Solve \(3^{2x} - 3^{x+2} = 3^{x+1} - 27\)
1 or 0
1 or 2
1 or -2
-1 or 2
Correct answer is B
\(3^{2x} - 3^{x+2} = 3^{x+1} - 27\)
= \((3^{x})^{2} - (3^{x}).(3^{2}) = (3^{x}).(3^{1}) - 27\)
Let \(3^{x}\) be B; we have
= \(B^{2} - 9B - 3B + 27 = B^{2} - 12B + 27 = 0\).
Solving the equation, we have B = 3 or 9.
\(3^{x} = 3\) or \(3^{x} = 9\)
\(3^{x} = 3^{1}\) or \(3^{x} = 3^{2}\)
Equating, we have x = 1 or 2.
A force (10i + 4j)N acts on a body of mass 2kg which is at rest. Find the velocity after 3 seconds.
\((\frac{5i}{3} + \frac{2j}{3})ms^{-1}\)
\((\frac{10i}{3} + \frac{4j}{3})ms^{-1}\)
\((5i + 2j)ms^{-1}\)
\((15i + 6j)ms^{-1}\)
Correct answer is D
Recall, \(F = mass \times acceleration \implies acceleration = \frac{force}{mass}\)
= \(\frac{10i + 4j}{2} = (5i + 2j) ms^{-2}\)
= \(v = u + at \implies v \text{at 3 seconds} = 0 + (5i + 2j \times 3)\)
= \((15i + 6j) ms^{-1}\)
Given that a = 5i + 4j and b = 3i + 7j, evaluate (3a - 8b).
9i + 44j
-9i + 44j
-9i - 44j
9i - 44j
Correct answer is C
= \(3(5i+4j) - 8(3i+7j) = 15i + 12j - 24i -56j\)
= \(-9i - 44j\)
| Face | 1 | 2 | 3 | 4 | 5 | 6 |
| Frequency | 12 | 18 | y | 30 | 2y | 45 |
Given the table above as the result of tossing a fair die 150 times, find the mode.
3
4
5
6
Correct answer is D
The mode is the occurrence with the highest frequency which, from the table, is 45 (the occurrence of obtaining a 6).
| Face | 1 | 2 | 3 | 4 | 5 | 6 |
| Frequency | 12 | 18 | y | 30 | 2y | 45 |
Given the table above as the results of tossing a fair die 150 times. Find the probability of obtaining a 5.
\(\frac{1}{10}\)
\(\frac{1}{6}\)
\(\frac{1}{5}\)
\(\frac{3}{10}\)
Correct answer is C
Probability of obtaining a 5 = \(\frac{\text{frequency of 5}}{\text{total frequency}}\)
\(12+18+y+30+2y+45 = 150 \implies 105+3y = 150\)
\(3y = 45; y = 15\)
Probability of 5 = \(\frac{2\times 15}{150} = \frac{1}{5}\)