Electrical Engineering GATE 2015 Set-1 Questions with Answer

Ques 27 Electrical Machines

A 200/400 V, 50 Hz, two-winding transformer is rated at 20 kVA. Its windings are connected as an auto-transformer of rating 200/600 V. A resistive load of 12 Ω is connected to the high voltage (600 V) side of the auto-transformer. The value of equivalent load resistance (in Ohm) as seen from low voltage side is ________.

Ques 28 Electrical Machines

Two single-phase transformers T₁ and T₂ each rated at 500 kVA are operated in parallel. Percentage impedances of T₁ and T₂ are (1+j6) and (0.8+j4.8), respectively. To share a load of 1000 kVA at 0.8 lagging power factor, the contribution of T₂ (in kVA) is ________.

Ques 29 Electrical Measurements

When the Wheatstone bridge shown in the figure is used to find the value of resistor R_X, the galvanometer G indicates zero current when R₁=50Ω, R₂=65Ω, and R₃=100Ω. If R₃ is known with ±5% tolerance on its nominal value of 100 Ω, what is the range of R_X in Ohms?

Ques 30 Electrical Measurements

A (0-50 A) moving coil ammeter has a voltage drop of 0.1 V across its terminals at full scale deflection. The external shunt resistance (in milliohms) needed to extend its range to (0-500 A) is ________.

Ques 31 Electrical Measurements

An unbalanced DC Wheatstone bridge is shown in the figure. At what value of p will the magnitude of V₀ be maximum?

Ques 32 Electromagnetics

Consider a one-turn rectangular loop of wire placed in a uniform magnetic field as shown in the figure. The plane of the loop is perpendicular to the field lines. The resistance of the loop is 0.4Ω, and its inductance is negligible. The magnetic flux density (in Tesla) is a function of time, and is given by B(t) = 0.25sin(ωt), where ω=2πx50 radian/second. The power absorbed (in Watt) by the loop from the magnetic field is ________.

Ques 33 Electromagnetics

A steady current I is flowing in the -x direction through each of two infinitely long wires at y = ±L/2 as shown in the figure. The permeability of the medium is μ₀. The B-field at (0,L,0) is

Ques 34 Electromagnetics

A parallel plate capacitor is partially filled with glass of dielectric constant 4.0 as shown below. The dielectric strengths of air and glass are 30 kV/cm and 300 kV/cm, respectively. The maximum voltage (in kilovolts), which can be applied across the capacitor without any breakdown, is ________.

Ques 35 Engineering Mathematics

A random variable X has probability density function f(x) as given below:

Ques 36 Engineering Mathematics

If a continuous function f(x) does not have a root in the interval [a, b], then which one of the following statements is TRUE?

Ques 37 Engineering Mathematics

If the sum of the diagonal elements of a 2x2 matrix is -6, then the maximum possible value of determinant of the matrix is ________.

Ques 38 Engineering Mathematics

Consider a function f = (1/r²)r̂ where r is the distance from the origin and r̂ is the unit vector in the radial direction. The divergence of this function over a sphere of radius R, which includes the origin, is

Ques 39 Engineering Mathematics

The maximum value of 'a' such that the matrix has three linearly independent real eigenvectors is