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Mathematics Questions

Question 261:

The 3rd and 7th term of a Geometric Progression (GP) are 81 and 16. Find the 5th term.

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A \(\frac{4}{729}\)
B \(\frac{81}{16}\)
C 27
D 36

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Question 262:

If \(B = \begin{pmatrix} 2 & 5 \\ 1 & 3 \end{pmatrix}\), find \(B^{-1}\).

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A \(A = \begin{pmatrix} -3 & -5 \\ 1 & 2 \end{pmatrix}\)
B \(A = \begin{pmatrix} 3 & -5 \\ 1 & 2 \end{pmatrix}\)
C \(A = \begin{pmatrix} 3 & -5 \\ -1 & 2 \end{pmatrix}\)
D \(A = \begin{pmatrix} -3 & 5 \\ 1 & -2 \end{pmatrix}\)

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Question 263:

\(\alpha\) and \(\beta\) are the roots of the equation \(2x^{2} - 3x + 4 = 0\). Find \(\frac{\alpha}{\beta} + \frac{\beta}{\alpha}\)

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A \(\frac{-9}{8}\)
B \(\frac{-7}{8}\)
C \(\frac{7}{8}\)
D \(\frac{9}{8}\)

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Question 264:

Given that \(\sin x = \frac{5}{13}\) and \(\sin y = \frac{8}{17}\), where x and y are acute, find \(\cos(x+y)\).

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A \(\frac{130}{221}\)
B \(\frac{140}{221}\)
C \(\frac{140}{204}\)
D \(\frac{220}{23}\)

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Question 265:

A circle with centre (4,5) passes through the y-intercept of the line 5x - 2y + 6 = 0. Find its equation.

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A \(x^{2} + y^{2} + 8x - 10y + 21 = 0\)
B \(x^{2} + y^{2} + 8x - 10y - 21 = 0\)
C \(x^{2} + y^{2} - 8x - 10y - 21 = 0\)
D \(x^{2} + y^{2} - 8x - 10y + 21 = 0\)

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