Question : If $x^2+y^2=29$ and $xy=10$, where $x>0,y>0$ and $x>y$. Then the value of $\frac{x+y}{x-y}$ is:

Option 1: $- \frac{7}{3}$

Option 2: $\frac{7}{3}$

Option 3: $\frac{3}{7}$

Option 4: $-\frac{3}{7}$

Question : If $x+y+z = 9$, then the value of $(x−4)^3+(y−2)^3+(z−3)^3−3(x−4)(y−2)(z−3)$ is:

Option 1: 6

Option 2: 9

Option 3: 0

Option 4: 1

Question : $\text { If } x^2+y^2+z^2=x y+y z+z x \text { and } x=1 \text {, then find the value of } \frac{10 x^4+5 y^4+7 z^4}{13 x^2 y^2+6 y^2 z^2+3 z^2 x^2}$.

Option 1: 2

Option 2: 0

Option 3: –1

Option 4: 1

Question : If $x=8(\sin \theta+\cos \theta)$ and $y=9(\sin \theta-\cos \theta)$, then the value of $\frac{x^2}{8^2}+\frac{y^2}{9^2}$ is:

Option 1: 4

Option 2: 6

Option 3: 8

Option 4: 2

Question : Direction: After interchanging + and -, 8 and 7, which one of the following becomes correct?

Option 1: 8 - 7 + 3 x 5 = 35

Option 2: 7 x 8 + 6 - 9 = 25

Option 3: 6 + 8 x 2 - 7 = 0

Option 4: 8 x 2 + 7 - 6 = 9