A short solenoid of length $4 \mathrm{c}\mathrm{m}$, radius $2 \mathrm{c}\mathrm{m}$ and $100$ turns is placed inside and on the axis of a long solenoid of length $80 \mathrm{c}\mathrm{m}$ and $1500$ turns. A current of $3$ A flows through the short solenoid. The mutual inductance of two solenoids is

A uniform and constant magnetic field $B$ coming out of the plane of the paper exists in a rectangular region as shown in figure. $A$conducting rod $PQ$ is rotated about its mid-point $O$ with a uniform angular speed $\omega$ in the plane of the paper. The emf $E_{PQ}$ induced between $P$ and $Q$ is best represented by the graph