In how many ways can a committee of 5 be selected from 8 students if 2 particular students are to be included?
- A. 20
- B. 28
- C. 54
- D. 58
A line passes through the origin and the point \((1\frac{1}{4}, 2\frac{1}{2})\). Find the y-coordinate of the line when x = 4.
- A. 2
- B. 4
- C. 6
- D. 8
A line passes through the origin and the point \((1\frac{1}{4}, 2\frac{1}{2})\), what is the gradient of the line?
- A. 1
- B. 2
- C. 3
- D. 4
Find the minimum value of \(y = x^{2} + 6x – 12\).
- A. -21
- B. -12
- C. -6
- D. -3
If \(36, p, \frac{9}{4}, q\) are consecutive terms of an exponential sequence (G.P.). Find the sum of p and q.
- A. \(\frac{9}{16}\)
- B. \(\frac{81}{16}\)
- C. \(9\)
- D. \(9\frac{9}{16}\)
Given that \(f : x \to \frac{2x – 1}{x + 2}, x \neq -2\), find \(f^{-1}\), the inverse of f.
- A. \(f^{-1} : x \to \frac{1+2x}{2-x}, x \neq 2\)
- B. \(f^{-1} : x \to \frac{1-2x}{x+2}, x \neq -2\)
- C. \(f^{-1} : x \to \frac{1-2x}{x-2}, x \neq 2\)
- D. \(f^{-1} : x \to \frac{1+2x}{x+2}, x \neq -2\)
Which of the following is a factor of the polynomial \(6x^{4} + 2x^{3} + 15x + 5\)?
- A. 3x + 1
- B. x + 1
- C. 2x + 1
- D. x + 2
Given that \(P = \begin{pmatrix} -2 & 1 \\ 3 & 4 \end{pmatrix}\) and \(Q = \begin{pmatrix} 5 & -3 \\ 2 & -1 \end{pmatrix}\), find PQ – QP.
- A. \(\begin{pmatrix} 0 & 0 \\ 0 & 0 \end{pmatrix}\)
- B. \(\begin{pmatrix} 27 & 12 \\ 16 & -15 \end{pmatrix}\)
- C. \(\begin{pmatrix} -20 & -6 \\ 12 & -8 \end{pmatrix}\)
- D. \(\begin{pmatrix} 11 & 12 \\ 30 & -11 \end{pmatrix}\)
Given that \(\frac{2x}{(x + 6)(x + 3)} = \frac{P}{x + 6} + \frac{Q}{x + 3}\), find P and Q.
- A. P = 4 and Q = 2
- B. P = 2 and Q = 4
- C. P = 4 and Q = -2
- D. P = -2 and Q = 4
Given that \(f : x \to x^{2}\) and \(g : x \to x + 3\), where \(x \in R\), find \(f o g(2)\).
- A. 25
- B. 9
- C. 7
- D. 5
Find the 3rd term of \((\frac{x}{2} – 1)^{8}\) in descending order of x.
- A. \(\frac{x^{7}}{8}\)
- B. \(\frac{7x^{6}}{16}\)
- C. \(\frac{7x^{5}}{4}\)
- D. \(\frac{35x^{4}}{8}\)
If \(\log_{3} x = \log_{9} 3\), find the value of x.
- A. \(3^{2}\)
- B. \(3^{\frac{1}{2}}\)
- C. \(3^{\frac{1}{3}}\)
- D. \(2^{13}\)
Solve: \(4(2^{x^2}) = 8^{x}\)
- A. (1, 2)
- B. (1, -2)
- C. (-1, 2)
- D. (-1, -2)
Solve: \(2\cos x – 1 = 0\).
- A. \((\frac{2\pi}{3}, \frac{4\pi}{3})\)
- B. \((\frac{\pi}{6}, \frac{5\pi}{6})\)
- C. \((\frac{\pi}{5}, \frac{2\pi}{5})\)
- D. \((\frac{\pi}{3}, \frac{5\pi}{3})\)
Simplify \(\frac{1 – 2\sqrt{5}}{2 + 3\sqrt{2}}\).
- A. \(14(2\sqrt{2} + 6\sqrt{5} - 4\sqrt{10})\)
- B. \(\frac{1}{14}(2 - 3\sqrt{2} - 4\sqrt{5} - 6\sqrt{10})\)
- C. \(\frac{1}{14}(3\sqrt{2} + 4\sqrt{5} - 6\sqrt{10} - 2)\)
- D. \(14(2 + 3\sqrt{2} - 6\sqrt{5} + 4\sqrt{10})\)
A ball falls from a height of 18m above the ground. Find the speed with which the ball hits the ground. \([g = 10ms^{-2}]\)
- A. 9\(ms^{-1}\)
- B. 9.49\(ms^{-1}\)
- C. 13.42\(ms^{-1}\)
- D. 18.97\(ms^{-1}\)
A man of mass 80kg stands in a lift. If the lift moves upwards with acceleration 0.5\(ms^{-2}\), calculate the reaction from the floor of the lift on the man. \([g = 10ms^{-2}]\)
- A. 760N
- B. 800N
- C. 805N
- D. 840N
A force 10N acts in the direction 060° and another force 6N acts in the direction 330°. Find the y component of their resultant force.
- A. \((3 + 3\sqrt{3})N\)
- B. \((-3 + 5\sqrt{3})N\)
- C. \((5 + 3\sqrt{3})N\)
- D. \((5 + 5\sqrt{3})N\)
A body of mass 10kg moving with a velocity of 5\(ms^{-1}\) collides with another body of mass 15kg moving in the same direction as the first with a velocity of 2\(ms^{-1}\). After collision, the two bodies move together with a common velocity v\(ms^{-1}\).
- A. 3.2
- B. 5.3
- C. 7.0
- D. 8.0
Find the unit vector in the direction of \(-2i + 5j\).
- A. \(\frac{1}{\sqrt{29}}(2i + 5j)\)
- B. \(\frac{1}{\sqrt{29}}(-2i + 5j)\)
- C. \(\frac{1}{29}(2i - 5j)\)
- D. \(\frac{1}{29}(-2i - 5j)\)
Given that \(r = 3i + 4j\) and \(t = -5i + 12j\), find the acute angle between them.
- A. 14.3°
- B. 55.9°
- C. 59.5°
- D. 75.6°