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