Two concentric circular coils having radii ' $r_1{ }^{\prime}$ and ' $r_2$ ' $\left(r_2 \ll r_1\right)$ are placed co-axially with centres coinciding. The mutual inductance of the arrangement is ( $\mu_0=$ permeability of free space) (Both coils have single turn)

An ordinary body cools from ' $4 \theta^{\prime}$ ' to ' $3 \theta^{\prime}$ ' in ' t ' minutes. The temperature of that body after next 't' minutes is (Assume Newton's law of cooling and room temperature is $\theta$)

Stationary wave is produced along the stretched string of length 80 cm . The resonant frequencies of string are $90 \mathrm{~Hz}, 150 \mathrm{~Hz}$ and 210 Hz . The speed of transverse wave in the string is

For the series $L C R$ circuit, $R=\frac{X_L}{2}=2 \mathrm{X}_{\mathrm{c}}$. The impedance of the circuit and the phase difference between V and I will be