Question : The least value of $\tan^2x+\cot^2x$ is:

Option 1: 3

Option 2: 2

Option 3: 0

Option 4: 1

Question : If $\tan^4\theta + \tan^2\theta=1$, what is the value of $11(\cos^4\theta+\cos^2\theta)$?

Option 1: – 11

Option 2: 8

Option 3: 0

Option 4: 11

Question : If $5 \sin^2 A+3 \cos^2 A=4$, $0<A<90°$, then what is the value of $\tan A$?

Option 1: 0

Option 2: 3

Option 3: 1

Option 4: 2

Question : If $\alpha$ and $\beta$ are the roots of equation $x^{2}-2x+4=0$, then what is the equation whose roots are $\frac{\alpha ^{3}}{\beta ^{2}}$ and $\frac{\beta ^{3}}{\alpha ^{2}}?$

Option 1: $x^{2}-4x+8=0$

Option 2: $x^{2}-32x+4=0$

Option 3: $x^{2}-2x+4=0$

Option 4: $x^{2}-16x+4=0$

Question : If $\cos \theta=\frac{\sqrt{3}}{2}$, then $\tan ^2 \theta \cos ^2 \theta=?$

Option 1: $\frac{1}{\sqrt{3}}$

Option 2: $\frac{1}{4}$

Option 3: $\frac{1}{2}$

Option 4: $\sqrt{3}$