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

Consider the four-variable Boolean function,

$$f(w,x,y,z)=\sum m(0,2,5,7,8,10,13,14,15)$$
with '$w$ ' as MSB and '$z$ ' as LSB.
Which of the following expressions is/are the valid form(s) of $f(w,x,y,z)$?

Consider a real, narrowband signal $x(t)=A(t)\cos [2\pi f_{c}t+\theta (t)]$ where the maximum frequency components of $A(t)$ and $\theta (t)$ are $f_M$ and $f_c(=1000f_M)$, respectively.

Which of the following statements is/are correct for $-\infty <t<\infty$?

Let $x_1(t)=\cos (2\pi nt)$ and $x_2(t)=2\sin (4\pi nt)$ represent two sinusoids for a positive integer $n$ and $-\infty <t<\infty$.

Which of the following statements about $x_1(t)$ and $x_2(t)$ is/are valid?

Consider the unity negative feedback control system shown in the Figure. The value of gain $K$ ($>0$) at which the given system will remain marginally stable is __.

(Answer in integer)

An n-channel MOSFET is connected as shown in the Figure.
Assume $V_{TH}=1\text{ V}$, $V_{DD}=5\text{ V}$, and $\mu C_{ox}\left(\frac{W}{L}\right)=2{\text{ mA V}}^{-2}$ and neglect channel length modulation effects.
The gate voltage ($V_G$) of the n-channel MOSFET (in Volt) is __.
(rounded off to two decimal places)