Question : Two points P and Q are at the distance of $x$ and $y$, where $y>x$, respectively from the base of a building and on a straight line. If the angles of elevation on the top of the building from points P and Q are complementary, then what is the height of the building?

Option 1: $xy$

Option 2: $\sqrt\frac{y}{x}$

Option 3: $\sqrt\frac{x}{y}$

Option 4: $\sqrt{xy}$

Question : If $x=\frac{\sqrt{5}+1}{\sqrt{5}-1}$ and $y=\frac{\sqrt{5}-1}{\sqrt{5}+1}$, then the value of $\frac{x^{2}+xy+y^{2}}{x^{2}-xy+y^{2}}$ is:

Option 1: $\frac{3}{4}$

Option 2: $\frac{4}{3}$

Option 3: $\frac{3}{5}$

Option 4: $\frac{5}{3}$

Question : If $x^2+y^2=29$ and $xy=10$, where $x>0,y>0$ and $x>y$. Then the value of $\frac{x+y}{x-y}$ is:

Option 1: $- \frac{7}{3}$

Option 2: $\frac{7}{3}$

Option 3: $\frac{3}{7}$

Option 4: $-\frac{3}{7}$

Question : If $x=\frac{\sqrt{5}-\sqrt{4}}{\sqrt{5}+\sqrt{4}}$ and $y=\frac{\sqrt{5}+\sqrt{4}}{\sqrt{5}-\sqrt{4}}$ then the value of $\frac{x^2-x y+y^2}{x^2+x y+y^2}=$?

Option 1: $\frac{361}{363}$

Option 2: $\frac{341}{343}$

Option 3: $\frac{384}{387}$

Option 4: $\frac{321}{323}$

Question : If $x=(0.25)^\frac{1}{2}$, $y=(0.4)^{2}$, and $z=(0.216)^{\frac{1}{3}}$, then:

Option 1: $y>x>z$

Option 2: $x>y>z$

Option 3: $z>x>y$

Option 4: $x>z>y$

Question : Two posts are $x$ metres apart and the height of one is double that of the other. If, from the midpoint of the line joining their feet, an observer finds the angular elevation of their tops to be complementary, then the height (in metres) of the shorter posts is:

Option 1: $\frac{x}{2\sqrt{2}}$

Option 2: $\frac{x}{4}$

Option 3: $x\sqrt{2}$

Option 4: $\frac{x}{\sqrt{2}}$