If log\(_{x^{\frac{1}{2}}}\)64 = 3, find the value of x
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(B)
16
9
If \(\frac{1+\sqrt{2}}{1-\sqrt{2}}\) is expressed in the form of x+y√2 find the values of x and y
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(A)
(-3, -2)
10
If X = {n\(^2\) + 1:n = 0,2,3} and Y = {n+1:n=2,3,5}, find X∩Y.
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(C)
∅
11
A book seller sells Mathematics and English books. If 30 customers buy Mathematics books, 20 customers buy English books and 10 customers buy the two books. How many customers has he altogether?
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(B)
40
12
Make Q the subject of formula when \(L=\frac{4}{3}M\sqrt{PQ}\)
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(A)
\(\frac{9L^2}{16M^2P}\)
13
If 2x\(^2\) - kx - 12 is divisible by x-4, Find the value of k.
The fifth term of an A.P is 24 and the eleventh term is 96. Find the first term.
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(D)
-24
20
A binary operation * is defined on the set of positive integers is such x*y = 2x-3y+2 for all positive integers x and y. The binary operation is?
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(B)
neither commutative nor closed on the set of positive integers
21
A binary operation on the real set of numbers excluding -1 is such that for all m, n ∈ R, mΔn = m+n+mn. Find the identity element of the operation.
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(B)
zero
22
In the diagram above, PQ//RS. The size of the angle marked x is?
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(B)
80o
23
Find the exterior angle of a 12 sided regular polygon
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(D)
30o
24
In the diagram above ∠OPQ is?
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(B)
53o
25
Find the area of the figure above
[π = 22/7]
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(D)
84.8 cm2
26
Find the angle subtended at the center of a circle by a chord which is equal in length to the radius of the circle.
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(C)
60o
27
Find the capacity in liters of a cylindrical well of radius 1 meter and depth 14 meters
[π = 22/7]
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(A)
44,000 liters
28
The locus of a point equidistant from two points p(6,2) and R(4,2) is a perpendicular bisector of PR passing through?
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(B)
(5,2)
29
Find the gradient of a line which is perpendicular to the line with the equation 3x + 2y + 1 = 0
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(B)
2/3
30
If sinθ = 3/5. Find Tanθ
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(A)
3/4
31
Find the derivative of \(y=\frac{x^7 - x^5}{x^4}\)
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(C)
3x2-1
32
Differentiate sin x - x cos x
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(B)
x sin x
33
Find the minimum value of the function y = x(1+x)
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(A)
-1/4
34
Evaluate \(\int_1 ^2(6x^2-2x)dx\)
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(D)
11
35
Evaluate \(\int^{\frac{\pi}{2}} _{\frac{-\pi}{2}} cos x dx\)
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(C)
2
36
On a pie chart there are six sectors of which four angles are 30°, 45°, 60°, 90° and the remaining two angles are in the ratio 2:1. Find the smallest angles of the remaining two angles.
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(C)
45o
37
The bar chart above shows the number of times the word "a, and , in, it, the ,to" appear in a paragraph in a book.
What is the ratio of the least frequent word to the most frequent word?
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(A)
1/6
38
What is the mean of the data t, 2t-1, t-2, 2t -1, 4t and 2t+2?
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(D)
2t-1/3
39
Find the median of 4, 1, 4, 1, 0, 4, 4, 2 and 0
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(C)
2
40
If x > 0, find the range of number x-3, 3x+2,x-1, 4x, 2x-1, x-2, 2x-2, 3x and 3x+1
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(A)
3x+3
41
Find the mean deviation of 2, 4, 5, and 9
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(B)
2
42
In how many ways can the letters of the word ACCEPTANCE be arranged?
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(A)
10! / (2!2!3!)
43
Find the number of ways of selecting 6 out of 10 subjects for an examination
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(D)
210
44
The probability of picking a letter T from the word OBSTRUCTION is?
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(B)
2/11
45
The result of rolling a fair die 150 times is as summarized in the table above. What is the probability of obtaining a 5?
