Express cos150° in surd form.
- A. \(-\sqrt{3}\)
- B. \(-\frac{\sqrt{3}}{2}\)
- C. \(-\frac{1}{2}\)
- D. \(\frac{\sqrt{2}}{2}\)
If \(\begin{pmatrix} 2 & 1 \\ 4 & 3 \end{pmatrix}\)\(\begin{pmatrix} 5 \\ 4 \end{pmatrix}\) = k\(\begin{pmatrix} 17.5 \\ 40.0 \end{pmatrix}\), find the value of k.
- A. 1.2
- B. 3.6
- C. 0.8
- D. 0.5
How many ways can 6 students be seated around a circular table?
- A. 36
- B. 48
- C. 120
- D. 720
Find the 21st term of the Arithmetic Progression (A.P.): -4, -1.5, 1, 3.5,…
- A. 43.5
- B. 46
- C. 48.5
- D. 51
Find the coefficient of \(x^{4}\) in the expansion of \((1-2x)^{6}\).
- A. -320
- B. -240
- C. 240
- D. 320
Given that \(\frac{6x+m}{2x^{2}+7x-15} \equiv \frac{4}{x+5} – \frac{2}{2x-3}\), find the value of m.
- A. 20
- B. 12
- C. -10
- D. -22
Given that \(f(x) = \frac{x+1}{2}\), find \(f^{1}(-2)\).
- A. -5
- B. -3
- C. \(-\frac{1}{2}\)
- D. 5
The function f: x \(\to \sqrt{4 – 2x}\) is defined on the set of real numbers R. Find the domain of f.
- A. \(x<2\)
- B. \(x \leq 2\)
- C. \(x = 2\)
- D. \(x > -2\)
Find the coordinates of the centre of the circle \(3x^{2}+3y^{2} – 4x + 8y -2=0\)
- A. (-2,4)
- B. (\(\frac{-2}{3}, \frac{4}{3}\))
- C. (\(\frac{2}{3}, \frac{-4}{3}\))
- D. (2, -4)
If \(x^{2} – kx + 9 = 0\) has equal roots, find the values of k.
- A. 3, 4
- B. \(\pm3\)
- C. \(\pm5\)
- D. \(\pm6\)
Simplify \(\frac{1}{(1-\sqrt{3})^{2}}\)
- A. \(1- \frac{1}{2}\sqrt{3}\)
- B. \(1+ \frac{1}{2}\sqrt{3}\)
- C. \(\sqrt{3}\)
- D. \(1+\sqrt{3}\)
A binary operation \(\Delta\) is defined on the set of real numbers, R, by \(a \Delta b = \frac{a+b}{\sqrt{ab}}\), where a\(\neq\) 0, b\(\neq\) 0. Evaluate \(-3 \Delta -1\).
- A. \(-4\sqrt{3}\)
- B. \(\frac{-4\sqrt{3}}{3}\)
- C. \(\frac{-3\sqrt{3}}{4}\)
- D. \(\frac{-3\sqrt{3}}{4}\)
If \(log_{y}\frac{1}{8}\) = 3, find the value of y.
- A. -2
- B. -\(\frac{1}{2}\)
- C. \(\frac{1}{2}\)
- D. 2