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

Consider the square region $R$ in the $X-Y$ plane as shown with the dark shading in the Figure. The value of ${\iint }_R(x^2+y^2-1)dxdy$ is ____.
(rounded off to two decimal places)

Consider an ideal OP-AMP circuit as shown in the Figure.
The resistances $R_1=R_2=R_3=R_4=50\text{ k}\Omega$.
The magnitude of the closed loop gain is ___.
(rounded off to two decimal places)

The average bit error rate at the input of a (7, 4, 1) Hamming decoder is 0.10.
The probability that the decoder will fail to decode a received word correctly is __.
(rounded off to two decimal places)

Consider that the concentration of electrons in a semiconductor bar varies linearly from $2\times 10^{17}{\text{cm}}^{-3}$ at $x=1\mu \text{m}$ to $1\times 10^{16}{\text{ cm}}^{-3}$ at $x=4\mu \text{m}$ along the $x$ -direction. Assume that the concentration of electrons is not varying along other directions (that is along $y$ - and $z$ -directions).
[Given: the mobility of electron is $1400{\text{ cm}}^2{\text{V}}^{-1}{\text{s}}^{-1}$, thermal voltage is $25\text{ mV}$ and electronic charge is $1.6\times 10^{-19}\text{ Coulomb}$.]
The density of electron diffusion current (in A/mm${}^2$) is __.
(rounded off to two decimal places)

Consider the ideal diodes D1 and D2 as shown in the Figure with cut-in voltage $V_{\gamma }=0\text{ Volt}$ and $v_i(t)$ is in Volt.
The maximum voltage (Volt) of the output $v_o(t)$ is __.
(rounded off to two decimal places)