21. Fourier transform of which of the following functions does not exist?
22. The value of \[\oint\limits_S {\frac{{\overrightarrow r \cdot d\overrightarrow S }}{{{r^3}}}} ,\] where \[\overrightarrow r \] is the position vector and S is a closed surface enclosing the origin, is
23. Can the following scalar and vector potentials describe an electromagnetic field? \[\phi \left( {\overrightarrow x ,\,t} \right) = 3xyz - 4t\]
\[\overrightarrow A \left( {\overrightarrow x ,\,t} \right) = \left( {2x - \omega t} \right)\hat i + \left( {y - 2z} \right)\hat j + \left( {z - 2{e^{i\omega t}}} \right)\hat k\]
where, ω is a constant.
\[\overrightarrow A \left( {\overrightarrow x ,\,t} \right) = \left( {2x - \omega t} \right)\hat i + \left( {y - 2z} \right)\hat j + \left( {z - 2{e^{i\omega t}}} \right)\hat k\]
where, ω is a constant.
24. The value of $$\int\limits_C {\frac{{dx}}{{\left( {{z^2} + {a^2}} \right)}},} $$ where C is a unit circle (anticlockwise) centred at the origin in the complex Z-plane is
25. 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?
26. The eigen values of a matrix are i, -2i and 3i. The matrix is
27. Consider the four statements given below about the function f(x) = x4 - x2 in the range $$ - \infty < x < + \infty .$$ 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.