If $R = \{ (x, y) | x, y \in Z, x^2 + y^2 \le 4 \}$ is a relation in $Z$,then the domain of $R$ is

In prokaryotes,chromatophores are

$A$ particle of mass $1 \times 10^{-26} \ kg$ and charge $1.6 \times 10^{-19} \ C$ travelling with a velocity $1.28 \times 10^6 \ ms^{-1}$ along the positive $X$-axis enters a region in which a uniform electric field $E$ and a uniform magnetic field of induction $B$ are present. If $E = -102.4 \times 10^3 \ \hat{k} \ NC^{-1}$ and $B = 8 \times 10^{-2} \ \hat{j} \ Wbm^{-2}$,the direction of motion of the particle is:

$A$ body is executing simple harmonic motion. At a displacement $x$ its potential energy is $E_1$ and at a displacement $y$ its potential energy is $E_2$. The potential energy $(E)$ at displacement $(x+y)$ is

In the standing wave shown,particles at the positions $A$ and $B$ have a phase difference of

$A$ parallel plate capacitor with a dielectric slab of dielectric constant $K$ between its plates has a capacitance $C$ and is charged to a potential $V$. The dielectric slab is slowly removed from between the plates and then reinserted. The net work done by the system is: