GATE EE 2023 Question Paper (05-Feb-2023) (Shift 1)

An infinite surface of linear current density 𝐊 = 5𝐚̂${}_{\text{x}}$ A/m exists on the x-y plane, as shown in the figure. The magnitude of the magnetic field intensity (H) at a point (1,1,1) due to the surface current in Ampere/meter is _______ (Round off to 2 decimal places).

The closed curve shown in the figure is described by

𝑟 = 1 + 𝑐𝑜𝑠 𝜃, where 𝑟 = $\sqrt{{\mathrm{x}}^2+{\mathrm{y}}^2}$; 𝑥 = 𝑟𝑐𝑜𝑠 𝜃, 𝑦 = 𝑟𝑠𝑖𝑛 𝜃

The magnitude of the line integral of the vector field 𝐹 = −𝑦𝑖̂ + 𝑥𝑗̂around the closed curve is ____________ (Round off to 2 decimal places).

A signal 𝑥(𝑡) = 2𝑐𝑜𝑠(180𝜋𝑡)𝑐𝑜𝑠(60𝜋𝑡) is sampled at 200 Hz and then passed through an ideal low pass filter having cut-off frequency of 100 Hz.

The maximum frequency present in the filtered signal in Hz is _____________ (Round off to the nearest integer).

A balanced delta connected load consisting of the series connection of one resistor (R = 15 Ω) and a capacitor (C = 212.21 μF) in each phase is connected to threephase, 50 Hz, 415 V supply terminals through a line having an inductance of L = 31.83 mH per phase, as shown in the figure. Considering the change in the supply terminal voltage with loading to be negligible, the magnitude of the voltage across the terminals V${}_{AB}$ in Volts is _____________ (Round off to the nearest integer).

A quadratic function of two variables is given as

$\mathrm{f}({\mathrm{x}}_1,{\mathrm{x}}_2)={\mathrm{x}}_1^2+2{\mathrm{x}}_2^2+3{\mathrm{x}}_1+3{\mathrm{x}}_2+{\mathrm{x}}_1{\mathrm{x}}_2+1$

The magnitude of the maximum rate of change of the function at the point (1,1) is _________ (Round off to the nearest integer).