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).
Απάντηση
(C)
x = 3 or -5
7
Express \(\frac{4π}{2}\) radians in degrees.
Απάντηση
(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.
Απάντηση
(D)
-2x + 3y - 6 = 0
9
Which of the following is the semi-interquartile range of a distribution?
Απάντηση
(D)
1/2 (Upper Quartile - Lower Quartile)
10
Evaluate \(∫^0_{-1}\) (x + 1)(x - 2) dx
Απάντηση
(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.
Απάντηση
(D)
9 \(\frac{9}{16}\)
12
Differentiate \(\frac{5x^ 3+x^2}{x}\), x ≠ 0 with respect to x.
Απάντηση
(A)
10x + 1
13
Given that \(\frac{8x+m}{x^2-3x-4} ≡ \frac{5}{x+1} + \frac{3}{x-4}\)
Απάντηση
(C)
-17
14
If \(x^2+y^2+-2x-6y+5 =0\), evaluate dy/dx when x=3 and y=2.
Απάντηση
(A)
2
15
Evaluate\({1_0^∫} x^2(x^3+2)^3\)
Απάντηση
(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.
Απάντηση
(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.
Απάντηση
(A)
(7, -2)
18
Evaluate \(4p_2 + 4C_2 - 4p_3\)
Απάντηση
(C)
-6
19
Find the coefficient of x\(^2\)in the binomial expansion of \((x + \frac{2}{x^2})^5\)
Απάντηση
(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.
Απάντηση
(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.
Απάντηση
(C)
36m
22
If Un = kn\(^2\) + pn, U\(_1\) = -1, U\(_5\) = 15, find the values of k and p.
Απάντηση
(C)
k = 1, p = -2
23
In how many ways can six persons be paired?
Απάντηση
(C)
15
24
Solve: \(3^{2x-2} - 28(3^{x-2}) + 3 = 0\)
Απάντηση
(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.
Απάντηση
(A)
(10 units, 053º)
26
If →PQ = -2i + 5j and →RQ = -i - 7j, find →PR
Απάντηση
(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.
Απάντηση
(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
Απάντηση
(C)
7
29
If g(x) = √(1-x\(^2\)), find the domain of g(x)
Απάντηση
(C)
-1 ≤ x ≤ 1
30
Find the coefficient of x\(^3\)y\(^2\) in the binomial expansion of (x-2y)\(^5\)
Απάντηση
(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.
Απάντηση
(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.
Απάντηση
(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.
Απάντηση
(B)
1.54m
34
Find correct to the nearest degree, the acute angle formed by the lines y = 2x + 5 and 2y = x - 6
Απάντηση
(C)
37\(^∘\)
35
Solve: 4sin\(^2\)θ + 1 = 2, where 0º < θ < 180º
Απάντηση
(B)
30º 0r 150º
36
Find the range of values of x for which 2x\(^2\) + 7x - 15 ≥ 0.
Απάντηση
(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?
Απάντηση
(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.
Απάντηση
(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.
Απάντηση
(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.
