The logic gate for which the output goes 'HIGH' or ' 1 ' only when an odd number of 'HIGH' or ' 1 ' are at its input, is

A long straight wire of radius ' $r$ ' carries a steady current ' $I$ '. The current is uniformly distributed over its cross-section. The ratio $\left(\frac{B}{B_1}\right)$ of the magnetic field ' B ' and ' $\mathrm{B}_1$ ' at radial distances ' $\frac{r}{2}$ ' and ' $3 r$ respectively, from the axis of the wire is

A sound source is moving towards a stationary observer with $\left(\frac{1}{10}\right)^{\text {th }}$ the speed of sound, The ratio of apparent to real frequency is

The velocity of small spherical ball of mass ' $m$ ' and density ' $\mathrm{d}_1$ ', when dropped in a container filled with glycerine becomes constant after some time. The viscous force acting on the ball if density of glycerine is ' $\mathrm{d}_2$ ' is