(\(\sqrt{a} +\sqrt{8a})^2\) = 54 + b\(\sqrt{2}\), a and b are positive integers. Find the value of a and the value of b.
- A. a = 24, b = 6
- B. a = 6, b = 2
- C. a = 6, b = 24
- D. a = 2, b = 6
Make q the subject of the relation t = \(\sqrt{(\frac{pq}{r} – r^2q)}\)
- A. q = \(\frac{rt^2}{p - r^3}\)
- B. q = \(\frac{p - r^3}{rt^2}\)
- C. q = \(\frac{t^2}{p - r^3}\)
- D. q = \(\frac{rt}{p - r^3}\)
The number of 144 students who registered for mathematics, physics, and chemistry in an examination are shown in the Venn diagram. How many registered for physics and mathematics?
- A. 16
- B. 24
- C. 62
- D. 4
The weights of 15 students in a class are given as 25, 30, 32, 30, 42, 45, 48, 50, 52, 51, 42, 38, 40, and 42. What is the mode of the given data?
- A. 51
- B. 45
- C. 42
- D. 25
A binary operation * is defined on a set of real numbers by x*y = x\(^y\) for all values of x and y, if x * 2 = x, find the possible values of x.
- A. 0, 2
- B. 1, 2
- C. 0, 1
- D. 2, 2
If tan\(\theta\) = \(\frac{8}{15}\), simplify \(\frac{ Sin\theta – Cos\theta}{Sin^2\theta – Sin\theta}\)
- A. \(\frac{-119}{72}\)
- B. \(\frac{119}{72}\)
- C. \(\frac{-7}{17}\)
- D. \(\frac{8}{17}\)
If A = \(\begin{pmatrix}3 & 2 & 1\\4 & 2 & -1\end{pmatrix}\) and B = \(\begin{pmatrix}1 & 4\\0 & 1\\3 & 2\end{pmatrix}\). Find A\(^T\) + B, ( where T means transpose)
- A. \(\begin{pmatrix}4 & 8\\3 & 2\\4 & 1\end{pmatrix}\)
- B. \(\begin{pmatrix}4 & -8\\3 & 2\\4 & 1\end{pmatrix}\)
- C. \(\begin{pmatrix}4 & 8\\4 & -2\\3 & 1\end{pmatrix}\)
- D. \(\begin{pmatrix}4 & 8\\2 & 3\\4 & 1\end{pmatrix}\)
Given P = \(\begin{bmatrix}1 & 2\\2 & 3\end{bmatrix}\), find P\(^2\) – 4P – I where I is the identity matrix
- A. \(\begin{bmatrix}1 & 0\\0 & 1\end{bmatrix}\)
- B. \(\begin{bmatrix}0 & 0\\0 & 0\end{bmatrix}\)
- C. \(\begin{bmatrix}-1 & 0\\0 & -1\end{bmatrix}\)
- D. \(\begin{bmatrix}0 & 1\\1 & 0\end{bmatrix}\)
If x is inversely proportional to y and x = 9 when y = 4, find the law containing x and y
- A. x = \(\frac{16}{y}\)
- B. x = \(\frac{36}{y}\)
- C. x = \(\frac{y}{36}\)
- D. x = \(\frac{13}{y}\)
Find the roots of x\(^3\) – 19x – 30=0
- A. -5, 3, and 2
- B. 5, 3, and -2
- C. 5, -3 and -2
- D. -5, -3 and 2
If B varies inversely as c\(^{\frac{1}{3}}\) and C = 27 when B = 2, find the value of the constant of proportionality K.
- A. 3
- B. 6
- C. 9
- D. 12
U varies directly as the square root of V when U = 24, V = 9, find the value of V when U = 16.
- A. 0.32
- B. 4
- C. 6
- D. 0.25
A bag contains 7 red and 4 black identical balls. Two balls were picked at random from the bag and replaced each time. Find the probability the two balls were of same colour.
- A. \(\frac{54}{121}\)
- B. \(\frac{65}{121}\)
- C. \(\frac{29}{55}\)
- D. \(\frac{27}{55}\)
In how many ways can a committee of 5 be selected from a group of 7 males and 3 females, if the committee must have one female?
- A. 105ways
- B. 135 ways
- C. 210 ways
- D. 231 ways
From a class of 5 girls and 7 boys, a committee consisting of 2 girls and 3 boys is to be formed. How many ways can this be done?
- A. 350 ways
- B. 420 ways
- C. 550 ways
- D. 720 ways
Calculate the standard deviation of the following scores 5, 4, 6, 7, and 8
- A. \(\sqrt{2}\)
- B. \(\sqrt{3}\)
- C. 2
- D. 3
Find the variance of a group of data whose standard deviation is 12.34 to the nearest whole number.
- A. 150
- B. 151
- C. 152
- D. 153
The mean of the numbers 13, 16, x, 18, 21, 2x, 35, is 22. Find the value of x
- A. 16
- B. 17
- C. 23
- D. 25
Differentiate Cos25º – Sin 25º
- A. - ( Sin25º + Cos25º)
- B. - ( Sec25 + Cot25)
- C. - ( Cot25 + Sec25)
- D. - ( Sin25 + Sec25)
How many proper and improper subsets are there in the set K = { a, b, c, d, e}?
- A. 10
- B. 25
- C. 32
- D. 50
The average age of the four female teachers in a school is 40 and the average age of eight male teachers in the school is 25. Calculate the average age of the teachers in the school.
- A. 20
- B. 31
- C. 32
- D. 30