Find the value of x for which 2(32x-1) = 162
5/2
3/2
2/5
1/2
Correct answer is A
2(32x-1) = 162
32x-1 = 162/2
32x-1 = 81
32x-1 = 32
2x - 1 = 4 (equating the indices)
2x = 5
5/2
x =
Evaluate \(\frac{(05652)^2 - (04375)^2}{0.04}\) correct to three significant figures
3.11
3.13
0.313
3.12
Correct answer is B
\(\frac{(0.5652)^2 - (0.4375)^2}{0.04}\\
\frac{(0.5625+0.4375)(0.5625-0.4375)}{0.04}\\
\frac{1.000\times 0.125}{0.04}\\
=3.125\\
=3.13\)
124
121
184
180
Correct answer is C
x10 = 12145
= x10 = 1 x 53 + 2 x 52 + 1 * 51 + 4 x 50
= 1 x 125 + 2 x 25 + 1 x 5 + 4 x 1
= 125 + 50 + 5 + 4
= 184
Find y, if \(\sqrt{12}-\sqrt{147}+y\sqrt{3} = 0\)
5
1
7
3
Correct answer is A
\(\sqrt{12}-\sqrt{147}+y\sqrt{3} = 0\\
\sqrt{4\times 3}-\sqrt{49\times 3}+y\sqrt{3} = 0\\
2\sqrt{3}-7\sqrt{3}+y\sqrt{3} = 0\\
y\sqrt{3} = 7\sqrt{3} - 2\sqrt{3}\\
y=\frac{5\sqrt{3}}{\sqrt{3}}\\
y = 5\)
Find the sum to infinity of the series \(2+\frac{3}{2}+\frac{9}{8}+\frac{27}{32}+......\)
1
2
8
4
Correct answer is C
\(a=2\\
r = \frac{3}{4}\\
S = \frac{a}{1-r}\\
S= \frac{2}{1-\frac{3}{4}}\\
= \frac{2}{\frac{1}{4}}\\
S = \frac{2}{1}\times \frac{4}{1}\\
= 8\)