GATE EE 2026 Question Paper (14-Feb-2026) (Shift 1)

Consider the infinite-length, discrete-time sequence $x[n]=0.9^{|n|}$, where $n$ is an integer. The region of convergence of its Z-transform $X(z)$ is given by:

(Note: $z$ is a complex variable)

Let $x_c(t)$ be any continuous-time periodic signal with period $T$. It is sampled uniformly with a sampling period $T_s$ where $T_s\ne T$, resulting in the discrete sequence

$x[n]=x_c(n{T}_s)$, where $n$ is an integer.

Which one of the following statements is correct about $x[n]$?

The Laplace transform of the step response of a system is given by
$$Y(s)=\frac{100}{s(s+100)}$$
The rise time is defined as the time taken for the response to go from 0.1 to 0.9 of its final value. The settling time is defined as the time taken for the response to reach 0.98 of its final value.

For this system, the rise time ($T_r$), settling time ($T_s$), and time constant ($T_c$), all expressed in seconds, are

Consider the following differential equation:
$$t^2\frac{d^{2}y}{d{t}^2}+7t\frac{dy}{dt}+8ty=10\sin (t)$$
Which one of the following options is correct?

A uniform ring charge of radius $R$ carries a total charge $Q$. Which one of the following options correctly quantifies the magnitude of the force on a point charge of strength $q$ kept at the center of the ring?

($ϵ$ is the permittivity of the medium)