Two forces 10N and 6N act in the directions 060° and 330° respectively. Find the x- component of their resultant.
- A. \(5\sqrt{3} - 3\)
- B. \(3 - 5\sqrt{3}\)
- C. \(5 - 3\sqrt{3}\)
- D. \(3\sqrt{3} - 5\)
Differentiate \(\frac{x}{x + 1}\) with respect to x.
- A. \(\frac{1}{x + 1}\)
- B. \(\frac{1}{(x + 1)^{2}}\)
- C. \(\frac{1 - x}{x + 1}\)
- D. \(\frac{1 - x}{(x + 1)^{2}}\)
A stone is dropped from a height of 45m. Find the time it takes to hit the ground. \([g = 10 ms^{-2}]\)
- A. 3.0 seconds
- B. 4.5 seconds
- C. 5.0 seconds
- D. 9.0 seconds
If r denotes the correlation coefficient between two variables, which of the following is always true?
- A. \(0 < r \leq 1\)
- B. \(-1 \leq r < 1\)
- C. \(-1 < r \leq 0\)
- D. \(-1 \leq r \leq 1\)
The marks obtained by 10 students in a test are as follows: 3, 7, 6, 2, 8, 5, 9, 1, 4 and 10. Find the variance.
- A. 8.25
- B. 8.50
- C. 9.00
- D. 9.17
The marks obtained by 10 students in a test are as follows: 3, 7, 6, 2, 8, 5, 9, 1, 4 and 10. Find the mean mark.
- A. 4.50
- B. 5.50
- C. 6.50
- D. 6.75
A binary operation, \(\Delta\), is defined on the set of real numbers by \(a \Delta b = a + b + 4\). Find the identity element.
- A. 4
- B. 2
- C. \(\frac{1}{4}\)
- D. -4
Given that \(P = \begin{pmatrix} 2 & 1 \\ 5 & -3 \end{pmatrix}\) and \(Q = \begin{pmatrix} 4 & -8 \\ 1 & -2 \end{pmatrix}\), Find (2P – Q).
- A. \(\begin{pmatrix} -6 & 17 \\ 3 & 1 \end{pmatrix}\)
- B. \(\begin{pmatrix} -2 & 9 \\ 4 & 1 \end{pmatrix}\)
- C. \(\begin{pmatrix} 0 & -6 \\ 9 & -8 \end{pmatrix}\)
- D. \(\begin{pmatrix} 0 & 10 \\ 9 & -4 \end{pmatrix}\)
If \(y = x^{3} – x^{2} – x + 6\), find the values of x at the turning point.
- A. \(\frac{1}{2}, 3\)
- B. \(\frac{1}{3}, -\frac{1}{2}\)
- C. \(1, -\frac{1}{3}\)
- D. \(1, \frac{1}{3}\)
Evaluate \(\int_{-2}^{3} (3x^{2} – 2x – 12) \mathrm {d} x\)
- A. -30
- B. -18
- C. -6
- D. 6
If the midpoint of the line joining (1 – k, -4) and (2, k + 1) is (-k, k), find the value of k.
- A. -4
- B. -3
- C. -2
- D. -1
The equation of a circle is \(3x^{2} + 3y^{2} + 24x – 12y = 15\). Find its radius.
- A. 2
- B. 3
- C. 4
- D. 5
A polynomial is defined by \(f(x + 1) = x^{3} + px^{2} – 4x + 2\), find f(2).
- A. -8
- B. -2
- C. 2
- D. 8
If (x + 1) is a factor of the polynomial \(x^{3} + px^{2} + x + 6\). Find the value of p.
- A. -8
- B. -4
- C. 4
- D. 8
QRS is a triangle such that \(\overrightarrow{QR} = (3i + 2j)\) and \(\overrightarrow{SR} = (-5i + 3j)\), find \(\overrightarrow{SQ}\).
- A. 8i + j
- B. 2i - j
- C. -2i - 3j
- D. -8i - j
Evaluate \(\log_{10}(\frac{1}{3} + \frac{1}{4}) + 2\log_{10} 2 + \log_{10} (\frac{3}{7})\)
- A. -3
- B. 0
- C. \(\frac{5}{6}\)
- D. 1
Given that \(\sin x = \frac{-\sqrt{3}}{2}\) and \(\cos x > 0\), find x.
- A. 300°
- B. 240°
- C. 120°
- D. 60°
Given that \(\sqrt{6}, 3\sqrt{2}, 3\sqrt{6}, 9\sqrt{2},…\) are the first four terms of an exponential sequence (G.P), find in its simplest form the 8th term.
- A. \(27\sqrt{2}\)
- B. \(27\sqrt{6}\)
- C. \(81\sqrt{2}\)
- D. \(81\sqrt{6}\)
Solve the inequality \(x^{2} – 2x \geq 3\)
- A. \(-1 \leq x \leq 3\)
- B. \(x \geq 3\) and \(x \leq -1\)
- C. \(x \geq 3\) or \(x < -1\)
- D. \(-1 \leq x < 3\)
Simplify: \(\frac{\cos 2\theta – 1}{\sin 2\theta}\)
- A. \(-\tan \theta\)
- B. \(-\cos \theta\)
- C. \(\tan \theta\)
- D. \(\cos \theta\)
Which of the following sets is equivalent to \((P \cup Q) \cap (P \cup Q’)\)?
- A. P
- B. \(P \cap Q\)
- C. \(P \cup Q\)
- D. \(\emptyset\)