If 5, 8, 6 and 2 occur with frequencies 3, 2, 4 and 1 respectively. Find the product of the modal and the median number
Answer
(A)
36
2
In a basket, there are 6 grapes, 11 bananas and 13 oranges. If one fruit is chosen at random. What is the probability that the fruit is either a grape or a banana
Answer
(C)
17/30
3
The histogram above represents the weights of students who traveled out to their school for an examination. How many people made the trip?
Answer
(C)
29
4
A senatorial candidate had planned to visit seven cities prior to a primary election. However, he could only visit four of the cities. How many different itineraries could be considered?
Answer
(B)
840
5
The pie chart above illustrate the amount of private time a student spends in a week studying various subjects. Find the value of k
Answer
(C)
30o
6
The table above shows the number of pupils in each age group in a class. What is the probability that a pupil chosen at random is at least 11 years old?
Answer
(B)
17/20
7
What is the mean deviation of 3, 5, 8, 11, 12 and 21?
Answer
(A)
4.7
8
Marks
3
4
5
6
7
8
Frequency
5
y - 1
y
9
4
1
The table above gives the frequency distribution of marks obtained by a group of students in a test. If the total mark scored is 200, calculate the value of y
Answer
(C)
11
9
In how many ways can 6 subjects be selected from 10 subjects for an examination
Answer
(D)
210
10
Integrate \(\frac{x^2 -\sqrt{x}}{x}\) with respect to x
Answer
(A)
\(\frac{x^2}{2}-2\sqrt{x}+K\)
11
If y = x cos x, find dy/dx
Answer
(D)
cos x - x sin x
12
Find the value of x for which the function f(x) = 2x\(^3\) - x\(^2\) - 4x + 4 has a maximum value
Answer
(C)
- 2/3
13
Determine the value of \(\int_0 ^{\frac{\pi}{2}
}(-2cos x)dx\)
Answer
(A)
-2
14
A binary operation ⊕ on real numbers is defined by x⊕y = xy + x + y for any two real numbers x and y. The value of (-3/4)⊕6 is
Answer
(A)
3/4
15
The graph above is represented by
Answer
(B)
y = x3 + 2x2 - x - 2
16
Make L the subjects of the formula if d = \(\sqrt{\frac{42w}{5l}}\)
Answer
(B)
\(\frac{42W}{5d^2}\)
17
The solution of the quadratic inequality (x\(^2\) + x - 12) ≥ 0 is
Answer
(D)
x ≥ 3 or x ≤ -4
18
Factorize 2t2 + t - 15
Answer
(B)
(t + 3)(2t - 5)
19
Solve the inequalities -3(x - 2) < -2(x + 3)
Answer
(A)
x > 12
20
W ∝ L2 and W = 6 when L = 4. If L = √17 find W
Answer
(C)
63/8
21
A binary operation Δ is defined by aΔb = a + b + 1 for any numbers a and b. Find the inverse of the real number 7 under the operation Δ, if the identity element is -1
Answer
(B)
-9
22
The nth term of the sequence \(\frac{3}{2}\), 3, 7, 16, 35, 74 ..... is
Answer
(A)
5 . 2n-2 - n
23
Find the sum to infinity of the series \(2+\frac{3}{2}+\frac{9}{8}+\frac{27}{32}+......\)
Answer
(C)
8
24
Find y, if \(\sqrt{12}-\sqrt{147}+y\sqrt{3} = 0\)
Answer
(A)
5
25
If x10 = 12145 find x
Answer
(C)
184
26
Evaluate \(\frac{(0.5625)^2 - (0.4375)^2}{0.04}\) correct to three significant figures
