Question : If $a, b,$ and $c$ are positive integers such that $a^2 + b^2 = 82$ and $b^2 + c^2 = 65$, then the value of $2a + 7b - 3c$ is:

Option 1: 2

Option 2: 5

Option 3: 49

Option 4: 1

Question : If $a,b,c$, and $d$ satisfy the equations:
$a+7b+3c+5d=0$, $8a+4b+6c+2d=–4$, $2a+6b+4c+8d=4$, $5a+3b+7c+d=–4$, then $\frac{a+d}{b+c}$?

Option 1: 0

Option 2: 1

Option 3: –1

Option 4: – 4

Question : If $2A=3B$, then what is the value of $\frac{A+B}{A}$?

Option 1: $\frac{5}{4}$

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

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

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

Question : If $a+b+c=1, ab+bc+ca=-1$ and $abc=-1$, then the value of $a^{3}+b^{3}+c^{3}$ is:

Option 1: 1

Option 2: – 1

Option 3: 2

Option 4: – 2

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 $a=331, b=336$ and $c=–667$, then the value of $a^3+b^3+c^3–3abc$ is:

Option 1: 1

Option 2: 63

Option 3: 3

Option 4: 0