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KVPY2014MathematicsQuadratic Equation

If n is a positive integer and 1 is a cube root of unity, the number of possible values of _ e k =0 ^ n ( array l n k array ) ^ k is

Options

  1. A2
  2. B3
  3. C4
  4. D6

Correct answer

C. 4

Step-by-step solution

|e^ _ R=0 ^ n ( n k ) w^ k |= |e^ (1+w)^ n |= |e^ (-w² )^ n | when n is multiplying of 3, then S = e , 1 / e when n is not multiple of three,then s = e ^ 1 / 2 e ^ -1 / 2

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