Question : If $a=b^p,b=c^q,c=a^r$, then $pqr$ is:

Option 1: $1$

Option 2: $0$

Option 3: $-1$

Option 4: $abc$

Question : If $a= 9.6,b= 4.44,$ and $c= 5.16$, then the value of $a^3- b^3- c^3- 3 abc$ is:

Option 1: 0

Option 2: –1

Option 3: 2

Option 4: 1

Question : If $a+b+c=0$, then the value of $\frac{a^2}{b c}+\frac{b^2}{c a}+\frac{c^2}{a b}$ is:

Option 1: 1

Option 2: 3

Option 3: - 1

Option 4: 0

Question : If $\left (2a-3 \right )^{2}+\left (3b+4 \right )^{2}+\left ( 6c+1\right)^{2}=0$, then the value of $\frac{a^{3}+b^{3}+c^{3}-3abc}{a^{2}+b^{2}+c^{2}}+3$ is:

Option 1: $abc+3$

Option 2: $6$

Option 3: $0$

Option 4: $3$

Question : If $a+\frac{1}{b}=b+\frac{1}{c}=c+\frac{1}{a}(a\neq b\neq c)$, then the value of $abc$ is:

Option 1: $\pm 1$

Option 2: $\pm 2$

Option 3: $0$

Option 4: $\pm \frac{1}{2}$

Question : If $a, b, c$ are all non-zero and $a+b+c=0$, then find the value of $\frac{a^2}{b c}+\frac{b^2}{c a}+\frac{c^2}{ab}$.

Option 1: $3$

Option 2: $4$

Option 3: $1$

Option 4: $\frac{1}{2}$