Given that F = 3i – 12j, R = 7i + 5j and N = pi + qj are forces acting on a body, if the body is in equilibrium. find the values of p and q.
- A. p=-10, q=7
- B. p=-10, q=-7
- C. p=10, q=- 7
- D. p-10, q=7
Find the angle between i + 5j and 5i – J
- A. 0\(^o\)
- B. 45\(^o\)
- C. 60\(^o\)
- D. 90\(^o\)
Calculate the probability that the product of two numbers selected at random with replacement from the set {-5,-2,4, 8} is positive
- A. \(\frac{2}{3}\)
- B. \(\frac{1}{2}\)
- C. \(\frac{1}{3}\)
- D. \(\frac{1}{6}\)
Find the median of the numbers 9,7, 5, 2, 12,9,9, 2, 10, 10, and 18.
- A. 7
- B. 9
- C. 10
- D. 11
If X = \(\frac{3}{5}\) and cos y = \(\frac{24}{25}\), where X and Y are acute, find the value of cos (X + Y).
- A. \(\frac{117}{125}\)
- B. \(\frac{24}{25}\)
- C. \(\frac{3}{5}\)
- D. \(\frac{7}{25}\)
Given that P = {x : 1 \(\geq\) x \(\geq\) 6} and Q = {x : 2 < x < 10}. Where x are integers, find n(p \(\cap\) Q)
- A. 4
- B. 6
- C. 8
- D. 10
Determine the coefficient of x\(^3\) in the binomial expansion of ( 1 + \(\frac{1}{2}\)x)
- A. \(\frac{5}{8}\)
- B. \(\frac{5}{6}\)
- C. \(\frac{5}{4}\)
- D. \(\frac{5}{2}\)
If V = plog\(_x\), (M + N), express N in terms of X, P, M and V
- A. N = X\(^{\frac{v}{p}}\) - M
- B. N = X\(^{\frac{p}{v}}\) - M
- C. N = X\(^{\frac{v}{p}}\) + M
- D. N = X\(^{\frac{p}{v}}\) + M
Given that 2x + 3y – 10 = 0 and 3x = 2y – 11, calculate the value of (x – y).
- A. 5
- B. 3
- C. - 3
- D. - 5
Differentiate \(\frac{x}{x + 1}\) with respect to x.
- A. \(\frac{x}{x + 1}\)
- B. \(\frac{-1}{x + 1}\)
- C. \(\frac{1 - x}{(x + 1)^2}\)
- D. \(\frac{1}{(x + 1)^2}\)
If \(\frac{6x + k}{2x^2 + 7x – 15}\) = \(\frac{4}{x + 5} – \frac{2}{2x – 3}\). Find the value of k.
- A. - 21
- B. - 22
- C. - 24
- D. - 25
Simplify; \(\frac{\sqrt{5} + 3}{4 – \sqrt{10}}\)
- A. \(\frac{2}{3}\)\(\sqrt{5}\) + \(\frac{5}{6}\sqrt{2}\) + 2
- B. \(\frac{2}{3}\)\(\sqrt{5}\) + \(\frac{5}{6}\sqrt{2}\) + \(\frac{1}{2}\sqrt{10}\)
- C. \(\frac{2}{3}\)\(\sqrt{5}\) + \(\frac{5}{6}\sqrt{2}\) + \(\frac{1}{2}\sqrt{10}\) + 2
- D. \(\frac{2}{3}\)\(\sqrt{5}\) - \(\frac{5}{6}\sqrt{2}\) + \(\frac{1}{2}\sqrt{10}\) + 2
Given that X : R \(\to\) R is defined by x = \(\frac{y + 1}{5 – y}\) , y \(\in\) R, find the domain of x.
- A. {y : y \(\in\) R, y \(\neq\) 0}
- B. {y : y \(\in\) R, y \(\neq\) 1}
- C. {y : y \(\in\) R, y \(\neq\) 5}
- D. {y : y \(\in\) R, y \(\neq\) 7}
If \(\begin{pmatrix} p+q & 1\\ 0 & p-q \end {pmatrix}\) = \(\begin{pmatrix} 2 & 1 \\ 0 & 8 \end{pmatrix}\)
Find the values of p and q
- A. p = 5, q = 3
- B. p = 5, q = -3
- C. p = -5, q = -3
- D. p = -5, q = 3
If \(\int^3_0(px^2 + 16)dx\) = 129. Find the value of p.
- A. 9
- B. 8
- C. 7
- D. 6
If cos x = -0.7133, find the values of x between 0\(^o\) and 360\(^o\)
- A. 44.5\(^o\) , 224.5\(^o\)
- B. 123.5\(^o\) , 190.5\(^o\)
- C. 135.5\(^o\) , 213.5\(^o\)
- D. 135.5\(^o\) , 224.5\(^o\)
Find the inverse of \(\begin{pmatrix} 3 & 5 \\ 1 & 2 \end{pmatrix}\)
- A. \(\begin{pmatrix} 5 & 1 \\ -3 & 2 \end{pmatrix}\)
- B. \(\begin{pmatrix} 2 & -5 \\ -1 & 3 \end{pmatrix}\)
- C. \(\begin{pmatrix} -5 & 2 \\ -1 & 3 \end{pmatrix}\)
- D. \(\begin{pmatrix} 5 & 1 \\ 2 & 3 \end{pmatrix}\)
A binary operation * is defined on the set of real number, R, by x*y = x\(^2\) – y\(^2\) + xy, where x, \(\in\) R. Evaluate (\(\sqrt{3}\))*(\(\sqrt{2}\))
\({\color{red}2x} \times 3\)
- A. 1 - \(\sqrt{6}\)
- B. \(\sqrt{6}\) - 1
- C. \(\sqrt{6}\)
- D. 1 + \(\sqrt{6}\)
The diagram is that of a light inextensible string of length 4.2m, whose ends are attached to two fixed points X and Y, 3m apart, and on the same horizontal level. A body of mass 800g is hung on the string at a point O, 2.4m from Y. If the system is kept in equilibrium by a horizontal force P acting on the body and the tensions are equal, calculate:
(a) < XOY;
(b) the magnitude of the force P;
(c) the tension T in the string.
(a) A car is moving with a velocity of 10ms\(^{-1}\) It then accelerates at 0.2ms\(^{-2}\) for 100m. Find, correct to two decimal places the time taken by the car to cover the distance.
(b) A particle moves along a straight line such that its distance S metres from a fixed point O is given by S = t\(^2\) – 5t + 6, where t is the time in seconds. Find its:
(i) initial velocity;
(ii) distance when it is momentarily at rest
The essays of 10 candidates were ranked by three examiners as shown in the table.
| candidates | A | B | C | D | E | F | G | H | I | J |
| Examiner I | 1st | 3rd | 6th | 2nd | 10th | 9th | 7th | 4th | 8th | 5th |
| Examiner II | 2nd | 1st | 3rd | 9th | 7th | 4th | 8th | 10th | 5th | 6th |
| Examiner III | 3rd | 2nd | 1st | 6th | 9th | 8th | 7th | 5th | 4th | 10th |
a) Calculate the Spearman’s rank correlation coefficient of the ranks assigned by:
(i) Examiners I and lI;
(ii) Examiners I and III
(iii) Examiners II and II.
(b) Using the results in (a), state which two examiners agree most.