Question : If $a + b + c = 6$ and $a^2+b^2+c^2=40$, then what is the value of $a^3+b^3+c^3-3abc$?

Option 1: 212

Option 2: 252

Option 3: 232

Option 4: 206

Question : If $a+b+c=9$ (where $a,b,c$ are real numbers), the minimum value of $a^2+b^2+c^2$ is:

Option 1: 100

Option 2: 9

Option 3: 27

Option 4: 81

Question : What is the value of $a^2+4 b^2+9 c^2-4 a b+12 b c-6 c a$?

Option 1: $(a+2 b-3 c)^2$

Option 2: $(2a- b-3 c)^2$

Option 3: $(2b-a-3 c)^2$

Option 4: $(a-2 b-3 c)^2$

Question : If $a^2+b^2+c^2=62$ and $a + b + c = 12$, then what is the value of $4ab + 4bc + 4ca$?

Option 1: 164

Option 2: 148

Option 3: 152

Option 4: 160

Question : If $a+b+c=16,ab+bc+ca=81$, then what is the value of $a^2+b^2+c^2$?

Option 1: 94

Option 2: 98

Option 3: 89

Option 4: 87