A boat is moving due east in a region where the earth's magnetic field is $3.6 \times 10^{-5} \mathrm{~N} / \mathrm{Am}$ due north and horizontal. The boat carries a vertical conducting rod 2 m long. If the speed of the boat is $2.00 \mathrm{~m} / \mathrm{s}$, the magnitude of the induced e.m.f. in the rod is

In the following electrical network, the value of I is

An inclined plane makes an angle $30^{\circ}$ with horizontal. A solid sphere rolls down from the top of the inclined plane from rest without slipping has a linear acceleration along the plane equal to (where $g$ is acceleration due to gravity) (given $\sin 30^{\circ}=0.5$)

An ink mark is made on a piece of paper. A glass slab of thickness ' $t$ ' is placed on it. The ink mark appears to be raised up through a distance ' $x$ ' when viewed at nearly normal incidence. If the refractive index of material of glass slab is ' $\mu$ ' then thickness of glass slab ' $t$ ' is given by