GATE EE format:nat PYQs & Answers — Page 2 — Exam Papers

Questions 11–20 of 256. Imported answers require independent review unless marked reviewed.

Topic practice 256 questionsPage 2 of 26

A uniform spherical volume charge distribution of radius 2 m, centered at the origin, has a strength of 3/π × 10⁻⁶ C/m³. A point charge of strength π × 8.854 × 10⁻¹² C is moved from (−3, 0, −4) to (0, 0, 4) in Cartesian coordinate system. The relative permittivity of the medium is 1 and the coordinate values are in meters.

The work done during the process is ________ μJ (Round off to two decimal places)

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Let X and Y be two real-valued random variables with E(X) = 1, E(Y) = 2, E(X²) = 4, E(Y²) = 9, and E(XY) = 0.9, where E denotes the expectation operator.

The value of α that minimizes E((X − αY)²) is __________ (Round off to one decimal place)

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The integral

evaluates to _________ (Round off to two decimal places)

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A continuous time periodic signal

is

. If

is the period of

, then

______ (round off to the nearest integer).

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The maximum percentage error in the equivalent resistance of two parallel-connected resistors of 100

and 900

with each having a maximum 5% error is ______ % (round off to nearest integer value).

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Consider a distribution feeder, with

ratio of 5. At the receiving end, a 350 kVA load is connected. The maximum voltage drop will occur from the sending end to the receiving end, when the power factor of the load is __________ (round off to three decimal places).

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The bus impedance matrix of a 3-bus system (in pu) is

. A symmetrical fault (through a fault impedance of

pu) occurs at bus 2. Neglecting pre-fault loading conditions, the voltage at bus 1, during the fault is ______ pu (round off to three decimal places).

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In the circuit with ideal devices, the power MOSFET is operated with a duty cycle of 0.4 in a switching cycle with

and

. The power delivered by the current source, in W, is __________ (round off to the nearest integer).

Diagram for Electrical Engineering question 34

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The induced emf in a 3 kV, 4 pole, 3-phase star connected synchronous motor is considered to be equal and in phase with the terminal voltage under no load condition. On application of a mechanical load, the induced emf phasor is deflected by an angle of 2° mechanical with respect to the terminal voltage phasor. If the synchronous reactance is

, and stator resistance is negligible, then the motor armature current magnitude, in ampere, during loaded condition is closest to, __________ (round off to two decimal places).

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Let

. The rate of change of the real valued function,

at the origin in the direction of the point (1,2) is __________ (round off to the nearest integer).

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