12 ,   20 4
  4. D24 ,   10 8

Correct answer

C. 12 ,   20 4

Step-by-step solution

2 5 x 3 + 1 - 5 x 3 - 1 8 +   2 5 x 3 + 1 + 5 x 3 - 1 8 Rationalizing denominators of both the brackets, = 5 x 3 + 1 +   5 x 3 - 1     8 +   5 x 3 + 1   -   5 x 3 - 1     8 = 2 8 C 0   5 x 3 + 1 8 + 8 C 2 5 x 3 + 1 6 5 x 3 - 1 2 + 8 C 4 5 x 3 + 1 4 5 x 3 - 1 4 + 8 C 6 5 x 3 + 1 2 5 x 3 - 1 6 + 8 C 8 5 x 3 - 1 8 = 2 5 x 3 - 1 4 + 28 5 x 3 + 1 3 5 x 3 - 1 + 70 5 x 3 + 1 2 5 x 3 - 1 2 + 28 5 x 3 + 1 5 x 3 - 1 3 + 5 x 3 + 1 4 So, n = 12 and m = 2 5 4 + 140 .5 3 + 70 .5

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