GATE EC 2026 Question Paper (15-Feb-2026) (Shift 1)

The response of a discrete time system $y[n]$ obeys the following relation:

$$y[n]=\frac{5}{6}y[n-1]-\frac{1}{6}y[n-2]+x[n].$$
The input to the system is $x[n]=\delta [n]-\frac{1}{3}\delta [n-1]$.
Which of the following options is TRUE for $y[n]$?

The ideal OP-AMP circuit shown in the Figure produces output voltage $V_o=x$ when the Switch, S, is open.
Which of the options represents the output voltage when S is closed?

Consider the circuit shown in the Figure with $V_i=3\text{ V}$ and $V_{CC}=12\text{ V}$.
Assume $V_{BE}=0.7\text{ V}$ and ${\beta }_{dc}=99$ for the BJT.
Which of the following options is the correct value of the current $I_o$?

A control system is shown in the Figure.
Which option represents the correct transfer function of the system?

In the circuit shown in the Figure, $A$ and $B$ are logic inputs and $Y$ is the logic output.
Which of the following logic operations is realized by the circuit?