1
GATE EE 2011
+2
-0.6
A capacitor is made with a polymeric dielectric having an $$\varepsilon_0$$ of 2.26 and a dielectric breakdown strength of 50 kV/cm. The permittivity of free space is 8.85 pF/m. If the rectangular plates of the capacitor have a width of 20 cm and a length of 40 cm, then the maximum electric charge in the capacitor is
A
2 µC
B
4 µC
C
8 µC
D
10 µC
2
GATE EE 2011
+2
-0.6
The two vectors $$\left[ {\matrix{ 1 & 1 & 1 \cr } } \right]$$ and $$\left[ {\matrix{ 1 & a & {{a^2}} \cr } } \right]$$ where $$a = - {1 \over 2} + j{{\sqrt 3 } \over 2}$$ and $$j = \sqrt { - 1}$$ are
A
orthonormal
B
orthogonal
C
parallel
D
collinear
3
GATE EE 2011
+2
-0.6
The matrix $$\left[ A \right] = \left[ {\matrix{ 2 & 1 \cr 4 & { - 1} \cr } } \right]$$ is decomposed into a product of lower triangular matrix $$\left[ L \right]$$ and an upper triangular $$\left[ U \right].$$ The properly decomposed $$\left[ L \right]$$ and $$\left[ U \right]$$ matrices respectively are
A
$$\left[ {\matrix{ 1 & 0 \cr 4 & { - 1} \cr } } \right]$$ and $$\left[ {\matrix{ 1 & 1 \cr 0 & { - 2} \cr } } \right]$$
B
$$\left[ {\matrix{ 1 & 0 \cr 2 & 1 \cr } } \right]$$ and $$\left[ {\matrix{ 2 & 1 \cr 0 & { - 3} \cr } } \right]$$
C
$$\left[ {\matrix{ 1 & 0 \cr 4 & 1 \cr } } \right]\,$$ and $$\left[ {\matrix{ 2 & 1 \cr 0 & { - 1} \cr } } \right]$$
D
$$\left[ {\matrix{ 2 & 0 \cr 4 & { - 3} \cr } } \right]$$ and $$\left[ {\matrix{ 1 & {0.5} \cr 0 & 1 \cr } } \right]$$
4
GATE EE 2011
+1
-0.3
Roots of the algebraic equation $${x^3} + {x^2} + x + 1 = 0$$ are
A
$$(1,j,-j)$$
B
$$(1, -1, 1)$$
C
$$(0,0,0)$$
D
$$(-1,j.-j)$$
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