Find m such that (m + \(\sqrt{3}\))(1 - \(\sqrt{3}\))2 = 6 - 2\(\sqrt{2}\)
1
2
3
4
Correct answer is C
(m + \(\sqrt{3}\))(1 - \(\sqrt{3}\))2 = 6 - 2\(\sqrt{2}\)
(m + \(\sqrt{3}\))(4 - 2\(\sqrt{3}\)) = 6 - 2\(\sqrt{2}\)
= 6 - 2\(\sqrt{3}\)
4m - 6 + 4 - 2m\(\sqrt{3}\) = 6 - 2\(\sqrt{3}\)
comparing co-efficients,
4m - 6 = 6.......(i)
4 - 2m = -2.......(ii)
in both equations, m = 3
0.3010
0.4771
0.6532
0.9542
Correct answer is C
If \(log_{10} 2 = 0.3010\) and \(log_{10} 3 = 0.4771\),
\(\log_{10} 4.5 = \log_{10} (\frac{3 \times 3}{2})\)
\(log_{10} 3 + log_{10} 3 - log_{10} 2 = 0.4771 + 0.4771 - 0.3010\)
= 0.6532
Evaluate \(\frac{8^{\frac{1}{3}} \times 5^{\frac{2}{3}}}{10^{\frac{2}{3}}}\)
\(\frac{2}{5}\)
\(\frac{5}{3}\)
3\(\sqrt{5}\)
3\(\sqrt{2}\)
Correct answer is D
\(\frac{8^{\frac{1}{3}} \times 5^{\frac{3}{2}}}{\frac{2}{10^3}}\) = \(\frac{(2^3)^{\frac{1}{3}} \times 5^{\frac{3}{2}}}{(2 \times 5)^{\frac{2}{3}}}\)
= \(\frac{2 \times 5}{2^{\frac{2}{3}} \times 5^{\frac{3}{2}}}\)
= 21 - \(\frac{2}{3}\)
= 2\(\frac{1}{3}\)
= 3\(\sqrt{2}\)
N560.00
N2,450.00
N2,800.00
N3,920.00
Correct answer is C
He pays tax on 1 - \(\frac{1}{8}\) = \(\frac{7}{8}\)th of his income
20% is 490, 100% is \(\frac{100}{20}\) x 490, N2,450.00
= \(\frac{7}{8}\) of his income = N2,450.00
\(\frac{1}{\frac{7}{8}}\) x 2450
= \(\frac{8 \times 2450}{7}\)
= \(\frac{19600}{7}\)
= N2800.00
1 : 1 : 1
4 : 2 : 1
5 : 1 : 1
4 : 1 : 1
Correct answer is D
Let x represent total number of balls in the basket.
If there are 10 blue balls, \(\frac{1}{8}\) of x = 10
x = 10 x 8 = 80 balls
Green balls will be \(\frac{5}{8}\) x 80 = 50 and black balls = \(\frac{2}{8}\) x 80 = 20
Ratio = Green : black : blue
50 : 20 : 10
-10 : -10 : -
------------------
New Ratio 40 : 10 : 10
4 : 1 : 1