A dipole antenna has a sin$$\theta $$ radiation pattern where the angle $$\theta $$ is measured from the axis of the dipole. The dipole is vertically located above an ideal ground plane (Fig.). What should be the height of the dipole H in terms of wave length so as to get a null in the radiation pattern at an angle of 45⁰ from the ground plane? Find the direction of maximum radiation also.

The units of $$\frac q{KT}$$ are

The curve given by the equation $${x^2} + {y^2} = 3axy$$ is

The laplace transform of $${e^{\alpha t}}\,\cos \,\alpha \,t$$ is equal to ____________.