Question : If the angles of a triangle are $( 2 x - 8 )^\circ, ( 2 x + 18 )^\circ$ and $6 x^\circ$. what is the value of $3 x$ (in degrees)?

Option 1: $17^\circ$

Option 2: $34^\circ$

Option 3: $51^\circ$

Option 4: $60^\circ$

Question : If $\tan 45^{\circ}+\sec 60^{\circ}=x$, find the value of $x$.

Option 1: 1

Option 2: 4

Option 3: 3

Option 4: 2

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

Option 1: $11$

Option 2: $18$

Option 3: $47$

Option 4: $51$

Question : If $x^2-8x+1=0$, what is the value of $(x^2+\frac{1}{x^2})$?

Option 1: $18$

Option 2: $34$

Option 3: $40$

Option 4: $62$

Question : The value of $\frac{\sin ^2 30^{\circ}+\cos ^2 60^{\circ}+\sec 45^{\circ} × \sin 45^{\circ}}{\sec 60^{\circ}+{\text{cosec}} 30^{\circ}}$ is:

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

Option 2: $-\frac{3}{8}$

Option 3: $\frac{3}{8}$

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

Question : The value of $\frac{\sin ^2 30^{\circ}+\cos ^2 60^{\circ}-\sec 35^{\circ} \cdot \sin 55^{\circ}}{\sec 60^{\circ}+\operatorname{cosec} 30^{\circ}}$ is equal to:

Option 1: $\frac{1}{8}$

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

Option 3: $\frac{1}{4}$

Option 4: $-\frac{1}{8}$