A spherical mirror is obtained as shown in the figure from a hollow glass sphere. If an object is positioned in front of the mirror, what will be the nature and magnification of the image of the object?
(Figure drawn as schematic and not to scale)

A small block starts slipping down from a point B on an inclined plane AB, which is making an angle $$\theta $$ with the horizontal section BC is smooth and the remaining section CA is rough with a coefficient of friction $$\mu $$. It is found that the block comes to rest as it reaches the bottom (point A) of the inclined plane. If BC = 2AC, the coefficient of friction is given by $$\mu $$ = ktan $$\theta $$ . The value of k is _________.

An engine takes in 5 moles of air at 20^oC and 1 atm, and compresses it adiabatically to 1/10^th of the original volume. Assuming air to be a diatomic ideal gas made up of rigid molecules, the change in its internal energy during this process comes out to be X kJ. The value of X to the nearest integer is________.

A beam of protons with speed 4 × 10⁵ ms^–1 enters a uniform magnetic field of 0.3 T at an angle of 60° to the magnetic field. The pitch of the resulting helical path of protons is close to :
(Mass of the proton = 1.67 $$ \times $$ 10^–27 kg, charge
of the proton = 1.69 $$ \times $$ 10^–19 C)