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"?
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(B)
\(q \edge \sim p\)
16
Find the locus of points which is equidistant from P(4, 5) and Q(-6, -1).
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(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 \(5 * x = 37\).
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(B)
2
18
Find the derivative of \(3x^{2} + \frac{1}{x^{2}}\)
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(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.
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(B)
\(\frac{1}{2}\)
20
Given that \(f '(x) = 3x^{2} - 6x + 1\) and f(3) = 5, find f(x).
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(C)
\(f(x) = x^{3} - 3x^{2} + x + 2\)
21
Express \(\frac{1}{1 - \sin 45°}\) in surd form.
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(A)
\(2 + \sqrt{2}\)
22
If \(\begin{vmatrix} 4 & x \\ 5 & 3 \end{vmatrix} = 32\), find the value of x.
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(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).
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(A)
\(\frac{3}{7}\)
24
Given that \(\overrightarrow{AB} = 5i + 3j\) and \(\overrightarrow{AC} = 2i + 5j\), find \(\overrightarrow{BC}\).
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(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.
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(D)
\(\frac{167}{576}\)
26
Two forces \(F_{1} = (10N, 020°)\) and \(F_{2} = (7N, 200°)\) act on a particle. Find the resultant force.
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(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?
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(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.
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(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?
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(C)
\(\frac{13}{40}\)
30
Express \(r = (12, 210°)\) in the form \(a i + b j\).
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(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?
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(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?
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(B)
250 m
33
If n items are arranged two at a time, the number obtained is 20. Find the value of n.
