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 $a^2+b^2+1=2 a$, then the value of $a^4+b^7$ is:

Option 1: 1

Option 2: 0

Option 3: 2

Option 4: 4

Question : If $x^4+y^4=x^2 y^2$, then the value of $x^6+y^6$ is:

Option 1: 2

Option 2: 0

Option 3: 1

Option 4: 3

Question : If $\sin^2\theta = \cos^3\theta$, then the value of $(\cot^2\theta -\cot^6\theta)$ is:

Option 1: –1

Option 2: 0

Option 3: 2

Option 4: 1

Question : If $\sin A+\sin ^2 A=1$, then the value of $\cos ^4 A+\cos ^6 A$ is:

Option 1: $\cos A$

Option 2: $\sin A$

Option 3: 1

Option 4: 0