Electrical Engineering Gate 2018 Questions with Answer

Ques 40 GATE 2018

The value of the integral ∮_C (z + 1)/(z² - 4) dz in counter clockwise direction around a circle C of radius 1 with center at the point z = -2 is

Ques 41 GATE 2018

Consider a non-singular ²×² square matrix A. If trace(A)=4 and trace(A²)=5, the determinant of the matrix A is ________ (up to 1 decimal place).

Ques 42 GATE 2018

Let f be a real-valued function of a real variable defined as f(x)=x-[x], where [x] denotes the largest integer less than or equal to x. The value of ∫₀¹ f(x)dx is ________ (up to 2 decimal places).

Ques 43 GATE 2018

If C is a circle |z| = 4 and f(z) = z² / (z² - 3z + 2)², then ∮_C f(z) dz is

Ques 44 GATE 2018

As shown in the figure, C is the arc from the point (3,0) to the point (0,3) on the circle x² + y² = 9. The value of the integral ∫_C (y² + 2yx)dx + (2xy + x²)dy is _____ (up to 2 decimal places).

Ques 45 GATE 2018

Let f(x) = 3x³ - 7x² + 5x + 6. The maximum value of f(x) over the interval [0, 2] is _____ (up to 1 decimal place).

Ques 46 GATE 2018

Let and B = A³ - 4A² + 5A + I, where I is the 3 x 3 identity matrix. The determinant of B is ________ (up to 1 decimal place).

Ques 47 GATE 2018

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?

Ques 48 Gate 2018

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?

Ques 49 Gate 2018

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)

Ques 50 GATE 2018

The waveform of the current drawn by a semi-converter from a sinusoidal AC voltage source is shown in the figure. If I₀=20A the rms value of fundamental component of the current is ________ A (up to 2 decimal places).

Ques 51 GATE 2018

A phase controlled single phase rectifier, supplied by an AC source, feeds power to an R-L-E load as shown in the figure. The rectifier output voltage has an average value given by V_o = (V_m / 2π) (3 + cos α), where V_m = 80π volts and α is the firing angle. If the power delivered to the lossless battery is 1600 W, α in degree is ________ (up to 2 decimal places).

Ques 52 GATE 2018

The figure shows two buck converters connected in parallel. The common input dc voltage for the converters has a value of 100 V. The converters have inductors of identical value. The load resistance is 1 Ω. The capacitor voltage has negligible ripple. Both converters operate in the continuous conduction mode. The switching frequency is 1 kHz, and the switch control signals are as shown. The circuit operates in the steady state. Assuming that the converters share the load equally, the average value of i_S1, the current of switch S1 (in Ampere), is _____ (up to 2 decimal places).