1
GATE EE 2005
MCQ (Single Correct Answer)
+2
-0.6
A $$1000$$ $$kVA,$$ $$6.6$$ $$kV,$$ $$3$$-phase star connected cylindrical pole synchronous generator has a synchronous reactance of $$20\Omega .$$ Neglect the armature resistance and consider operation at full load and unity power factor.

The power angle is close to

A
$$13.9$$ degrees
B
$$18.3$$ degrees
C
$$24.6$$ degrees
D
$$33.0$$ degrees
2
GATE EE 2005
MCQ (Single Correct Answer)
+1
-0.3
In the matrix equation $$PX=Q$$ which of the following is a necessary condition for the existence of atleast one solution for the unknown vector $$X.$$
A
Augmented matrix $$\left[ {P|Q} \right]$$ must have the same rank as matrix $$P.$$
B
vector $$Q$$ must have only non-zero elements.
C
matrix $$P$$ must be singular
D
matrix $$P$$ must be square
3
GATE EE 2005
MCQ (Single Correct Answer)
+2
-0.6
For the matrix $$P = \left[ {\matrix{ 3 & { - 2} & 2 \cr 0 & { - 2} & 1 \cr 0 & 0 & 1 \cr } } \right],$$ one of the eigen values is $$-2.$$ Which of the following is an eigen vector?
A
$$\left( {\matrix{ 3 \cr { - 2} \cr 1 \cr } } \right)$$
B
$$\left[ {\matrix{ { - 3} \cr 2 \cr { - 1} \cr } } \right]$$
C
$$\left[ {\matrix{ 1 \cr { - 2} \cr 3 \cr } } \right]$$
D
$$\left[ {\matrix{ 2 \cr 5 \cr 0 \cr } } \right]$$
4
GATE EE 2005
MCQ (Single Correct Answer)
+2
-0.6
If $$R = \left[ {\matrix{ 1 & 0 & { - 1} \cr 2 & 1 & { - 1} \cr 2 & 3 & 2 \cr } } \right]$$ then the top row of $${R^{ - 1}}$$ is
A
$$\left[ {\matrix{ 5 & 6 & 4 \cr } } \right]$$
B
$$\left[ {\matrix{ 5 & -3 & 1 \cr } } \right]$$
C
$$\left[ {\matrix{ 2 & 0 & -1 \cr } } \right]$$
D
$$\left[ {\matrix{ 2 & -1 & 0 \cr } } \right]$$
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