Question : What is the equation of the line whose y-intercept is $-\frac{3}{4}$ and making an angle of $45^{\circ}$ with the positive x-axis?

Option 1: $4x–4y=3$

Option 2: $4x-4y=–3$

Option 3: $3x–3y=4$

Option 4: $3x–3y=–4$

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: $x+3y=–7$

Question : Simplify the given expression $\frac{(x^3-y^3)(x+y)}{x^2+x y+y^2}$.

Option 1: $x - y$

Option 2: $x^2-y^2$

Option 3: $x + y$

Option 4: $x^2+y^2$

Question : Simplify the given expression. $\frac{x^3+y^3+z^3-3 x y z}{(x-y)^2+(y-z)^2+(z-x)^2}$

Option 1: $\frac{1}{3}(x+y+z)$

Option 2: $(x+y+z)$

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

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

Question : The equation $\cos ^{2}\theta=\frac{(x+y)^{2}}{4xy}$ is only possible when,

Option 1: $x=-y$

Option 2: $x>y$

Option 3: $x=y$

Option 4: $x<y$