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

Question : The distance between the two pillars is 120 metres. The height of one pillar is three times the other. The angles of elevation of their tops from the midpoint of the line connecting their feet are complementary to each other. The height (in metres) of the taller pillar is:

Option 1: 34.64

Option 2: 51.96

Option 3: 69.28

Option 4: 103.92

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 $x=\frac{4\sqrt{ab}}{\sqrt a+ \sqrt b}$, then what is the value of $\frac{x+2\sqrt{a}}{x-2\sqrt a}+\frac{x+2\sqrt{b}}{x-2\sqrt b}$(when $a\neq b$)?

Option 1: 0

Option 2: 2

Option 3: 4

Option 4: $\frac{(\sqrt a+\sqrt b)}{(\sqrt a - \sqrt b)}$

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 $x^2-\frac{1}{x^2}=4 \sqrt{2}$, what is the value of $x^4-\frac{1}{x^4}?$

Option 1: $16 \sqrt{2}$

Option 2: $8\sqrt{2}$

Option 3: $24 \sqrt{2}$

Option 4: $32 \sqrt{2}$