Question : If for an isosceles triangle, the length of each equal side is $a$ units and that of the third side is $b$ units, then its area will be:

Option 1: $\frac{1}{4}\sqrt{4b^{2}-a^{2}}$ sq. units

Option 2: $\frac{a}{2}\sqrt{2a^{2}-b^{2}}$ sq. units

Option 3: $\frac{b}{4}\sqrt{4a^{2}-b^{2}}$ sq. units

Option 4: $\frac{b}{2}\sqrt{a^{2}-2b^{2}}$ sq. units

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 $\cos27^{\circ}$ = $x$, then the value of $\tan 63°$ is:

Option 1: $\frac{x}{\sqrt{1–x^2}}$

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

Option 3: $\frac{\sqrt{1–x^2}}{x}$

Option 4: $\frac{\sqrt{1+x^2}}{x}$

Question : If $\cos x=-\frac{1}{2}, x$ lies in third quadrant, then $\tan x=?$

Option 1: $\sqrt{3}$

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

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

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

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