Question : The third proportional to $\left(x^2-y^2\right)$ and $(x-y)$ is:

Option 1: $(x -y)$

Option 2: $\frac{x-y}{x+y}$

Option 3: $\frac{x+y}{x-y}$

Option 4: $(x + y)$

Question : Simplify the given expression.
$y+2 x-[(y-(y-x+y)-(x+y)+y]-2 y$

Option 1: $-y$

Option 2: $-2x$

Option 3: $y$

Option 4: $2x$

Question : The third proportional of the following numbers $(x-y)^2, (x^2-y^2)^2$ is:

Option 1: $(x+y)^3(x-y)^2$

Option 2: $(x+y)^4(x-y)^2$

Option 3: $(x+y)^2(x-y)^2$

Option 4: $(x+y)^2(x-y)^3$

Question : If the areas of two isosceles triangles with equal corresponding angles are in the ratio of $x^2:y^2$, then the ratio of their corresponding heights is:

Option 1: $x: y$

Option 2: $\sqrt{x}: \sqrt{y}$

Option 3: $x^3: y^3$

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

Question : What is the simplified value of $\frac{(x+y+z)(x y+y z+z x)–x y z}{(x+y)(y+z)(z+x)}$?

Option 1: $y$

Option 2: $z$

Option 3: $1$

Option 4: $x$