Consider an air filled rectangular waveguide with a cross-section of $$5\,\,cm\,\, \times \,\,3\,cm$$. For this waveguide, the cut-off frequency (in MHz) of $$T{E_{21}}\,$$ mode is __________________

Given the vector $$$\mathrm A=\left(\cos\;\mathrm x\right)\left(\sin\;\mathrm y\right)\;{\widehat{\mathrm a}}_\mathrm x\;+\;\left(\sin\;\mathrm x\right)\left(\cos\;\mathrm y\right){\widehat{\mathrm a}}_\mathrm y$$$ where $${\widehat{\mathrm a}}_\mathrm x$$ , $${\widehat{\mathrm a}}_\mathrm y$$ denote unit vectors along x, y directions, respectively. The magnitude of curl of A is ________

A thin P-type silicon sample is uniformly illuminated with light which generates excess carriers. The recombination rate is directly proportional to

At T = 300 K, the hole mobility of a semiconductor $$\mu_p\;=500\;cm^2/V-s$$ and $$\frac{kT}q\;=\;26\;mV$$.The hole diffusion constant D_p in cm²/s is__________.