A charge particle is moving in a uniform magnetic field $$(2 \hat{i}+3 \hat{j}) \,\mathrm{T}$$. If it has an acceleration of $$(\alpha \hat{i}-4 \hat{j})\, \mathrm{m} / \mathrm{s}^{2}$$, then the value of $$\alpha$$ will be :

$$\mathrm{B}_{X}$$ and $$\mathrm{B}_{\mathrm{Y}}$$ are the magnetic fields at the centre of two coils $$\mathrm{X}$$ and $$\mathrm{Y}$$ respectively each carrying equal current. If coil $$X$$ has 200 turns and $$20 \mathrm{~cm}$$ radius and coil $$Y$$ has 400 turns and $$20 \mathrm{~cm}$$ radius, the ratio of $$B_{X}$$ and $$B_{Y}$$ is :

An electron with energy 0.1 keV moves at right angle to the earth's magnetic field of 1 $$\times$$ 10^$$-$$4 Wbm^$$-$$2. The frequency of revolution of the electron will be

(Take mass of electron = 9.0 $$\times$$ 10^$$-$$31 kg)

Two charged particles, having same kinetic energy, are allowed to pass through a uniform magnetic field perpendicular to the direction of motion. If the ratio of radii of their circular paths is $$6: 5$$ and their respective masses ratio is $$9: 4$$. Then, the ratio of their charges will be :