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CAPE Pure Mathematics Unit 2 · May/June 2010 · Paper 2 · Question 5(a)(i)

Calculate the number of different permutations of the 8 letters of the word SYLLABUS.

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  1. 5(a)(ii)Calculate the number of different selections of 5 letters which can be made from the letters of the word SYLLABUS.[5 marks]
  2. 5(b)(i)Find P(A \cap B).[3 marks]
  3. 5(b)(ii)a)Stating a reason, determine whether or not the events A and B are mutually exclusive.[3 marks]
  4. 5(b)(ii)b)Stating a reason, determine whether or not the events A and B are independent.[3 marks]
  5. 5(c)(i)Express the complex number (2 + 3i) + \frac{i - 1}{i + 1} in the form a + ib, where a and b are both real numbers.[4 marks]
  6. 5(c)(ii)Given that 1 - i is the root of the equation z^3 + z^2 - 4z + 6 = 0, find the remaining roots.[4 marks]

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