1
GATE EE 2007
MCQ (Single Correct Answer)
+2
-0.6
A solid sphere made of insulating material has a radius $$R$$ and has a total charge $$Q$$ distributed uniformly in its volume. What is the magnitude of the electric field intensity, $$E,$$ at distribution $$r\left( {0 < r < R} \right)$$ inside the sphere?
A
$${1 \over {4\pi {\varepsilon _0}}}{{{Q_r}} \over {{R^3}}}$$
B
$${3 \over {4\pi {\varepsilon _0}}}{{Qr} \over {{R^3}}}$$
C
$${Q \over {4\pi {\varepsilon _0}{r^2}}}$$
D
$${1 \over {4\pi {\varepsilon _0}}}{{QR} \over {{r^3}}}$$
2
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 current in the inductor is

A
$$18.08$$ $$A$$
B
$$9.04$$ $$A$$
C
$$4.56$$ $$A$$
D
$$2.28$$ $$A$$
3
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
$$6664.84$$ $$N$$
4
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
$$n$$
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