A radioactive element $$X$$ convents into another stable element $$Y$$. Half-life of $$X$$ is 2 hrs. Initially only $$X$$ is present. After time $$t$$, the ratio of atoms of $$X$$ and $$Y$$ is found to be $$1: 4$$, then $$t$$ in hours is

A coil 10 turns and a resistance of $$40 \Omega$$ is connected in series with B.G. of resistance $$30 \Omega$$. The coil is placed with its plane perpendicular to the direction of a uniform magnetic field of induction $$10^{-2} \mathrm{~T}$$. If it is now turned through an angle of $$60^{\circ}$$ about on axis in its plane. Find the charge indicted in the coil. (Area of a coil $$=10^{-2} \mathrm{~m}^2$$ )

A geostationary satellite revolves around the Earth in a circular orbit of radius $$4 R$$. Here, $R$ is the radius of the Earth. Then, the time period of another satellite moving in a circular orbit of radius $$2 R$$ is:

Two long parallel wires carry equal current $$i$$ flowing in the same directions are at a distance $$4 d$$ apart. The magnetic field $$B$$ at a point $$P$$ lying on the perpendicular line joining the wires and at a distance $$x$$ from the mid-point is