Electrical Engineering Gate 2020 Questions with Answer

Ques 27 GATE 2020

The static electric field inside a dielectric medium with relative permittivity, ε_r = 2.25 expressed in cylindrical coordinate system is given by the following expression:
E = a_r2r + a_φ(3 / r) + a_z6
where a_r, a_φ, a_z are unit vectors along r, φ, and z directions, respectively. If the above expression represents a valid electrostatic field inside the medium, then the volume charge density associated with this field in terms of free space permittivity, ε₀, in SI units is given by:

Ques 28 GATE 2020

Let a_r, a_φ, and a_z be unit vectors along r, φ, and z directions, respectively in the cylindrical coordinate system.
For the electric flux density given by D = (a_r15 + a_φ2r − a_z3rz) Coulomb/m²,
the total electric flux, in Coulomb, emanating from the volume enclosed by a solid cylinder of radius 3 m and height 5 m oriented along the z-axis with its base at the origin is:

Ques 29 GATE 2020

The cross-section of a metal-oxide-semiconductor structure is shown schematically. Starting from an uncharged condition, a bias of +3 V is applied to the gate contact with respect to the body contact. The charge inside the silicon dioxide layer is then measured to be +Q. The total charge contained within the dashed box shown, upon application of bias, expressed as a multiple of Q (absolute value in Coulombs, rounded off to the nearest integer) is _________.

Ques 30 GATE 2020

A non-ideal diode is biased with a voltage of -0.03 V, and a diode current of I₁ is measured. The thermal voltage is 26 mV and the ideality factor for the diode is 15/13.
The voltage, in V, at which the measured current increases to 1.5I₁ is closest to:

Ques 31 GATE 2020

A non-ideal Si-based pn junction diode is tested by sweeping the bias applied across its terminals from −5 V to +5 V. The effective thermal voltage, V_T, for the diode is measured to be (29 ± 2) mV. The resolution of the voltage source in the measurement range is 1 mV.
The percentage uncertainty (rounded off to 2 decimal places) in the measured current at a bias voltage of 0.02 V is _______

Ques 32 GATE 2020

ax³+bx²+cx+d is a polynomial on real x over real coefficients a, b, c, d wherein a≠0. Which of the following statements is true?

Ques 33 GATE 2020

Which of the following is true for all possible non-zero choices of integers m,n; m≠n or all possible non-zero choices of real numbers p,q; p≠q. as applicable?

Ques 34 GATE 2020

The value of the following complex integral, with C representing the unit circle centered at origin in the counterclockwise sense, is:
∫_C(z²+1)/(z²-2z)dz

Ques 35 GATE 2020

Consider the initial value problem below. The value of y at x=ln 2 (rounded off to 3 decimal places) is ________.
dy/dx=2x-y, y(0)=1

Ques 36 GATE 2020

For real numbers, x and y, with y = 3x² + 3x + 1, the maximum and minimum value of y for x ∈ [-2, 0] are respectively. __________.

Ques 37 GATE 2020

The number of purely real elements in a lower triangular representation of the given 3×3 matrix, obtained through the given decomposition is

Ques 38 GATE 2020

Let a_x and a_y be unit vectors along x and y directions, respectively. A vector function is given by:
F = a_xy − a_yx
The line integral of the above function
∫_CF · dl
along the curve C, which follows the parabola y = x² as shown below is _______ (rounded off to 2 decimal places).

Ques 39 GATE 2020

This book, including all its chapters, ________ interesting. The students as well as the instructor ________ in agreement about it.