Consider two BJT's biased at the same collector current with area A₁ = 0.2 μm × 0.2 μm and A₂ = 300 μm × 300 μm. Assuming that all other device parameters are identical, kT/q = 26 mV, the intrinsic carrier concentration is 1 × 10¹⁰ cm^-3, and q = 1.6 × 10^-19 C, the difference between the base-emitter voltages (in mV) of the two BJT's (i.e., V_BE1 – V_BE2) is___________.

For a right angled triangle, if the sum of the lengths of the hypotenuse and a side is kept constant, in order to have maximum area of the triangle, the angle between the hypotenuse and the side is

The series $$\sum\limits_{n = 0}^\infty {{1 \over {n!}}\,} $$ converges to

The magnitude of the gradient for the function $$f\left( {x,y,z} \right) = {x^2} + 3{y^2} + {z^3}\,\,$$ at the point $$(1,1,1)$$ is _________.