Question : If $a+b+c=6$ and $a^2+b^2+c^2=14$, then what is the value of $(a-b)^2+(b-c)^2+(c-$ a) ${ }^2$?

Option 1: –8

Option 2: 8

Option 3: 10

Option 4: 6

Question : What is the value of ${a}^3+{b}^3+{c}^3$ if $(a+b+c)=0$?

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

Option 2: $0$

Option 3: $3abc$

Option 4: $a^2+b^2+c^2-ab-bc-ca$

Question : If $\frac{(a+b)}{c}=\frac{6}{5}$ and $\frac{(b+c)}{a}=\frac{9}{2}$, then what is the value of $\frac{(a+c)}{b}\; ?$

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

Option 2: $\frac{11}{7}$

Option 3: $\frac{7}{11}$

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

Question : If $x^{4}+2x^{3}+ax^{2}+bx+9$ is a perfect square, where a and b are positive real numbers, then the value of $a$ and $b$ are:

Option 1: $a=5, b=6$

Option 2: $a=6, b=7$

Option 3: $a=7, b=7$

Option 4: $a=7, b=8$

Question : Directions: If A denotes +, B denotes –, C denotes × and D denotes ÷, then which of the following equations is true?

Option 1: 8 B 6 D 2 A 4 C 3 = 15

Option 2: 8 A 8 B 8 C 8 = – 48

Option 3: 9 C 9 B 9 D 9 A 9 = 17

Option 4: 3 A 3 B 3 C 3 A 3 D 3 = 4