Which of the following forms a colloidal solution in water?

Identify the operation performed by the circuit given below.

From a uniform wire,two circular loops are made: $(i)$ $P$ of radius $r$ and $(ii)$ $Q$ of radius $nr$. If the moment of inertia of $Q$ about an axis passing through its centre and perpendicular to its plane is $8$ times that of $P$ about a similar axis,the value of $n$ is (diameter of the wire is very much smaller than $r$ or $nr$).

The following figure shows a logic gate circuit with two inputs $A$ and $B$ and an output $C$. The voltage waveforms of $A$,$B$,and $C$ are as shown in the figure. The logic gate is:

If $\alpha + \beta = \frac{\pi}{2}$ and $\beta + \gamma = \alpha$,then $\tan \alpha$ equals

If $m_1$ and $m_2$ are the roots of the equation $x^2+(\sqrt{3}+2) x+(\sqrt{3}-1)=0$,then the area of the triangle formed by the lines $y=m_1 x, y=m_2 x$ and $y=c$ is: