GATE EC 2014 Question Paper (15-Feb-2014) (Shift 1)

Consider the Boolean function, F(w,x,y,z) = wy +xy + w̅x̅y + xz + x̅y̅z̅. Which one of the following is the complete set of essential prime implicants?

The digital logic shown in the figure satisfies the given state diagram when Q1 is connected to input A of the XOR gate.



Suppose the XOR gate is replaced by an XNOR gate. Which one of the following options preserves the state diagram?

Let $x\left[n\right]={\left(-\frac{1}{9}\right)}^{n}u\left[n\right]-{\left(-\frac{1}{3}\right)}^{n}u\left[-n-1\right]$. The Region of convergence (ROC) of the z-transform

Consider a discrete-time periodic signal $\mathrm{x}\left[\mathrm{n}\right]=\sin \left(\frac{\pi \mathrm{n}}{5}\right)$. Let aₖ be the complex Fourier Series Coefficient (FSC) of x[n]. aₖis non-zero when k = Bm ± 1 , where 'm' is any integer. The value of B is_______.

A LTI system described by the following differential equation, where x(t) is the input to system and y(t) is output of system

y${}^{{}^{\prime }}$ (t) + 3y(t) = x(t)

When y (0) = 2, the output y (t) for an unit step input is