Let $z = a - \frac{i}{2}$,where $a \in R$. Then $|i + z|^2 - |i - z|^2$ is equal to

If two glass plates have water between them and are separated by a very small distance (see figure),it is very difficult to pull them apart. This is because the water in between forms a cylindrical surface on the side that gives rise to a lower pressure in the water in comparison to the atmosphere. If the radius of the cylindrical surface is $R$ and the surface tension of water is $T$,then the pressure in the water between the plates is lower by:

$A$ gas mixture consists of $2$ moles of oxygen and $4$ moles of argon at temperature $T$. Neglecting all vibrational modes,the total internal energy of the system is: (in $RT$)

The figure shows three similar lamps $L_1, L_2$,and $L_3$ connected across a power supply. If the lamp $L_3$ fuses,how will the light emitted by $L_1$ and $L_2$ change?

$A$ railway line is taken round a circular arc of radius $1000 \ m$,and is banked by raising the outer rail $h \ m$ above the inner rail. If the lateral force on the inner rail when a train travels round the curve at $10 \ ms^{-1}$ is equal to the lateral force on the outer rail when the train's speed is $20 \ ms^{-1}$,the value of $4g \tan \theta$ is equal to: (The distance between the rails is $1.5 \ m$).

Platinum crystallizes in a face-centered cubic $(FCC)$ crystal with a unit cell length $a$. The distance between nearest neighbors is