Question : If $\sin(\theta+30^{\circ})=\frac{3}{\sqrt{12}}$, then the value of $\cos^{2}\theta$ is:

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

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

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

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

Question : H, O and D were partners in a firm sharing profits and losses in the ratio of 2:2:1. The partners decide to share future profits and losses in the ratio of 3:2:1. Each partner’s gain or sacrifice due to change in ratio will be :

Option 1: H Gain 3/30, O Sacrifice 2/30, D sacrifice 1/30

Option 2: H Sacrifice 3/30, O gain 2/30, D Gain 1/30

Option 3: H Sacrifice 2/30, O Sacrifice 1/30, D Gain 3/30

Option 4: None of the above

Question : If $\frac{x-x\tan^{2}30^{\circ}}{1+\tan^{2}30^{\circ}}=\sin^{2}30^{\circ}+4\cot^{2}45^{\circ}-\sec^{2}60^{\circ}$, then value of $x$ is:

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

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

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

Option 4: $\frac{1}{\sqrt3}$

Question : Find the value of the given expression.
$\frac{4}{3} \tan^2 45^{\circ}+3 \cos^2 30^{\circ}-2 \sec^2 30^{\circ}-\frac{3}{4} \cot^2 60^{\circ}$

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

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

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

Option 4: $\frac{3}{\sqrt{2}}$