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JEE Main202127 Jul 2021Morning ShiftMathematicsBinomial TheoremActual

If the coefficients of x 7 in x 2 + 1 b x 11 and x - 7 in x - 1 b x 2 11 , b ≠ 0 , are equal, then the value of b is equal to:

Options

  1. A2
  2. B- 1
  3. C1
  4. D- 2

Correct answer

C. 1

Step-by-step solution

Coefficient of x 7 in x 2 + 1 b x 11 = C r 11 x 2 11 - r · 1 b x r = C r 11 x 22 - 3 r · 1   b r So, 22 - 3 r = 7 ⇒ r = 5 So, the term is C 5 11 · 1   b 5 · x 7 Coefficient of x - 7 in x - 1 b x 2 11 = C r 11 x 11 - r · - 1   b x 2 r = C r 11 x 11 - 3 r · - 1 r b r So, 11 - 3 r = - 7       ∴   r = 6 So, the term is C 6 11 · 1   b 6 x - 7 Hence, C 5 11 · 1   b 5 = C 6 11 · 1   b 6 Since b ≠ 0   &#875

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