2006 - JAMB Mathematics Past Questions and Answers - page 6
51
The binary operation \(\oplus\) defined on the set of real numbers is such that x \(\oplus\) y = \(\frac{xy}{6}\) for all x, y \(\epsilon\) R. Find the inverse of 20 under this operation when the identity element is 6
A
\(\frac{9}{5}\)
B
\(\frac{1}{20}\)
C
\(\frac{10}{3}\)
D
\(\frac{1}{12}\)
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52
If p varies inversely as the cube of q and q varies directly as the square of r, what is the relationship between P and r?
A
p varies directly as r3
B
p varies directly as r6
C
p varies as 6\(\sqrt{r}\)
D
p varies inversely as r6
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53
a binary operation \(\oplus\) o the set of rational numbers is defined as x \(\oplus\) y = \(\frac{x^2 - y^2}{2xy}\). Find -5 \(\oplus\) 3
A
\(\frac{8}{15}\)
B
-\(\frac{17}{15}\)
C
\(\frac{17}{15}\)
D
\(\frac{8}{-15}\)
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54
If T = 2\(\pi\) \(\sqrt{\frac{L}{g}}\), make g the subject of the formula
A
\(\frac{4\pi L^2}{T}\)
B
\(\frac{4\pi^2 L^2}{T}\)
C
\(\frac{4\pi ^2 L}{T}\)
D
\(\frac{2\pi \sqrt{T}}{T}\)
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55
The sum of the first n positive integers is
A
\(\frac{1}{2}\)(n + 1)
B
n \(\frac{1}{2}\)(n + 1)
C
n(n - 1)
D
n(n + 1)
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56
If x = \(\begin{vmatrix} 1 & 0 & 1 \ 2 & -1 & 0 \ -1 & 0 & 1\end{vmatrix}\) and y = \(\begin{vmatrix} -1 & 1 & 2 \ 0 & -1 & -1 \ 2 & 0 & 1\end{vmatrix}\)
find 2x - y
find 2x - y
A
\(\begin{vmatrix} 3 & -1 & 0 \ 4 & -3 & -1 \ -4 & 1 & 1\end{vmatrix}\)
B
\(\begin{vmatrix} 3 & -1 & 0 \ 4 & -1 & 1 \ -4 & 1 & 1\end{vmatrix}\)
C
\(\begin{vmatrix} 3 & -1 & 0 \ 4 & -3 & 1 \ -4 & 1 & 1\end{vmatrix}\)
D
\(\begin{vmatrix} 3 & -1 & 0 \ 4 & 1 & 1 \ -4 & -1 & 1\end{vmatrix}\)
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57
Find the value of k if the expression kx3 + x2 - 5x - 2 leaves a remainder 2 when it is is divided by 2X = 1
A
10
B
8
C
-8
D
-10
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58
How many terms of the series 3, -6, 12, 24,... are needed to make a total of 1 - 28?
A
9
B
8
C
12
D
10
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59
If y = x2 - x - 12, find the range of values of x for which y \(\geq\) 0,
A
-3 < x \(\leq\) 4
B
x , -3 or x > 4
C
-3 \(\leq\) x \(\leq\) 4
D
x \(\leq\) -3 or x \(\geq\) 4
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60
Find the roots of x3 - 2x2 - 5x + 6 = 0
A
1, -2, 3
B
1, 2, -3,
C
-1, -2, 3
D
-1, 2, -3
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