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      Question

      If the sum of the coefficients of all even powers of x

      in the product (1 + x + x2 + … + x2n) (1 – x + x2 – x3 + … + x2n) is 89, then find the value of n.
      A 88 Correct Answer Incorrect Answer
      B 11 Correct Answer Incorrect Answer
      C 44 Correct Answer Incorrect Answer
      D 22 Correct Answer Incorrect Answer

      Solution

      Let (1 + x + x2 + … + x2n) (1 – x + x2 – x3 + … + x2n) = a0 + a1 + a2 + a3+ …… Put x = 1 => 2n + 1 = a0 + a1 + a2 + a3 + …… …(i) Put x = -1 => 2n + 1 = a0 – a1 + a2 – a3 + …… …..(ii) Add (i) and (ii), we get 2n + 1 = 89 Or n = 44

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