Question : If $\small x=a\left (b-c \right),\; y=b\left (c-a \right) ,\; z=c\left (a-b \right)$, then the value of $\left (\frac{x}{a} \right)^{3}+\left (\frac{y}{b} \right)^{3}+\left (\frac{z}{c} \right)^{3}$ is:

Option 1: $\frac{2xyz}{abc}$

Option 2: $\frac{xyz}{abc}$

Option 3: $0$

Option 4: $\frac{3xyz}{abc}$

Question : If $\left (2a-1 \right )^{2}+\left (4b-3 \right)^{2}+\left (4c+5 \right)^{2}=0$, then the value of $\frac{a^{3}+b^{3}+c^{3}-3abc}{a^{2}+b^{2}+c^{2}}$ is:

Option 1: $1\tfrac{3}{8}$

Option 2: $2\tfrac{3}{8}$

Option 3: $3\tfrac{3}{8}$

Option 4: $0$

Question : If $\left (a+b \right):\left (b+c \right):\left (c+a \right)= 6:7:8$ and $\left (a+b+c \right) = 14,$ then value of $c$ is:

Option 1: 6

Option 2: 7

Option 3: 8

Option 4: 14

Question : The value of $2 \frac{3}{5} \div\left[2 \frac{1}{3} \div\left\{4 \frac{1}{3}-\left(2 \frac{1}{2}+\frac{2}{3}\right)\right\}\right]$ is equal to:

Option 1: $1 \frac{3}{10}$

Option 2: $2 \frac{7}{10}$

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

Option 4: $1 \frac{3}{7}$

Question : If $\left(3 y+\frac{3}{y}\right)=8$, then find the value of $\left(y^2+\frac{1}{y^2}\right)$.

Option 1: $5\frac{1}{9}$

Option 2: $4\frac{5}{6}$

Option 3: $7\frac{1}{9}$

Option 4: $9\frac{1}{9}$