The difference in length between two rods A and B is 60 cm at all temperatures. If $\alpha_{\mathrm{A}}=18 \times 10^{-6} /{ }^{\circ} \mathrm{C}$ and $\alpha_{\mathrm{B}}=27 \times 10^{-6} /{ }^{\circ} \mathrm{C}$, then the length of $\operatorname{rod} \mathrm{A}$ and $\operatorname{rod} \mathrm{B}$ at $0^{\circ} \mathrm{C}$ is respectively

An infinitely long straight conductor carrying current ' $I$ ' is bent into a shape as shown in figure. The radius of the circular loop is ' $r$ '. The magnetic induction at the centre of the loop at point ' O ' is

( $\mu_0=$ permeability of free space)

Let $R_1, R_2$ and $R_3$ be the radii of three mercury drops. A big mercury drop is formed from them under isothermal conditions. The radius of the resultant drop is

Fundamental frequency of sonometer wire is ' $n$ '. If the tension and length are increased 3 times and diameter is increased twice, the new frequency will be