If the power factor changes from 0.5 to 0.25 because impedance changes from $Z_1$ to $Z_2$ then $\mathrm{Z}_1=\mathrm{xZ}_2$. The value of x is (Resistance remains constant)

The motion of the particle is given by the equation $\mathrm{x}=\mathrm{A} \sin \omega \mathrm{t}+\mathrm{B} \cos \omega \mathrm{t}$.

The motion of the particle is

The relation between magnetic moment $(\mathrm{M})$ of a current carrying circular coil and length (L) of the wire used is

In Young's double slit experiment, the intensity of light at a point on the screen where the path difference is $\lambda$ is ' $I$ '. The intensity at a point where the path difference is $\lambda / 6$ is $\left[\cos \frac{\pi}{6}=\frac{\sqrt{3}}{2}\right] [\lambda=$ wavelength of light $][\cos \pi=-1]$