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
correct option: b
(\frac{\frac{1}{20} \times 6}{6}) = (\frac{6}{20}) x (\frac{1}{6}) = (\frac{1}{20})
Users' Answers & Comments 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?
C
p varies as 6\(\sqrt{r}\)
D
p varies inversely as r6
correct option: d
p (\alpha) (\frac{1}{q^3}), q (\alpha) r2 , p (\alpha) (r2 )3 , p (\alpha) (\frac{1}{r^6})
Users' Answers & Comments 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
correct option: d
(\frac{(-5)^2 - (3^2)}{2(-5)(+3)})
= (\frac{25 - 9}{-30})
= (\frac{16}{-30})
= (\frac{8}{-15})
Users' Answers & Comments 54
If T = 2\(\pi\) \(\sqrt{\frac{L}{g}}\), make g the subject of the formula
B
\(\frac{4\pi^2 L^2}{T}\)
D
\(\frac{2\pi \sqrt{T}}{T}\)
correct option: c
T = 2(\pi) (\sqrt{\frac{L}{g}})
T2 = 4(\pi^2 \frac{L}{g})
g = (\frac{4\pi ^2 L}{T})
Users' Answers & Comments 55
The sum of the first n positive integers is
B
n \(\frac{1}{2}\)(n + 1)
56
If x = \(\begin{vmatrix} 1 & 0 & 1 \ 2 & -1 & 0 \ -1 & 0 & 1\end{vmatrix}\) and y = \(\begin{vmatrix} -1 & 1 & 2 \ 0 & -1 & -1 \ 2 & 0 & 1\end{vmatrix}\)
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
\(\begin{vmatrix} 3 & -1 & 0 \ 4 & 1 & 1 \ -4 & -1 & 1\end{vmatrix}\)
correct option: b
2(10 - (-1) = 3 2(2) - (0) = 4 2(-1) - (2) = -4
2(0) - (1) = -1 2(-1) - (-1) = -1 2(0) - (-1) = 1
2(10 - (20) = 0 2(0) - (-1) = 1 2(1) - (1) = 1
(\begin{vmatrix} 3 & -1 & 0 \ 4 & -1 & 1 \ -4 & 1 & 1\end{vmatrix})
Users' Answers & Comments 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
58
How many terms of the series 3, -6, 12, 24,... are needed to make a total of 1 - 28 ?
correct option: b
Sn = (\frac{a(1 - (r)^n)}{1 - r})
255 = (\frac{3(1 - (-2))^n}{1 - (2)})
255 = (\frac{3(1-(-2)^n}{3}))
2n = 256
2n = 28
n = 8
Users' Answers & Comments 59
If y = x2 - x - 12, find the range of values of x for which y \(\geq\) 0,
C
-3 \(\leq\) x \(\leq\) 4
D
x \(\leq\) -3 or x \(\geq\) 4
correct option: c
y = x2 - x - 12, let y = 0
x2 - x - 12 = 0, (x + 3)(x - 4) = 0
x = -3 or 4
ranges are -3 and 4
Users' Answers & Comments 60
Find the roots of x3 - 2x2 - 5x + 6 = 0