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