Quantitative Aptitude
The table shows number of officers working in 6 companies.
| Companies | Officers |
| D | 400 |
| E | 500 |
| F | 600 |
| G | 350 |
| H | 450 |
| I | 800 |
What is the total number of officers working in all the companies?
If \( \cos(A - B) = \frac{\sqrt{3}}{2}, \) and cos(A + B) = 0, where A and B are positive acute angles and A ≥ B, then the measures of A and B are:
If \( x^{2} + \frac{1}{x^{2}} = 66, \) the value of \( x - \frac{1}{x} \) is ?
If \( \tan A = \frac{2}{3}, \) then find sin A.
\( \frac{1}{3} \)
\( \frac{2}{\sqrt{13}} \)
\( \frac{2}{3} \)
\( \frac{3}{\sqrt{13}} \)
If \(
\frac{\sin \theta + \cos \theta}{\sin \theta - \cos \theta} = \frac{3}{2}
\) , then the value of sin4θ − cos4θ is:
\(\frac{5}{12}\)
\(\frac{12}{13}\)
\(\frac{11}{12}\)
\(\frac{5}{13}\)
In a circle of radius 3 cm, two chords of length 2 cm and 3 cm lie on the same side of a diameter. What is the perpendicular distance between the two chords?
\(
\frac{4\sqrt{3} - 3\sqrt{2}}{2} \, \text{cm}
\)
\(
\frac{4\sqrt{2} - 3\sqrt{3}}{2} \, \text{cm}
\)
\(
\frac{4\sqrt{2} - 3\sqrt{3}}{3} \, \text{cm}
\)
\(
\frac{4\sqrt{2} - 3\sqrt{3}}{4} \, \text{cm}
\)
If \( k + \frac{1}{k} = 4, \) then what is the value of \(
k^4 + \frac{1}{k^4}
\) ?