A diode has Zener voltage of 10 V and maximum power dissipation of 0.5 W , then the minimum resistance to be used in series with this diode for safety when it is connected to a 25 V power supply is $\_\_\_\_$ $\Omega$.

A gun mounted on the ground fires bullets in all directions with same speed. The farthest distance the bullets could reach is 6.4 m . The speed of the bullets from the gun is $\_\_\_\_$ $\mathrm{m} / \mathrm{s}$.

$$ \text { (take } \mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2 \text { ) } $$

Two identical small bar magnets each of dipole moment $3 \sqrt{5} \mathrm{~J} / \mathrm{T}$ are placed at a center to center separation of 10 cm , with their axes perpendicular to each other as shown in figure. The value of magnetic field at the point P midway between the magnets is $\alpha \times 10^{-3} \mathrm{~T}$. The value of $\alpha$ is $\_\_\_\_$

$$ \left(\mu_0=4 \pi \times 10^{-7} \mathrm{Tm} / \mathrm{A}\right) $$

A circular coil of radius 2 cm and 125 turns carries a current of 1 A . The coil is placed in a uniform magnetic field of magnitude 0.4 T . The axis of the coil makes an angle of $30^{\circ}$ with the direction of the magnetic field. The torque acting on the coil is $\alpha \times 10^{-4} \mathrm{~N} . \mathrm{m}$. The value of $\alpha$ is $\_\_\_\_$ .

$$ (\pi=3.14) $$