Question : If $x$ runs are scored by A, $y$ runs by B, and $z$ runs by C then, $x:y=y:z=3:2$. If the total number of runs scored by A, B, and C is 342, the runs scored by each would be:

Option 1: 144, 96, and 64

Option 2: 162,108, and 72

Option 3: 180, 120, and 80

Option 4: 189, 126, and 84

Question : If $a^2+b^2+c^2=16$, $x^2+y^2+z^2=25$ and $ax+by+cz=20$, then the value of $\frac{a+b+c}{x+y+z}$ is:

Option 1: $\frac{3}{5}$

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

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

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

Question : If $a^{2}=by+cz$, $b^{2}=cz+ax$, $c^{2}=ax+by$, then the value of $\frac{x}{a+x}+\frac{y}{b+y}+\frac{z}{c+z}$ is:

Option 1: $1$

Option 2: $a+b+c$

Option 3: $\frac{1}{a}+\frac{1}{b}+\frac{1}{c}$

Option 4: $0$

Question : If $x+y+z=0$, then what is the value of $\frac{x^2}{(y z)}+\frac{y^2}{(x z)}+\frac{z^2}{(x y)}$?

Option 1: 1

Option 2: 0

Option 3: 2

Option 4: 3

Question : If $x=y+z$, then $x^{3}-y^{3}-z^{3}$ is:

Option 1: $0$

Option 2: $3xyz$

Option 3: $-3xyz$

Option 4: $1$

Question : If $x=(0.25)^\frac{1}{2}$, $y=(0.4)^{2}$, and $z=(0.216)^{\frac{1}{3}}$, then:

Option 1: $y>x>z$

Option 2: $x>y>z$

Option 3: $z>x>y$

Option 4: $x>z>y$