An infinite number of charges, each equal to $$'q'$$ are placed along the $$x=1,x=2, x=4, x=8, x=16$$ and so on, Find the potential and electric field at point $$x=0,$$ due to these system of charges.

The Laplace transform of $$\,\left( {{t^2} - 2t} \right)\,u\left( {t - 1} \right)$$ is ______________.

The value of $$\,\,\,\int\limits_1^2 {{1 \over x}\,\,\,dx\,\,\,\,} $$ computed using simpson's rule with a step size of $$h=0.25$$ is

If $$A = \left[ {\matrix{ 5 & 0 & 2 \cr 0 & 3 & 0 \cr 2 & 0 & 1 \cr } } \right]$$ then $${A^{ - 1}} = $$