GATE IN 2018 Question Paper (04-Feb-2018) (Shift 2)

In the figure, an RLC load is supplied by a 230 V, 50 Hz single phase source. The magnitude of the reactive power (in VAr) supplied by the source is ________.

In the given circuit, the mesh currents I₁, I₂ and I₃ are

The Fourier transform of a signal x(t), denoted by X(jω), is shown in the figure.



Let y(t) = x(t) + e${}^{jt}$ x(t). The value of Fourier transforms of y(t) evaluated at the angular frequency ω = 0.5 rad/s is

Let y[n] = x[n] ∗ h[n], where ∗ denotes convolution and x[n] and h[n] are two discrete time sequences. Given that the z-transform of y[n] is Y(z) = 2 + 3z ⁻¹+ z ⁻², the z-transform of p[n] = x[n] ∗ h[n − 2] is

For the sequence x[n] = {1, -1, 1, -1}, with n = 0, 1, 2, 3, the DFT is computed as $X\left(k\right)=\sum _{n=0}^{3}x\left[n\right]e^{-j\frac{2\pi }{4}nk}$, for k = 0, 1, 2, 3. The value of k for which X(k) is not zero is