Practice Test: Gate Electrical Engineering GATE 2018 Paper - Electrical Engineering (EE) MCQ

For what values of k given below is  an integer?

Functions F(a, b) and G(a, b) are defined as follows:   represents the absolute value of x. What would be the value of G(F(1, 3), G(1, 3))?

An e-mail password must contain three characters. The password has to contain one numeral from 0 to 9, one upper case and one lower case character from the English alphabet. How many distinct passwords are possible?

In a certain code, AMCF is written as EQGJ and NKUF is written as ROYJ. How will DHLP be written in that code?

A class of twelve children has two more boys than girls. A group of three children are randomly picked from this class to accompany the teacher on a field trip. What is the probability that the group accompanying the teacher contains more girls than boys?

A designer uses marbles of four different colours for his designs. The cost of each marble is the same, irrespective of the colour. The table below shows the percentage of marbles of each colour used in the current design. The cost of each marble increased by 25%. Therefore, the designer decided to reduce equal numbers of marbles of each colour to keep the total cost unchanged. What is the percentage of blue marbles in the new design? 

P, Q, R and S crossed a lake in a boat that can hold a maximum of two persons, with only one set of oars. The following additional facts are available.
(i) The boat held two persons on each of the three forward trips across the lake and one person on each of the two return trips.
(ii) P is unable to row when someone else is in the boat.
(iii) Q is unable to row with anyone else except R.
(iv) Each person rowed for at least one trip.
(v) Only one person can row during a trip.
Who rowed twice?

A single-phase 100 kVA, 1000 V / 100 V, 50 Hz transformer has a voltage drop of 5% across its series impedance at full load. Of this, 3% is due to resistance. The percentage regulation of the transformer at full load with 0.8 lagging power factor is

In a salient pole synchronous motor, the developed reluctance torque attains the maximum value when the load angle in electrical degrees is

A single phase fully controlled rectifier is supplying a load with an anti-parallel diode as shown in the figure. All switches and diodes are ideal. Which one of the following is true for instantaneous load voltage and current?
 

Four power semiconductor devices are shown in the figure along with their relevant terminals. The device(s) that can carry dc current continuously in the direction shown when gated appropriately is (are)

Two wattmeter method is used for measurement of power in a balanced three-phase load supplied from a balanced three-phase system. If one of the wattmeters reads half of the other (both positive), then the power factor of the load is

Consider a lossy transmission line with V₁ and V₂ as the sending and receiving end voltages, respectively. Z and X are the series impedance and reactance of the line, respectively.  The steady-state stability limit for the transmission line will be

The graph of a network has 8 nodes and 5 independent loops. The number of branches of the graph is

In the figure, the voltages are The circuit is in sinusoidal steady state, and �� << ����. ��₁, ��₂ and ��₃ are the average power outputs. Which one of the following statements is true?

Match the transfer functions of the second-order systems with the nature of the systems given below.

A positive charge of 1 nC is placed at (0, 0, 0.2) where all dimensions are in metres. Consider the x - y plane to be a conducting ground plane. Take 12 ε₀= 8.85X10^-12 F/m. The z component of the E field at (0, 0, 0.1) is closest to

Let f be a real-valued function of a real variable defined as f ( x) = x 2 for x ≥ 0 , and 2f ( x) =- x² for x < 0 . Which one of the following statements is true?

The value of the directional derivative of the function at the point (2, -1, 1) in the direction of the vector is

The value of the integral in counter clockwise direction around a circle C of radius 1 with center at the point z = −2 is

In the logic circuit shown in the figure, Y is given by

The op-amp shown in the figure is ideal. The input impedance  is given by

A continuous-time input signal x(t) is an eigenfunction of an LTI system, if the output is

Consider a non-singular 2×2 square matrix A . If trace(A) = 4 and trace (A ² ) = 5 , the determinant of the matrix A is  _________(up to 1 decimal place).

Let  f be a real-valued function of a real variable defined as denotes the largest integer less than or equal to x. The value of   is _______ (up  to 2 decimal places).

In the two-port network shown, the h 11 parameter is _____________ (up to 2 decimal places).

The series impedance matrix of a short three-phase transmission line in phase coordinates is . If the positive sequence impedance is , and the zero sequence is , then the imaginary part of is ______(up to 2 decimal places).