Question : If $X$ is 20% less than $Y$, then find the values of$\frac{Y–X}{Y}$ and $\frac{X}{X–Y}$.

Option 1: $\frac{1}{5}$ and $-4$

Option 2: $5$ and $-\frac{1}{4}$

Option 3: $\frac{2}{5}$ and $-\frac{5}{2}$

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

Question : If $\sin (x - y) = \frac{1}2$ and $\cos (x + y) = \frac{1}2$, then what is the value of $\sin x \cos x + 2\sin^2x + cos^3x \sec x$?

Option 1: $2$

Option 2: $\sqrt{2}+1$

Option 3: $1$

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

Question : If $x\cos \theta -y\sin \theta =\sqrt{x^{2}+y^{2}}$ and $\frac{\cos ^2{\theta }}{a^{2}}+\frac{\sin ^{2}\theta}{b^{2}}=\frac{1}{x^{2}+y^{2}},$ then the correct relation is:

Option 1: $\frac{x^{2}}{b^{2}}-\frac{y^{2}}{a^{2}}=1$

Option 2: $\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1$

Option 3: $\frac{x^{2}}{b^{2}}+\frac{y^{2}}{a^{2}}=1$

Option 4: $\frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=1$

Question : If $x^2+y^2=427$ and $xy=202$, then find the value of $\frac{x+y}{x-y}$.

Option 1: $\sqrt{\frac{835}{23}}$

Option 2: $\sqrt{\frac{830}{29}}$

Option 3: $\sqrt{\frac{831}{23}}$

Option 4: $\sqrt{\frac{830}{23}}$

Question : What is the value of $\frac{4x^2+9y^2+12xy}{144}$?

Option 1: $(\frac{x}{3} + \frac{y}{4})^2$

Option 2: $(\frac{x}{3} + y)^2$

Option 3: $(\frac{x}{4} + \frac{y}{6})^2$

Option 4: $(\frac{x}{6} + \frac{y}{4})^2$