GATE IN 2026 Question Paper (07-Feb-2026) (Shift-1)

A signal $x(t)$ is shown below.



The plot of $y(t)=1-x(4-t)$ is shown in ______.

In the table shown below, List-I are the system responses to input $x(t)$ and List-II are the system properties. The correct matching is ____.

Given two signals: $x(t)=u(t-2)-u(t-3)$, and $y(t)=e^{-4t}u(t)$.

If $z(t)=x(t)\ast y(t)$, then $Z(s)$ is _______.

A linear time invariant (LTI) system is described by:
$$\left[\begin{array}{c}{\dot{x}}_1\\ {\dot{x}}_2\end{array}\right]=\left[\begin{array}{cc}0& 1\\ -10& -7\end{array}\right]\left[\begin{array}{c}{x}_1\\ x_2\end{array}\right]+\left[\begin{array}{c}1\\ 1\end{array}\right]u$$

$$y=\left[\begin{array}{cc}1& 1\end{array}\right]\left[\begin{array}{c}{x}_1\\ x_2\end{array}\right]$$
The poles of the system are ____.

In the circuit shown below, $R$ is $1\text{ k}\Omega$ and $R_f$ is $10\text{ k}\Omega$. If $V_{\text{in}}$ is $100\text{ mV}$ and the op-amps have supply voltages of $\pm 15\text{ V}$, then $V_{\text{out}}$ is _______ V.