The functions f:x → 2x\(^2\) + 3x -7 and g:x →5x\(^2\) + 7x - 6 are defined on the set of real numbers, R. Find the values of x for which 3f(x) = g(x).
Одговорити
(C)
x = 3 or -5
7
Express \(\frac{4π}{2}\) radians in degrees.
Одговорити
(C)
144º
8
A straight line makes intercepts of -3 and 2 on the x and y axes respectively. Find the equation of the line.
Одговорити
(D)
-2x + 3y - 6 = 0
9
Which of the following is the semi-interquartile range of a distribution?
Одговорити
(D)
1/2 (Upper Quartile - Lower Quartile)
10
Evaluate \(∫^0_{-1}\) (x + 1)(x - 2) dx
Одговорити
(D)
-7/6
11
If 36, p,\(\frac{9}{4}\) and q are consecutive terms of an exponential sequence (G.P), find the sum of p and q.
Одговорити
(D)
9 \(\frac{9}{16}\)
12
Differentiate \(\frac{5x^ 3+x^2}{x}\), x ≠ 0 with respect to x.
Одговорити
(A)
10x + 1
13
Given that \(\frac{8x+m}{x^2-3x-4} ≡ \frac{5}{x+1} + \frac{3}{x-4}\)
Одговорити
(C)
-17
14
If \(x^2+y^2+-2x-6y+5 =0\), evaluate dy/dx when x=3 and y=2.
Одговорити
(A)
2
15
Evaluate\({1_0^∫} x^2(x^3+2)^3\)
Одговорити
(B)
\(\frac{65}{12}\)
16
Given \(\begin{vmatrix} 2 & -3 \\ 1 & 4 \end{vmatrix} \begin{vmatrix} -6 \\ k \end{vmatrix} \begin{vmatrix} 3 \\ -26 \end{vmatrix} = 15\). Solve for k.
Одговорити
(B)
-5
17
A linear transformation T is defined by T: (x,y) → (3x - y, x + 4y). Find the image of (2, -1) under T.
Одговорити
(A)
(7, -2)
18
Evaluate \(4p_2 + 4C_2 - 4p_3\)
Одговорити
(C)
-6
19
Find the coefficient of x\(^2\)in the binomial expansion of \((x + \frac{2}{x^2})^5\)
Одговорити
(A)
10
20
Given that P = {x: x is a multiple of 5}, Q = {x: x is a multiple of 3} and R = {x: x is an odd number} are subsets of μ = {x: 20 ≤ x ≤ 35}, (P⋃Q)∩R.
Одговорити
(B)
{21, 25, 27, 33, 35}
21
A particle moving with a velocity of 5m/s accelerates at 2m/s\(^2\). Find the distance it covers in 4 seconds.
Одговорити
(C)
36m
22
If Un = kn\(^2\) + pn, U\(_1\) = -1, U\(_5\) = 15, find the values of k and p.
Одговорити
(C)
k = 1, p = -2
23
In how many ways can six persons be paired?
Одговорити
(C)
15
24
Solve: \(3^{2x-2} - 28(3^{x-2}) + 3 = 0\)
Одговорити
(D)
x = 0 or x = 3
25
Given that P = (-4, -5) and Q = (2,3), express →PQ in the form (k,θ). where k is the magnitude and θ the bearing.
Одговорити
(A)
(10 units, 053º)
26
If →PQ = -2i + 5j and →RQ = -i - 7j, find →PR
Одговорити
(C)
-i + 12j
27
The table shows the distribution of the distance (in km) covered by 40 hunters while hunting.
Distance(km)
3
4
5
6
7
8
Frequency
5
4
x
9
2x
1
If a hunter is selected at random, find the probability that the hunter covered at least 6km.
Одговорити
(A)
\(\frac{3}{5}\)
28
The table shows the distribution of the distance (in km) covered by 40 hunters while hunting.
What is the mode of the distribution?
Distance(km)
3
4
5
6
7
8
Frequency
5
4
x
9
2x
1
Одговорити
(C)
7
29
If g(x) = √(1-x\(^2\)), find the domain of g(x)
Одговорити
(C)
-1 ≤ x ≤ 1
30
Find the coefficient of x\(^3\)y\(^2\) in the binomial expansion of (x-2y)\(^5\)
Одговорити
(C)
40
31
The first, second and third terms of an exponential sequence (G.P) are (x - 4), (x + 2), and (3x + 1) respectively. Find the values of x.
Одговорити
(A)
\(\frac{-1}{2}, 8\)
32
A body of mass 18kg moving with velocity 4ms-1 collides with another body of mass 6kg moving in the opposite direction with velocity 10ms-1. If they stick together after the collision, find their common velocity.
Одговорити
(A)
\(\frac{1}{2}\) m/s
33
The mean heights of three groups of students consisting of 20, 16 and 14 students each are 1.67m, 1.50m and 1.40m respectively. Find the mean height of all the students.
Одговорити
(B)
1.54m
34
Find correct to the nearest degree, the acute angle formed by the lines y = 2x + 5 and 2y = x - 6
Одговорити
(C)
37\(^∘\)
35
Solve: 4sin\(^2\)θ + 1 = 2, where 0º < θ < 180º
Одговорити
(B)
30º 0r 150º
36
Find the range of values of x for which 2x\(^2\) + 7x - 15 ≥ 0.
Одговорити
(A)
x ≤ -5 or x ≥ \(\frac{3}{2}\)
37
The probability that a student will graduate from college is 0.4. If 3 students are selected from the college, what is the probability that at least one student will graduate?
Одговорити
(C)
0.78
38
The equation of a circle is given as 2x\(^2\) + 2y\(^2\) - x - 3y - 41 = 0. Find the coordinates of its centre.
Одговорити
(B)
(\(\frac{1}{4}\), \(\frac{3}{4}\))
39
The gradient of a function at any point (x,y) 2x - 6. If the function passes through (1,2), find the function.
Одговорити
(D)
x\(^2\) - 6x + 7
40
A particle of mass 3kg moving along a straight line under the action of a F N, covers a line distance, d, at time, t, such that d = t\(^2\) + 3t. Find the magnitude of F at time t.
