1
GATE EE 2007
MCQ (Single Correct Answer)
+2
-0.6
An inductor designed with $$400$$ turns coil wound on an iron core of $$16\,\,c{m^2}$$ cross sectional area and with a cut of an air gap length of $$1$$ $$mm$$. The coil is connected to a $$230$$ $$V,$$ $$50$$ $$Hz$$ ac supply. Neglect coil resistance, core loss, iron reluctance and leakage inductance. $$\left( {{\mu _0} = 4\pi \times {{10}^{ - 7}}\,H/m} \right)$$

The average force on the core to reduce the air gap will be

A
$$832.29$$ $$N$$
B
$$1666.22$$ $$N$$
C
$$3332.47$$ $$N$$
D
$$6664.84$$ $$N$$
2
GATE EE 2007
MCQ (Single Correct Answer)
+2
-0.6
$${q_1},\,{q_2},{q_3},.......{q_m}$$ are $$n$$-dimensional vectors with $$m < n.$$ This set of vectors is linearly dependent. $$Q$$ is the matrix with $${q_1},\,{q_2},{q_3},.......{q_m}$$ as the columns. The rank of $$Q$$ is
A
less than $$m$$
B
$$m$$
C
between $$m$$ and $$n$$
D
$$n$$
3
GATE EE 2007
MCQ (Single Correct Answer)
+1
-0.3
$$X = {\left[ {\matrix{ {{x_1}} & {{x_2}} & {.......\,{x_n}} \cr } } \right]^T}$$ is an $$n$$-tuple non-
zero vector. The $$n\,\, \times \,\,n$$ matrix $$V = X{X^T}$$
A
has rank zero
B
has rank $$1$$
C
is orthogonal
D
has rank $$n$$
4
GATE EE 2007
MCQ (Single Correct Answer)
+2
-0.6
If $$A = \left[ {\matrix{ { - 3} & 2 \cr { - 1} & 0 \cr } } \right]\,$$ then $${A^9}$$ equals
A
$$511\,\,A + 510\,\,I$$
B
$$309\,\,A + 104\,\,I$$
C
$$154\,\,A + 155\,\,I$$
D
$${e^{9A}}$$
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