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Given that \(\tan x = \frac{5}{12}\), and \(\tan y = \frac{3}{4}\), Find \(\tan (x + y)\).
Evaluate \(\cos 75°\), leaving the answer in surd form.
If \(P = \begin{pmatrix} 1 & 2 \\ 5 & 1 \end{pmatrix}\) and \(Q = \begin{pmatrix} 0 & 1 \\ 1 & 3 \end{pmatrix}\), find PQ.
If \(\begin{vmatrix} m-2 & m+1 \\ m+4 & m-2 \end{vmatrix} = -27\), find the value of m.
Given that \(-6, -2\frac{1}{2}, ..., 71\) is a linear sequence , calculate the number of terms in the sequence.
The 3rd and 6th terms of a geometric progression (G.P.) are \(\frac{8}{3}\) and \(\frac{64}{81}\) respectively, find the common ratio.
Find the fourth term in the expansion of \((3x - y)^{6}\).
Find the coefficient of \(x^{3}\) in the expansion of \([\frac{1}{3}(2 + x)]^{6}\).
Given n = 3, evaluate \(\frac{1}{(n-1)!} - \frac{1}{(n+1)!}\)
Simplify \(\frac{^{n}P_{5}}{^{n}C_{5}}\).
If \(\log_{10}y + 3\log_{10}x \geq \log_{10}x\), express y in terms of x.
Solve for x in the equation \(5^{x} \times 5^{x + 1} = 25\).
If (2t - 3s)(t - s) = 0, find \(\frac{t}{s}\).
The remainder when \(x^{3} - 2x + m\) is divided by \(x - 1\) is equal to the remainder when \(2x^{3} + x - m\) is divided by \(2x + 1\). Find the value of m.
If the solution set of \(x^{2} + kx - 5 = 0\) is (-1, 5), find the value of k.
Factorize completely: \(x^{2} + x^{2}y + 3x - 10y + 3xy - 10\).
If \(y = 4x - 1\), list the range of the domain \({-2 \leq x \leq 2}\), where x is an integer.
If \(f(x) = \frac{4}{x} - 1, x \neq 0\), find \(f^{-1}(7)\).
Consider the statements:
p : Musa is short
q : Musa is brilliant
Which of the following represents the statement "Musa is short but not brilliant"?
An operation * is defined on the set, R, of real numbers by \(p * q = p + q + 2pq\). If the identity element is 0, find the value of p for which the operation has no inverse.