1
GATE EE 2010
+2
-0.6
A $$50$$ $$Hz$$ synchronous generator is initially connected to a long lossless transmission line which is open circuited at the receiving end. With the field voltage held constant, the generator is disconnected from the transmission line. Which of the following may be said about the steady state terminal voltage and field current of the generator?
A
The magnitude of terminal voltages decreases, and the field current does not change.
B
The magnitude of terminal voltage increases, and the field current dose not change.
C
The magnitude of terminal voltages decreases, and the field current increases.
D
The magnitude of terminal voltage does not change, and the field current decreases.
2
GATE EE 2010
+1
-0.3
Divergence of the three-dimentional radial vector field $$\overrightarrow F$$ is
A
3
B
1/r
C
$$\widehat i+\widehat j+\widehat k$$
D
$$3\left(\widehat i+\widehat j+\widehat k\right)$$
3
GATE EE 2010
+2
-0.6
For the set of equations $${x_1} + 2{x_2} + {x_3} + 4{x_4} = 2,$$$$$3{x_1} + 6{x_2} + 3{x_3} + 12{x_4} = 6.$$$
The following statement is true
A
only the trivial solution $${x_1} = {x_2} = {x_3} = {x_4} = 0$$ exist
B
there are no solutions
C
a unique non-trivial solution exist
D
multiple non-trivial solution exist
4
GATE EE 2010
+1
-0.3
An eigen vector of $$p = \left[ {\matrix{ 1 & 1 & 0 \cr 0 & 2 & 2 \cr 0 & 0 & 3 \cr } } \right]$$ is
A
$${\left[ {\matrix{ { - 1} & 1 & 1 \cr } } \right]^T}$$
B
$${\left[ {\matrix{ { 1} & 2 & 1 \cr } } \right]^T}$$
C
$${\left[ {\matrix{ { 1} & - 1 & 2 \cr } } \right]^T}$$
D
$${\left[ {\matrix{ { 2} & 1 & -1 \cr } } \right]^T}$$
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