Question : If $\frac{1}{x^2+a^2}=x^2-a^2$, then the value of $x$ is:

Option 1: $\left(1-a^4\right)^\frac{1}{4}$

Option 2: $a$

Option 3: $\left(a^4-1\right)^\frac{1}{4}$

Option 4: $\left(a^4+1\right)^\frac{1}{4}$

Question : If $\left (a+\frac{1}{b} \right)=1$ and $\left (b+\frac{1}{c} \right)=1$, the value of $\left (c+\frac{1}{a} \right)$ is:

Option 1: 0

Option 2: 1

Option 3: – 1

Option 4: 2

Question : If $x^{2} -3x +1=0$, then the value of $\frac{\left(x^4+\frac{1}{x^2}\right)}{\left(x^2+5 x+1\right)}$ is:

Option 1: $\frac{9}{4}$

Option 2: $\frac{27}{8}$

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

Option 4: $2$

Question : If $x+y+z=0$, then what is the value of $\frac{\left (3y^{2}+x^{2}+z^{2} \right )}{\left (2y^{2}-xz \right)}$?

Option 1: $2$

Option 2: $1$

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

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

Question : If $\left(\frac{\cos A}{1-\sin A}\right)+\left(\frac{\cos A}{1+\sin A}\right)=4$, then what will be the value of $A$? $\left(0^{\circ}<\theta<90^{\circ}\right)$

Option 1: $90^{\circ}$

Option 2: $45^{\circ}$

Option 3: $60^{\circ}$

Option 4: $30^{\circ}$