Mathematics Past Questions and Answers

If \(P = \begin{pmatrix} 1 & 2 \\ 5 & 1 \end{pmatrix}\) and \(Q = \begin{pmatrix} 0 & 1 \\ 1 & 3 \end{pmatrix}\), find PQ.

Solve for x in the equation \(5^{x} \times 5^{x + 1} = 25\).

If \(\log_{10}y + 3\log_{10}x \geq \log_{10}x\), express y in terms of x.

Simplify \(\frac{^{n}P_{5}}{^{n}C_{5}}\).

Given n = 3, evaluate \(\frac{1}{(n-1)!} - \frac{1}{(n+1)!}\)