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