For the function at the point (1, 2, -1), find its rate of change with distance in the direction
Evaluate the line integral (exy + cos x sin y) dx + (ex + sin x cos y)dy, around the curve 'C'
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If a unitary matrix U is written as A + iB, where A and B are Hermitian matrix with non degenerate eigenval ues. then
If (A)nxn is a square matrix, and elements of matrix A(aij) are such that
then value of det (eA) is equal to
If solution y(x), of the differential equation subjected to the boundary conditions y(0) = 2, y'(0) = 1 has the form y(x) = Ae-x + Bex + Ce2x, then the value of A + B - C is
(upto two decimal places)
The range of values ofz, for which the following complex power series converges, is Izl < A, then A is .................. (answer should be an integer)
If the matrix can be diagonalised by a transformation of the form S* AS = A', where S has the normalized eigenvectors of A as its columns, then A' is
If is the fourier transformation of then the fourier trans form of f ' (t) is
If a complex function f (z) lias a pole of order m at z = z0. then f'(z) has a pole of order
If the fourier series for Isin θ| in the range -π < θ < π is given by then the value of A is .........
If the fourier expansion of then the value of a2 if
If z = xy, where y = tan-1 t and x = sin t, then the value of dz/dt is equal to
If y (x) is the solution of the differential equation with y(1) = -1, then
then the value of integral where ‘S’ is the surface given by z = 12, x2 - y2 < 25 (taken anticlockwise), is
then which of the following statements is true about A and B
The value of the integral where C is closecl contour defined by the equation 2 |z - 1| - 3 = 0, traversed in the clockwise direction, is _______________________ (answer should be an integers)
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