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JEE Math Practice Question

Let N denote the number that turns up when a fair die is rolled. If the probability that the system of equations $$x + y + z = 1$$ $$2x + \mathrm{N}y + 2z = 2$$ $$3x + 3y + \mathrm{N}z = 3$$ has unique solution is $${k \over 6}$$, then the sum of value of k and all possible values of N is :

  1. A.18
  2. B.21
  3. C.20
  4. D.19

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