Simplify \(\frac{9*3^{n+1} - 3^{n+2}}{3^{n+1} - 3^{n}}\)
3
9
27
81
Correct answer is B
\(\frac{9*3^{n+1} - 3^{n+2}}{3^{n+1} - 3^{n}}\)
= \(\frac{3^n * 3^n * 3^1 * - 3^2 * 3^2}{3^n * 3^1 - 3^n}\)
= \(\frac{3^n (3^2 * 3^1)}{3^n (3^1 - 1)}\)
= \(\frac{27-9}{3-1}\)
= \(\frac{18}{2}\)
= 9
If \(log_{10}(3x+1) + log_{10}4 = log_{10}(9x+2)\), find the value of x
\(\frac{1}{3}\)
1
2
3
Correct answer is C
\(log_{10}(3x+1) + log_{10}4 = log_{10}(9x+2)\)
\(log_{10}4(3x+1) = log_{10}(9x+2)\)
4(3x+1) = 9x + 2
12x -4 = 9x + 2
12x - 9x = 2 + 4
3x = 6
x = 2
(\(\frac{3√6}{√5} + \frac{√54}{3√5}\))\(^{-1}\)
\(\frac{5√3}{6}\)
\(\frac{3√15}{6}\)
\(\frac{5√6}{12}\)
\(\frac{5√3}{12}\)
Correct answer is C
(\(\frac{3√6}{√5} + \frac{√54}{3√5}\))\(^{-1}\)
= \(\frac{√5(3√5)}{3√6 + 3√6}\)
= \(\frac{3*5}{6√6} = \frac{5}{2√6}\)
= \(\frac{5*2√6}{2√6+2√6} = \frac{10√6}{4*6}\)
= \(\frac{5√6}{12}\)
16
8
4
2
Correct answer is D
x∆y = \(\sqrt{x+y - \frac{xy}{4}}\)
4∆3 = \(\sqrt{4+3 - \frac{4*3}{4}}\)
= \(\sqrt{4+3-3}\)
= \(\sqrt{4}\)
= 2.
The table shows the distribution of marks obtained by some students in a test
| Marks | 0-9 | 10-19 | 20-29 | 30-39 | 40-49 |
| Frequency | 4 | 12 | 16 | 6 | 2 |
Find the modal class mark.
4.5
14.5
24.5
34.5
Correct answer is C
Modal class 20 - 29
Modal class mark = \(\frac{20+29}{2}\)
= \(\frac{49}{2}\)
= 24.5