1
GATE EE 2022
+1
-0.33

If the magnetic field intensity ($$\overrightarrow H$$) in a conducting region is given by the expression, $$\overrightarrow H = {x^2}\widehat i + {x^2}{y^2}\widehat j + {x^2}{y^2}{z^2}\widehat k$$ A/m. The magnitude of the current density, in A/m2, at x = 1 m, y = 2 m and z = 1 m is

A
8
B
12
C
16
D
20
2
GATE EE 2022
+1
-0.33

As shown in the figure below, to concentric conducting spherical shells, centred at r = 0 and having radii r = c and r = d are maintained at potentials such that the potential V(r) at r = c is V1 and V(r) at r = d is V2. Assume that V(r) depends only on r, where r is the radial distance. The expression for V(r) in the region between r = c and r = d is

A
$$V(r) = {{cd({V_2} - {V_1})} \over {(d - c)r}} - {{{V_1}c + {V_2}d - 2{V_1}d} \over {d - c}}$$
B
$$V(r) = {{cd({V_1} - {V_2})} \over {(d - c)r}} + {{{V_2}d - {V_1}c} \over {d - c}}$$
C
$$V(r) = {{cd({V_1} - {V_2})} \over {(d - c)r}} - {{{V_1}c - {V_2}c} \over {d - c}}$$
D
$$V(r) = {{cd({V_2} - {V_1})} \over {(d - c)r}} - {{{V_2}c - {V_1}c} \over {d - c}}$$
3
GATE EE 2022
+1
-0.33

Consider a 3 $$\times$$ 3 matrix A whose (i, j)-th element, ai,j = (i $$-$$ j)3. Then the matrix A will be

A
symmetric
B
skew-symmetric
C
unitary
D
null
4
GATE EE 2022
+1
-0.33

e4 denotes the exponential of a square matrix A. Suppose $$\lambda$$ is an eigen value and v is the corresponding eigen-vector of matrix A.

Consider the following two statements:

Statement 1 : e$$\lambda$$ is an eigen value of eA.

Statement 2 : v is an eigen-vector of eA.

Which one of the following options is correct?

A
Statement 1 is true and statement 2 is false.
B
Statement 1 is false and statement 2 is true.
C
Both the statements are correct.
D
Both the statements are false.
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