GATE 2017-2018 :: GATE Mathematics
- The order of the smallest possible non trivial group containing elements x and y such that x7 = y2 = e and yx = x4y is
-
The flux of the vector field
flowing out through the surface of the ellipsoid
is -
The integral surface satisfying the partial differential equation
and passing through the straight line x = 1, y = z is -
The diffusion equation
admits the solution -
Let f(x) and xf(x) be the particular solutions of a differential equation y'' + R(x)y' + S(x)y = 0.Then the solution of the differential equation y'' + R(x)y' + S(x)y = f(x) is
-
Let the Legendre equation (1 - x2)y'' - 2xy' + n(n + 1)y = 0 have nth degree polynomial solution yn(x) such that yn(1) = 3. If
,then n is - The maximum value of the function f (x, y, z) = xyz subject to the constraint xy + yz + zx - a = 0,a > 0 is
-
The functional
, y(0) = -4/3 , y(1) = -4e/3 possesses : -
For the matrix
,which of the following statements are correct?P : M is skew-Hermitian and iM is HermitianQ : M is Hermitian and iM is skew HermitianR : eigenvalues of M are realS : eigenvalues of iM are real
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