Question : $P(4,2)$ and $R(–2,0)$ are vertices of a rhombus $PQRS$. What is the equation of diagonal $QS$?

Option 1: $x–3y=–2$

Option 2: $3x+y=4$

Option 3: $3x+y=–4$

Option 4: $x–3y=2$

Question : If $\tan (x + y)=1$ and $\cos (x-y)={\frac{\sqrt3}{2}}$, then what is the value of $x$ and $y$?

Option 1: $x = 3^\circ, y = 4.5^\circ$

Option 2: $x = 37.5^\circ, y = 7.5^\circ$

Option 3: $x = 7.5^\circ, y = 37.5^\circ$

Option 4: $x = 4.5^\circ, y = 3^\circ$

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

Question : If $x+\frac{1}{x}=3$, then the value of $\frac{3x^{2}-4x+3}{x^{2}-x+1}$ is:

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

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

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

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

Question : For the triangle $PQR$, find the equation of altitude $PS$, if the co-ordinates of $P, Q, R$ are (1, 2), (2, –1), and (0, 5), respectively.

Option 1: $x–3y=–7$

Option 2: $x+3y=–5$

Option 3: $x–3y=–5$

Option 4: $x+3y=–7$