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