Quantitative Aptitude
Evaluate the expression
\(
\begin{aligned}
\frac{\sin^{2} 63^{\circ} + \sin^{2} 27^{\circ}}{\cos^{2} 17^{\circ} + \cos^{2} 73^{\circ}}
\end{aligned}
\)
The graph shows the profit ( in lakhs) made by a company from 2001-2002 to 2008-2009.
The ratio of the number of years in which the company's profit is above the average profit, to those in which the profit is below the average is:
The table shows number os officers working in 6 companies.
| Companies | Officers |
| P | 150 |
| Q | 250 |
| R | 350 |
| S | 100 |
| T | 200 |
| U | 550 |
What is the ratio of number of officers working in Q to the number of officers working in R?
If \(\, K + \frac{1}{K} = 3, \,\) then what is the value of \(\, k^{2} + \frac{1}{k^{2}} \, ? \)