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Further Mathematics Past Questions

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496

A committee of 4 is to be selected from a group of 5 men and 3 women. In how many ways can this be done if the chairman of the committee must be a man?

  • A. 15
  • B. 40
  • C. 70
  • D. 175
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497

Simplify \(\frac{^{n}P_{4}}{^{n}C_{4}}\)

  • A. 24
  • B. 18
  • C. 12
  • D. 6
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498

Which of the following is a singular matrix?

  • A. \(\begin{pmatrix} 1 & 0 \\ 0 & 1 \end{pmatrix}\)
  • B. \(\begin{pmatrix} 2 & 1 \\ 3 & 2 \end{pmatrix}\)
  • C. \(\begin{pmatrix} 3 & 8 \\ 5 & 16 \end{pmatrix}\)
  • D. \(\begin{pmatrix} 0 & 1 \\ 1 & 0 \end{pmatrix}\)
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499

Simplify \(8^{n} \times 2^{2n} \div 4^{3n}\)

  • A. \(2^{-n}\)
  • B. \(2^{1 - n}\)
  • C. \(2^{n}\)
  • D. \(2^{n + 1}\)
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500

The area of a sector of a circle is 3\(cm^{2}\). If the sector subtends an angle of 1.5 radians at the centre, calculate the radius of the circle.

  • A. 1 cm
  • B. \(\sqrt{2}\) cm
  • C. 2 cm
  • D. 4 cm
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