Fourier transform of which of the following functions does not exist?
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Mathematical Physics
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The value of where is the position vector and S is a closed surface enclosing the origin, is
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Can the following scalar and vector potentials describe an electromagnetic field?
where, ω is a constant.
where, ω is a constant.
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The value of where C is a unit circle (anticlockwise) centred at the origin in the complex Z-plane is
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If a function f(z) = u (x, y) + iv (x, y) of the complex variable z = x + iy, where x, y, u and v are real, is analytic in a domain D of z, then which of the following is true?
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The eigen values of a matrix are i, -2i and 3i. The matrix is
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Consider the four statements given below about the function f(x) = x4 - x2 in the range Which one of the following statement is correct?
P. The plot of f(x) versus x has two maxima and two minima.
Q. The plot of f(x) versus x cuts the x axis at four points.
R. The plot of f(x) versus x has three extrema.
S. No part of the plot f(x) versus x lies in the fourth quadrant.
Pick the right combination of correct choices from those given below.
P. The plot of f(x) versus x has two maxima and two minima.
Q. The plot of f(x) versus x cuts the x axis at four points.
R. The plot of f(x) versus x has three extrema.
S. No part of the plot f(x) versus x lies in the fourth quadrant.
Pick the right combination of correct choices from those given below.
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If is the Laplace transform of f(t) the transform of f(at), where a is a constant is
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The determinant of a 3 × 3 real symmetric matrix is 36. If two of its eigen values are 2 and 3 then the third eigen value is
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The curl of a vector field is Identify the appropriate vector field from the choices given below.
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Consider a cylinder of height h and radius a, closed at both ends, centred at the origin. Let be the position vector and a unit vector normal to the surface. The surface integral over the closed surface-of the cylinder is
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The kth Fourier component of f(x) = δ(x) is
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The value of contour integral, for a circle C of radius r with centre at the origin is
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The solution of the differential equation for subject to the initial conditions y(0) = 0 and is
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If S is the closed surface enclosing a volume V and is the unit normal vector to the surface and is the positive vector, then the value of the following integral is
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The value of the integral where C is a circle (anticlockwise) with |z| = 4, is
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A periodic function f(x) = x for -π < x < +π has the Fourier series representation
Using this, one finds the sum to be
Using this, one finds the sum to be
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An unitary matrix \left[ {\begin{array}{*{20}{c}}
{a{e^{i\alpha }}}&b \\
{c{e^{i\beta }}}&d
\end{array}} \right] is given, were a, b, c, d, α and β are real. The inverse of the matrix is
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If f\left( x \right) = \left\{ {\begin{array}{*{20}{c}}
{0,}&{{\text{for }} < 3} \\
{x - 3,}&{{\text{for }} \geqslant 3}
\end{array}} \right. then, the Laplace transform of f(x) is
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Consider the set of vectors in three-dimensional real vector space
R3, S = {(1, 1, 1), (1, -1, 1), (1, 1, -1)}. Which one of the following statement is true?
R3, S = {(1, 1, 1), (1, -1, 1), (1, 1, -1)}. Which one of the following statement is true?
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