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

The RLC filter shown below acts as a ________.

A single phase step-down transformer has a high voltage primary winding and a low voltage secondary winding. The secondary winding is connected to a load impedance $Z_2$. The impedance $Z_2$ when referred to the primary winding is denoted by $Z_2^{\prime }$. Which of the following conditions is true?

A square wave signal of frequency 20 kHz is passed through an ideal low-pass filter with cut-off frequency of 21 kHz. The output signal is a _______.

Given $x(t)=4\sin (15\pi t)+7\cos (4\pi t)$, where $t$ is in seconds.

The fundamental period of $x(t)$ is _____ seconds.

Among the following, the differential equation(s) not representative of a linear dynamical system is/are ____.

(i) $\frac{d^{2}x}{d{t}^2}+2t\frac{dx}{dt}+x(t)=u(t)$

(ii) ${\left(\frac{dx}{dt}\right)}^2+2\frac{dx}{dt}+x(t)=u(t)$

(iii) $\frac{d^{2}x}{d{t}^2}+2\frac{dx}{dt}+x(t)=u(t)$