Express \(\frac{8 - 3\sqrt{6}}{2\sqrt{3} + 3\sqrt{2}}\) in the form \(p\sqrt{3} + q\sqrt{2}\).

If \(P = {x : -2 < x < 5}\) and \(Q = {x : -5 < x < 2}\) are subsets of \(\mu = {x : -5 \leq x \leq 5}\), where x is a real number, find \((P \cup Q)\).

Consider the statements: p : Musa is short q : Musa is brilliant Which of the following represents the statement "Musa is short but not brilliant"?

Factorize completely: \(x^{2} + x^{2}y + 3x - 10y + 3xy - 10\).

If the solution set of \(x^{2} + kx - 5 = 0\) is (-1, 5), find the value of k.

If \(y = 4x - 1\), list the range of the domain \({-2 \leq x \leq 2}\), where x is an integer.

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.

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 operatio...

If \(f(x) = \frac{4}{x} - 1, x \neq 0\), find \(f^{-1}(7)\).