Question : The value of $\frac{5 \cos ^2 60^{\circ}+4 \sec ^2 30^{\circ}-\tan ^2 45^{\circ}}{\tan ^2 60^{\circ}-\sin ^2 30^{\circ}-\cos ^2 45^{\circ}}$ is:

Option 1: $\frac{67}{27}$

Option 2: $\frac{22}{9}$

Option 3: $\frac{67}{24}$

Option 4: $\frac{19}{9}$

Question : What will be the value of $\frac{\sin 30^{\circ} \sin 40^{\circ} \sin 50^{\circ} \sin 60^{\circ}}{\cos 30^{\circ} \cos 40^{\circ} \cos 50^{\circ} \cos 60^{\circ}}$?

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

Option 2: $\sqrt{3}$

Option 3: $1$

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

Question : If $x\sin ^{2}60^{\circ}-\frac{3}{2}\sec 60^{\circ}\tan^{2}30^{\circ}+\frac{4}{5}\sin ^{2}45^{\circ}\tan ^{2}60^{\circ}=0$, then $x$ is:

Option 1: $-\frac{1}{15}$

Option 2: $–4$

Option 3: $-\frac{4}{15}$

Option 4: $–2$

Question : The value of $\cos^{2}30^{\circ}+\sin^{2}60^{\circ}+\tan^{2}45^{\circ}+\sec^{2}60^{\circ}+\cos0^{\circ}$ is:

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

Option 2: $5\frac{1}{2}$

Option 3: $6\frac{1}{2}$

Option 4: $7\frac{1}{2}$

Question : The value of $\left(\sin 30^{\circ} \cos 60^{\circ}-\cos 30^{\circ} \sin 60^{\circ}\right)$ is equal to:

Option 1: $-\cos 30^{\circ}$

Option 2: $-\sin 30^{\circ}$

Option 3: $\cos 30^{\circ}$

Option 4: $\sin 30^{\circ}$