Electronics and Communication Gate 2022 Questions with Answer

Ques 40 GATE 2022

Consider the circuit shown with an ideal long channel nMOSFET (enhancement-mode, substrate is connected to the source). The transistor is appropriately biased in the saturation region with V_GG and V_DD such that it acts as a linear amplifier. v_i is the small-signal ac input voltage. v_A and v_B represent the small-signal voltages at the nodes A and B, respectively. The value of v_A/v_B is ________ (rounded off to one decimal place).

(0.5) is the correct answer.

Ques 41 Gate 2022

Select the CORRECT statement(s) regarding semiconductor devices.

Electrons and holes are of equal density in an intrinsic semiconductor at equilibrium.

Collector region is generally more heavily doped than Base region in a BJT.

Total current is spatially constant in a two terminal electronic device in dark under steady state condition.

Mobility of electrons always increases with temperature in Silicon beyond 300 K.

(a,c) is the correct answer.

Ques 42 GATE 2022

Consider a long rectangular bar of direct bandgap p-type semiconductor. The equilibrium hole density is 10¹⁷ cm⁻³ and the intrinsic carrier concentration is 10¹⁰ cm⁻³. Electron and hole diffusion lengths are 2 μm and 1 μm, respectively.
The left side of the bar (x = 0) is uniformly illuminated with a laser having photon energy greater than the bandgap of the semiconductor. Excess electron-hole pairs are generated ONLY at x = 0 because of the laser. The steady state electron density at x = 0 is 10¹⁴ cm⁻³ due to laser illumination. Under these conditions and ignoring electric field, the closest approximation (among the given options) of the steady state electron density at x = 2 μm, is _______

0.37 × 10¹⁴ cm⁻³

0.63 × 10¹³ cm⁻³

3.7 × 10¹⁴ cm⁻³

10³ cm⁻³

(a) is the correct answer.

Ques 43 GATE 2022

In a non-degenerate bulk semiconductor with electron density n = 10¹⁶ cm⁻³, the value of E_C − E_Fn = 200 meV, where E_C and E_Fn denote the bottom of the conduction band energy and electron Fermi level energy, respectively. Assume thermal voltage as 26 meV and the intrinsic carrier concentration is 10¹⁰ cm⁻³. For n = 0.5 × 10¹⁶ cm⁻³, the closest approximation of the value of (E_C − E_Fn), among the given options, is ________.

226 meV

174 meV

218 meV

182 meV

Ques 44 GATE 2022

Consider the CMOS circuit shown in the figure (substrates are connected to their respective sources). The gate width (W) to gate length (L) ratios (W/L) of the transistors are as shown. Both the transistors have the same gate oxide capacitance per unit area. For the pMOSFET, the threshold voltage is −1 V and the mobility of holes is 40 cm²/(V.s). For the nMOSFET, the threshold voltage is 1 V and the mobility of electrons is 300 cm²/(V.s). The steady state output voltage V_O is ________.

equal to 0 V

more than 2 V

less than 2 V

equal to 2 V

(b) is the correct answer.

Ques 45 GATE 2022

The ideal long channel nMOSFET and pMOSFET devices shown in the circuits have threshold voltages of 1 V and −1 V, respectively. The MOSFET substrates are connected to their respective sources. Ignore leakage currents and assume that the capacitors are initially discharged. For the applied voltages as shown, the steady state voltages are _________________

V₁ = 5 V, V₂ = 5 V

V₁ = 5 V, V₂ = 4 V

V₁ = 4 V, V₂ = 5 V

V₁ = 4 V, V₂ = −5 V

(v₁ = 4 v, v₂ = 5 v) is the correct answer.

Ques 46 GATE 2022

An ideal MOS capacitor (p-type semiconductor) is shown in the figure. The MOS capacitor is under strong inversion with V_G = 2 V. The corresponding inversion charge density (Q_IN) is 2.2 μC/cm². Assume oxide capacitance per unit area as C_OX = 1.7 μF/cm². For V_G = 4 V, the value of Q_IN is ______ μC/cm² (rounded off to one decimal place).

(5.6) is the correct answer.

Ques 47 GATE 2022

Consider an ideal long channel nMOSFET (enhancement-mode) with gate length 10 μm and width 100 μm. The product of electron mobility (μ_n) and oxide capacitance per unit area (C_OX) is μ_nC_OX = 1 mA/V². The threshold voltage of the transistor is 1 V. For a gate-to-source voltage V_GS = [2 − sin(2t)] V and drain-to-source voltage V_DS = 1 V (substrate connected to the source), the maximum value of the drain-to-source current is ________.

40 mA

20 mA

15 mA

5 mA

Ques 48 GATE 2022

The value of the integral
∬_D 3(x² + y²)dxdy,
where D is the shaded triangular region shown in the diagram, is _____ (rounded off to the nearest integer).

(4) is the correct answer.

Ques 49 GATE 2022

Consider the two-dimensional vector field F⃗(x, y) = x î + y ĵ, where î and ĵ denote the unit vectors along the x-axis and the y-axis, respectively. A contour C in the x-y plane, as shown in the figure, is composed of two horizontal lines connected at the two ends by two semicircular arcs of unit radius. The contour is traversed in the counter-clockwise sense. The value of the closed path integral ∮_C F⃗(x, y) ⋅ (dx î + dy ĵ) is _______

8 + 2π

−1

(8 + 2π) is the correct answer.

Ques 50 GATE 2022

Consider a system of linear equations Ax = b, where

This system of equations admits _______

a unique solution for x

infinitely many solutions for x

no solutions for x

exactly two solutions for x

(no solutions for x) is the correct answer.

Ques 51 GATE 2022

Consider the following partial differential equation (PDE)
a ∂²f(x, y)/∂x² + b ∂²f(x, y)/∂y² = f(x, y),
where a and b are distinct positive real numbers. Select the combination(s) of values of the real parameters ξ and η such that f(x, y) = e^(ξx+ηy) is a solution of the given PDE.

ξ = 1/√(2a), η = 1/√(2b)

ξ = 1/√a, η = 0

ξ = 0, η = 0

ξ = 1/√a, η = 1/√b

(b) is the correct answer.

Ques 52 GATE 2022

Consider the following wave equation,
∂²f(x, t)/∂t² = 10000 ∂²f(x, t)/∂x²
Which of the given options is/are solution(s) to the given wave equation?

f(x, t) = e^{−(x−100t)²} + e^{−(x+100t)²}

f(x, t) = e^{−(x−100t)} + 0.5e^−(x+1000t)

f(x, t) = e^{−(x−100t)} + sin(x + 100t)

f(x, t) = e^{j100π(−100x+t)} + e^{j100π(100x+t)}

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