A box contains 14 white balls and 6 black balls. Find the probability of first drawing a black ball and then a white ball without replacement.
- A. 0.21
- B. 0.22
- C. 0.30
- D. 0.70
A fair coin is tossed 3 times. Find the probability of obtaining exactly 2 heads.
- A. \(\frac{1}{8}\)
- B. \(\frac{3}{8}\)
- C. \(\frac{5}{8}\)
- D. \(\frac{7}{8}\)
Find the variance of 11, 12, 13, 14 and 15.
- A. 2
- B. 3
- C. \(\sqrt{2}\)
- D. 13
Given that \(n = 10\) and \(\sum d^{2} = 20\), calculate the Spearman’s rank correlation coefficient.
- A. 0.121
- B. 0.733
- C. 0.879
- D. 0.979
Find an expression for y given that \(\frac{\mathrm d y}{\mathrm d x} = x^{2}\sqrt{x}\)
- A. \(\frac{1x^{\frac{2}{7}}}{7} + c\)
- B. \(\frac{2x^{\frac{3}{2}}}{7} + c\)
- C. \(\frac{2x^{\frac{7}{2}}}{7} + c\)
- D. \(\frac{1x^{\frac{7}{2}}}{7} + c\)
The radius of a circle increases at a rate of 0.5\(cms^{-1}\). Find the rate of change in the area of the circle with radius 7cm. \([\pi = \frac{22}{7}]\)
- A. 11\(cm^{2}s^{-1}\)
- B. 22\(cm^{2}s^{-1}\)
- C. 33\(cm^{2}s^{-1}\)
- D. 44\(cm^{2}s^{-1}\)
Find the minimum value of \(y = 3x^{2} – x – 6\).
- A. \(-6\frac{1}{6}\)
- B. \(-6\frac{1}{12}\)
- C. \(-6\)
- D. \(0\)
Find the gradient to the normal of the curve \(y = x^{3} – x^{2}\) at the point where x = 2.
- A. \(\frac{-1}{8}\)
- B. \(\frac{1}{8}\)
- C. \(\frac{-1}{24}\)
- D. \(1\)
Find \(\lim\limits_{x \to 3} \frac{2x^{2} + x – 21}{x – 3}\).
- A. 0
- B. 1
- C. 7
- D. 13
The lines \(2y + 3x – 16 = 0\) and \(7y – 2x – 6 = 0\) intersect at point P. Find the coordinates of P.
- A. (4, 2)
- B. (4, -2)
- C. (-4, 2)
- D. (-4, -2)
Points E(-2, -1) and F(3, 2) are the ends of the diameter of a circle. Find the equation of the circle.
- A. \(x^{2} + y^{2} - 5x + 3 = 0\)
- B. \(x^{2} + y^{2} - 2x - 6y - 13 = 0\)
- C. \(x^{2} + y^{2} - x + 5y - 6 = 0\)
- D. \(x^{2} + y^{2} - x - y - 8 = 0\)
Find the equation of the line which passes through (-4, 3) and parallel to line y = 2x + 5.
- A. y = 2x + 11
- B. y = 3x + 11
- C. y = 3x - 5
- D. y = 2x - 11
Given that \(\tan x = \frac{5}{12}\), and \(\tan y = \frac{3}{4}\), Find \(\tan (x + y)\).
- A. \(\frac{16}{33}\)
- B. \(\frac{33}{56}\)
- C. \(\frac{33}{16}\)
- D. \(\frac{56}{33}\)
Evaluate \(\cos 75°\), leaving the answer in surd form.
- A. \(\frac{\sqrt{2}}{2}(\sqrt{3} + 1)\)
- B. \(\frac{\sqrt{2}}{4}(\sqrt{3} - 1)\)
- C. \(\frac{\sqrt{2}}{4}(\sqrt{3} + 1)\)
- D. \(\frac{\sqrt{2}}{2}(\sqrt{3} - 1)\)
If \(P = \begin{pmatrix} 1 & 2 \\ 5 & 1 \end{pmatrix}\) and \(Q = \begin{pmatrix} 0 & 1 \\ 1 & 3 \end{pmatrix}\), find PQ.
- A. \(\begin{pmatrix} 5 & 1 \\ 16 & 5 \end{pmatrix}\)
- B. \(\begin{pmatrix} 2 & 16 \\ 1 & 10 \end{pmatrix}\)
- C. \(\begin{pmatrix} 2 & 7 \\ 1 & 8 \end{pmatrix}\)
- D. \(\begin{pmatrix} 2 & 5 \\ -1 & -8 \end{pmatrix}\)
If \(\begin{vmatrix} m-2 & m+1 \\ m+4 & m-2 \end{vmatrix} = -27\), find the value of m.
- A. \(3\frac{8}{9}\)
- B. \(3\)
- C. \(2\frac{1}{2}\)
- D. \(2\)
Given that \(-6, -2\frac{1}{2}, …, 71\) is a linear sequence , calculate the number of terms in the sequence.
- A. 20
- B. 21
- C. 22
- D. 23
The 3rd and 6th terms of a geometric progression (G.P.) are \(\frac{8}{3}\) and \(\frac{64}{81}\) respectively, find the common ratio.
- A. \(\frac{1}{3}\)
- B. \(\frac{2}{3}\)
- C. \(\frac{3}{4}\)
- D. \(\frac{4}{3}\)
Find the fourth term in the expansion of \((3x – y)^{6}\).
- A. \(-540x^{3}y^{3}\)
- B. \(-540x^{4}y^{2}\)
- C. \(-27x^{3}y^{3}\)
- D. \(540x^{4}y^{2}\)
Find the coefficient of \(x^{3}\) in the expansion of \([\frac{1}{3}(2 + x)]^{6}\).
- A. \(\frac{135}{729}\)
- B. \(\frac{149}{729}\)
- C. \(\frac{152}{729}\)
- D. \(\frac{160}{729}\)
Given n = 3, evaluate \(\frac{1}{(n-1)!} – \frac{1}{(n+1)!}\)
- A. \(12\)
- B. \(2\frac{1}{2}\)
- C. \(2\)
- D. \(\frac{11}{24}\)