A magnet hung at $$45^{\circ}$$ with magnetic meridian makes an angle of $$60^{\circ}$$ with the horizontal. The actual value of the angle of dip is -

A direct current of $$4 \mathrm{~A}$$ and an alternating current of peak value $$4 \mathrm{~A}$$ flow through resistance of $$3\, \Omega$$ and $$2\,\Omega$$ respectively. The ratio of heat produced in the two resistances in same interval of time will be :

A beam of light travelling along $$X$$-axis is described by the electric field $$E_{y}=900 \sin \omega(\mathrm{t}-x / c)$$. The ratio of electric force to magnetic force on a charge $$\mathrm{q}$$ moving along $$Y$$-axis with a speed of $$3 \times 10^{7} \mathrm{~ms}^{-1}$$ will be :

(Given speed of light $$=3 \times 10^{8} \mathrm{~ms}^{-1}$$)

A microscope was initially placed in air (refractive index 1). It is then immersed in oil (refractive index 2). For a light whose wavelength in air is $$\lambda$$, calculate the change of microscope's resolving power due to oil and choose the correct option.