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Gate 2019: Engineering Mathematics Quiz 6
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Question 1
Consider the time-varying vector
in Cartesian coordinates,
Where
is a constant. When the vector magnitude III is at its minimum value, the angle 0 that I make with the x axis (in degrees, such that
) is
in Cartesian coordinates, Where
is a constant. When the vector magnitude III is at its minimum value, the angle 0 that I make with the x axis (in degrees, such that) isQuestion 2
The magnitude of the gradient for the function 
at the point (1,1,1) is
at the point (1,1,1) is Question 3
If the vector function
is irrotational, then the values of the constants k1, k2 and k3 respectively, are
is irrotational, then the values of the constants k1, k2 and k3 respectively, are Question 4
A vector field D = 
exists inside a cylindrical region enclosed by the surfaces r = 1, z = 0 and z = 5. Let S be the surface bounding this cylindrical region. The surface integral of this field on S 
is _____.
exists inside a cylindrical region enclosed by the surfaces r = 1, z = 0 and z = 5. Let S be the surface bounding this cylindrical region. The surface integral of this field on S is _____.Question 5
The residues of a function f(z) 
are
are Question 6
Let U and V be two independent zero mean Gaussian random variables of variances 
and 
respectively. The probability 
is
and respectively. The probability is - 445 attempts
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Feb 23ESE & GATE EC
