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

A time-limited waveform $g(x)$ is specified as follows:
$$g(x)=\{\begin{array}{ll}-k,& -\pi <x\le 0\\ +k,& 0<x\le \pi \\ 0,& \text{otherwise}\end{array}$$
A new waveform $f(x)$ is constructed from $g(x)$ as follows:
$$f(x)=\sum _{m=-\infty }^{\infty }g(x+2\pi m),\text{for all }x\in \mathbb{R}$$
The sum of the coefficients of the third harmonics of the sine and cosine terms in the trigonometric Fourier series expansion of $f(x)$ is $\frac{2}{3\pi }$.

What is the value of $k$?

In the circuit shown, the open loop gain of the operational amplifier is $A_0=10^5$.



What is the voltage gain of the circuit?

(Round off to two decimal places)

Three single-phase 11kV/3.3kV transformers are connected to form a three-phase transformer bank with connections as shown.



Considering ABC phase sequence, the vector group of the transformer is:

In the circuit shown, the phase currents are

$I_A=572.812+j50.115\text{ A}$

$I_B=-254.525-j459.175\text{ A}$

$I_C=-207.083+j444.091\text{ A}$



Given that the CTs are ideal with no saturation, and the turns ratio of the Main CT is 300:5 and that of the Auxiliary Transformer ($Yn\Delta$) is 2:1 on every phase, the value of $I_{AR}$, rounded off to three decimal places, is:

The operating characteristic of a reactance relay is given by $X\le 1\Omega$, where $X$ is the reactance calculated by the relay. Its operating characteristic in the admittance plane ($G-B$ plane, where $G$ and $B$ denote conductance and susceptance, respectively, expressed in $\mho$) is given by: