A square coil of $$10$$ turns and $$10$$ $$cm$$ side is moved through a steady magnetic field of $$1$$ $$Wb/{m^2}$$ at a constant velocity of $$2$$ $$m/sec$$ with its plane perpendicular to the field as shown in Fig. Plot the variation of induced $$e.m.f$$ as the coil moves along the field.

Express the given matrix $$A = \left[ {\matrix{ 2 & 1 & 5 \cr 4 & 8 & {13} \cr 6 & {27} & {31} \cr } } \right]$$
as a product of triangular matrices $$L$$ and $$U$$ where the diagonal elements of the lower triangular matrices $$L$$ are unity and $$U$$ is an upper triangular matrix.

$$\mathop {Lim}\limits_{\theta \to 0} \,{{\sin \,m\,\theta } \over \theta },$$ where $$m$$ is an integer, is one of the following :

If a diode is connected in anti - parallel with a thyristor, then