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

In the following active filter circuit with ideal op-amps, $R$ is $1\text{ k}\Omega$, $C$ is $1\mu \text{F}$, and $V_{\text{in}}$ has an amplitude of $1\text{ V}$ at $1000\text{ rad/s}$.

The amplitude of $V_{\text{out}}$ is __________ V.

The initial state of $Q_3{Q}_2{Q}_1{Q}_0$ in the digital circuit shown below is $1011$.

The new value of $Q_3{Q}_2{Q}_1{Q}_0$ after two rising edges of the clock (CLK) will be _____.

A closed Lissajous pattern observed on an oscilloscope in the $\mathbf{X}-\mathbf{Y}$ mode has three horizontal tangencies and two vertical tangencies in steady state. If the signal frequency on channel-$\mathbf{X}$ is $600\text{ Hz}$, then the signal-frequency on channel-$\mathbf{Y}$ is ___________ Hz.

If the definition of SI unit ‘X’ is required to define SI unit ‘Y’, the dependency is indicated as X $\to$ Y. A valid order of dependencies, as per present convention, is ___________.

A parallel plate capacitive displacement sensor has a plate area of $2{\text{ cm}}^2$. The air gap between the plates is decreased by $0.1\text{ mm}$ from an initial value of $0.5\text{ mm}$. The percentage change in the capacitance value is ______ %.

(Assume permittivity as ${ϵ}_0=8.854\times 10^{-12}\text{ F/m}$)