A binary operation * is defined on the set of real number, R, by x*y = x\(^2\) - y\(^2\) + xy, where x, \(\in\) R. Evaluate (\(\sqrt{3}\))*(\(\sqrt{2}\))
\({\color{red}2x} \times 3\)
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(D)
1 + \(\sqrt{6}\)
2
Find the inverse of \(\begin{pmatrix} 3 & 5 \\ 1 & 2 \end{pmatrix}\)
If \(\frac{6x + k}{2x^2 + 7x - 15}\) = \(\frac{4}{x + 5} - \frac{2}{2x - 3}\). Find the value of k.
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(B)
- 22
9
Differentiate \(\frac{x}{x + 1}\) with respect to x.
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(D)
\(\frac{1}{(x + 1)^2}\)
10
Given that 2x + 3y - 10 = 0 and 3x = 2y - 11, calculate the value of (x - y).
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(D)
- 5
11
If V = plog\(_x\), (M + N), express N in terms of X, P, M and V
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(A)
N = X\(^{\frac{v}{p}}\) - M
12
Determine the coefficient of x\(^3\) in the binomial expansion of ( 1 + \(\frac{1}{2}\)x)
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(C)
\(\frac{5}{4}\)
13
Given that P = {x : 1 \(\geq\) x \(\geq\) 6} and Q = {x : 2 < x < 10}. Where x are integers, find n(p \(\cap\) Q)
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(A)
4
14
If X = \(\frac{3}{5}\) and cos y = \(\frac{24}{25}\), where X and Y are acute, find the value of cos (X + Y).
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(C)
\(\frac{3}{5}\)
15
Find the median of the numbers 9,7, 5, 2, 12,9,9, 2, 10, 10, and 18.
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(B)
9
16
Calculate the probability that the product of two numbers selected at random with replacement from the set {-5,-2,4, 8} is positive
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(B)
\(\frac{1}{2}\)
17
Find the angle between i + 5j and 5i - J
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(D)
90\(^o\)
18
Given that F = 3i - 12j, R = 7i + 5j and N = pi + qj are forces acting on a body, if the body is in equilibrium. find the values of p and q.
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(C)
p=10, q=- 7
19
A stone was dropped from the top of a building 40m high. Find, correct to one decimal place, the time it took the stone to reach the ground. [Take g = 9.8ms\(^{-2}\)]
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(A)
2.9.seconds
20
In which of the following series can be the formula S = \(\frac{a}{1 - r}\) where a is the first term and r is the common ratio, be used to find the sum of all the terms?
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(D)
128 + 64 + 32 + 16 + ...
21
If the binomial expansion of (1 + 3x)\(^6\) is used to evaluate (0.97)\(^6\), find the value of x.
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(C)
- 0.01
22
Find the nth term of the linear sequence (A.P) (5y + 1), ( 2y + 1), (1- y),...
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(C)
(8 - 3n)y + 1
23
A circle with centre (5,-4) passes through the point (5, 0). Find its equation.
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(C)
x\(^2\) + y\(^2\) - 10x + 8y + 25 =0
24
Calculate, correct to two decimal places, the area enclosed by the line 3x - 5y + 4 = 0 and the axes.
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(C)
0.53 square units
25
In how many ways can the letters of the word MEMBER be arranged?
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(C)
180
26
Which of the following is not an equation of a circle?
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(D)
x\(^2\) - y\(^2\) + 3x - 5y = 2
27
A function f defined by f : x -> x\(^2\) + px + q is such that f(3) = 6 and f(3) = 0. Find the value of q.
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(C)
15
28
In what interval is the function f : x -> 2x - x\(^2\) increasing?
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(C)
x > 1
29
A force of 230N acts in its direction 065\(^o\). Find its horizontal component.
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(D)
97.2
30
Calculate the variance of \(\sqrt{2}\), (1 + \(\sqrt{2}\)) and (2 + \(\sqrt{2}\))
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(C)
\(\frac{2}{3}\)
31
A three-digit odd number less than 500 is to be formed from 1,2,3,4 and 5. If repetition of digits is allowed, in how many ways can this be done?
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(C)
60
32
The variables x and y are such that y =2x\(^3\) - 2x\(^2\) - 5x + 5. Calculate the corresponding change in y and x changes from 2.00 to 2.05.
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(A)
0.58
33
A bag contains 5 red and 5 blue identical balls. Three balls are selected at random without replacement. Determine the probability of selecting balls alternating in color.
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(C)
\(\frac{5}{36}\)
34
The distance(s) in metres covered by a particle in motion at any time, t seconds, is given by S =120t - 16t\(^2\). Find in metres, the distance covered by the body before coming to rest.
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(D)
225
35
P(3,4) and Q(-3, -4) are two points in a plane. Find the gradient of the line that is normal to the line PQ.
