The figure above shows coil $$1$$ and $$2,$$ with dot markings as shown, having $$4000$$ and $$6000$$ turns respectively. Both the coils have a rated current of $$25$$ $$A.$$ Coil $$1$$ is excited with single phase, $$400$$ $$V,$$ $$50$$ $$Hz$$ supply.

In the auto-transformer obtained in Question $$30,$$ the current in each coil is

The figure above shows coil $$1$$ and $$2,$$ with dot markings as shown, having $$4000$$ and $$6000$$ turns respectively. Both the coils have a rated current of $$25$$ $$A.$$ Coil $$1$$ is excited with single phase, $$400$$ $$V,$$ $$50$$ $$Hz$$ supply.

The coils are to be connected to obtain a single-phase, $${{400} \over {1000}}\,\,V,$$ auto-transformer to drive a load of $$10$$ $$kVA.$$ Which of the options given should be exercised to realize the required auto-transformer?

$$$F\left(x,y\right)=\left(x^2\;+\;xy\right)\;{\widehat a}_x\;+\;\left(y^2\;+\;xy\right)\;{\widehat a}_y$$$. Its line integral over the straight line from (x, y)=(0,2) to (2,0) evaluates to

The trace and determinant of a $$2 \times 2$$ matrix are shown to be $$-2$$ and $$-35$$ respectively. Its eigen values are