Two statements are represented by p and q as follows:
p : He is brilliant; q : He is regular in class
Which of the following symbols represent "He is regular in class but dull"?
إجابة
(B)
\(q \edge \sim p\)
16
Find the locus of points which is equidistant from P(4, 5) and Q(-6, -1).
إجابة
(D)
5x + 3y - 1 = 0
17
A binary operation ,*, is defined on the set R, of real numbers by \(a * b = a^{2} + b + ab\). Find the value of x for which \(5 * x = 37\).
إجابة
(B)
2
18
Find the derivative of \(3x^{2} + \frac{1}{x^{2}}\)
إجابة
(C)
\(6x - \frac{2}{x^{3}}\)
19
The coefficient of the 5th term in the binomial expansion of \((1 + kx)^{8}\), in ascending powers of x is \(\frac{35}{8}\). Find the value of the constant k.
إجابة
(B)
\(\frac{1}{2}\)
20
Given that \(f '(x) = 3x^{2} - 6x + 1\) and f(3) = 5, find f(x).
إجابة
(C)
\(f(x) = x^{3} - 3x^{2} + x + 2\)
21
Express \(\frac{1}{1 - \sin 45°}\) in surd form.
إجابة
(A)
\(2 + \sqrt{2}\)
22
If \(\begin{vmatrix} 4 & x \\ 5 & 3 \end{vmatrix} = 32\), find the value of x.
إجابة
(D)
-4
23
If events A and B are independent and \(P(A) = \frac{7}{12}\) and \(P(A \cap B) = \frac{1}{4}\), find P(B).
إجابة
(A)
\(\frac{3}{7}\)
24
Given that \(\overrightarrow{AB} = 5i + 3j\) and \(\overrightarrow{AC} = 2i + 5j\), find \(\overrightarrow{BC}\).
إجابة
(B)
-3i + 2j
25
The probability of Jide, Atu and Obu solving a given problem are \(\frac{1}{12}\), \(\frac{1}{6}\) and \(\frac{1}{8}\) respectively. Calculate the probability that only one solves the problem.
إجابة
(D)
\(\frac{167}{576}\)
26
Two forces \(F_{1} = (10N, 020°)\) and \(F_{2} = (7N, 200°)\) act on a particle. Find the resultant force.
إجابة
(A)
(3 N, 020°)
27
Marks
2
3
4
5
6
7
8
No of students
5
7
9
6
3
6
4
The table above shows the distribution of marks by some candidates in a test. What is the median score?
إجابة
(B)
4.0
28
Marks
2
3
4
5
6
7
8
No of students
5
7
9
6
3
6
4
The table above shows the distribution of marks by some candidates in a test. Find, correct to one decimal place, the mean of the distribution.
إجابة
(D)
4.7
29
Marks
2
3
4
5
6
7
8
No of students
5
7
9
6
3
6
4
The table above shows the distribution of marks by some candidates in a test. If a student is selected at random, what is the probability that she scored at least 6 marks?
إجابة
(C)
\(\frac{13}{40}\)
30
Express \(r = (12, 210°)\) in the form \(a i + b j\).
إجابة
(B)
\(6(-\sqrt{3} i - j)\)
31
A test consists of 12 questions out of which candidates are to answer 10. If the first 6 are compulsory, in how many ways can each candidate select her questions?
إجابة
(C)
15
32
A body starts from rest and moves in a straight line with uniform acceleration of \(5 ms^{-2}\). How far, in metres, does it go in 10 seconds?
إجابة
(B)
250 m
33
If n items are arranged two at a time, the number obtained is 20. Find the value of n.
