If \(\begin{vmatrix} 3 & x \\ 2 & x - 2 \end{vmatrix} = -2\), find the value of x.
პასუხი
(A)
-8
16
Given that \(P = {x : \text{x is a factor of 6}}\) is the domain of \(g(x) = x^{2} + 3x - 5\), find the range of x.
პასუხი
(D)
{-1, 5, 13, 49}
17
The third of geometric progression (G.P) is 10 and the sixth term is 80. Find the common ratio.
პასუხი
(A)
2
18
Find the axis of symmetry of the curve \(y = x^{2} - 4x - 12\).
პასუხი
(C)
x = 2
19
Find the equation of the tangent to the curve \(y = 4x^{2} - 12x + 7\) at point (2, -1).
პასუხი
(C)
y - 4x + 9 = 0
20
The mean age of 15 pupils in a class is 14.2 years. One new pupil joined the class and the mean changed to 14.1 years. Calculate the age of the new pupil.
პასუხი
(B)
12.6 years
21
The distance s metres of a particle from a fixed point at time t seconds is given by \(s = 7 + pt^{3} + t^{2}\), where p is a constant. If the acceleration at t = 3 secs is \(8 ms^{-2}\), find the value of p.
პასუხი
(A)
\(\frac{1}{3}\)
22
The probabilities that a husband and wife will be alive in 15 years time are m and n respectively. Find the probability that only one of them will be alive at that time.
პასუხი
(C)
m + n - 2mn
23
In a class of 50 pupils, 35 like Science and 30 like History. What is the probability of selecting a pupil who likes both Science and History?
პასუხი
(B)
0.30
24
P, Q, R, S are points in a plane such that PQ = 8i - 5j, QR = 5i + 7j, RS = 7i + 3j and PS = xi + yj. Find (x, y).
პასუხი
(C)
(20, 5)
25
Find the least value of n for which \(^{3n}C_{2} > 0, n \in R\).
პასუხი
(C)
\(\frac{2}{3}\)
26
If \(\overrightarrow{OA} = 3i + 4j\) and \(\overrightarrow{OB} = 5i - 6j \) where O is the origin and M is the midpoint of AB, find OM.
პასუხი
(C)
4i - j
27
Find the direction cosines of the vector \(4i - 3j\).
პასუხი
(C)
\(\frac{4}{5}, -\frac{3}{5}\)
28
Yomi was asked to label four seats S, R, P, Q. What is the probability he labelled them in alphabetical order?
პასუხი
(A)
\(\frac{1}{24}\)
29
Two forces (2i - 5j)N and (-3i + 4j)N act on a body of mass 5kg. Find in \(ms^{-2}\), the magnitude of the acceleration of the body.
პასუხი
(A)
\(\frac{\sqrt{2}}{5}\)
30
Two particles are fired together along a smooth horizontal surface with velocities 4 m/s and 5 m/s. If they move at 60° to each other, find the distance between them in 2 seconds.
პასუხი
(C)
\(2\sqrt{21}\)
31
Two forces \(F_{1} = (7i + 8j)N\) and \(F_{2} = (3i + 4j)N\) act on a particle. Find the magnitude and direction of \(F_{1} - F_{2}\).
პასუხი
(B)
\((4\sqrt{2} N, 045°)\)
32
A stone is thrown vertically upwards and its height at any time t seconds is \(h = 45t - 9t^{2}\). Find the maximum height reached.
პასუხი
(D)
56.25 m
33
Given that \(\frac{\mathrm d y}{\mathrm d x} = 3x^{2} - 4\) and y = 6 when x = 3, find the equation for y.
პასუხი
(A)
\(x^{3} - 4x - 9\)
34
If \(h(x) = x^{3} - \frac{1}{x^{3}}\), evaluate \(h(a) - h(\frac{1}{a})\).
პასუხი
(C)
\(2a^{3} - \frac{2}{a^{3}}\)
35
A company took delivery of 12 vehicles made up of 7 buses and 5 saloon cars for two of its departments; Personnel and General Administration. If the Personnel department is to have at least 3 saloon cars, in how many ways can these vehicles be distributed equally between the departments?
