Question : If $a =\cot A+\cos A$ and $b =\cot A-\cos A$, then find the value of $a^2-b^2-4 \sqrt{ab}$.

Option 1: 0

Option 2: –1

Option 3: 1

Option 4: –4

Question : If $a+b+c=0$ and $a^2+b^2+c^2=40$, then what is the value of $a b+b c+c a$?

Option 1: –30

Option 2: –20

Option 3: –25

Option 4: –40

Question : The value of $(x^{b+c})^{b–c}(x^{c+a})^{c–a}(x^{a+b})^{a–b}$, where $(x\neq 0)$ is:

Option 1: 1

Option 2: 2

Option 3: –1

Option 4: 0

Question : If a, b, c are real and $a^{2}+b^{2}+c^{2}=2(a-b-c)-3, $ then the value of $2a-3b+4c$ is:

Option 1: –1

Option 2: 0

Option 3: 1

Option 4: 2

Question : If a + b + c = 0, then the value of (a + b – c)² + ( b + c – a)² + ( c + a – b)² is:

Option 1: 0

Option 2: 8abc

Option 3: 4(a² + b² + c²)

Option 4: 4(ab + bc + ca)