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Instrumentation Engineering (IN) 2011
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The matrix M =
has eigenvalues -3, -3, 5. An eigenvector corresponding to the eigenvalue 5 is [1 2 -1]T. One of the eigenvectors of the matrix M3 is
The contour integral ∮ ex/z dz with C as the counter-clockwise unit circle in the z-plane is equal to
Consider the signal x(t) = e−t, t ≥ 0; 0, t < 0. Let X(ω) denote the Fourier transform of this signal. The integral 1/2π ∫ X(ω) dω is
The continuous-time signal x(t) = sin ω0t is a periodic signal. However, for its discrete-time counterpart x[n] = sin ω0n to be periodic, the necessary condition is
Consider a periodic signal x(t) as shown below
It has a Fourier series representation x(t) = ∑ ak ej(2π/T)kt. Which one of the following statements is TRUE?
The integral 1/√(2π) ∫ from -∞ to ∞ r2 e−r2/2 δ(1-2r) dr is equal to