Question 1

The diodes D1 and D2 in the figure are ideal and the capacitors are identical. The product RC is very large compared to the time period of the ac voltage. Assuming that the diodes do not breakdown in the reverse bias, the output voltage V0 (in volt) at the steady state is -----------

The

Accepted Answer

20. In steady state, the ideal diodes D1 and D2 conduct during the positive and negative halves of the AC cycle, respectively, allowing the full amplitude of the AC voltage to appear across the load resistor R. Since the AC source has a peak voltage of 10 volts, the output voltage V0 across R effectively doubles to 20 volts due to the contributions from both halves of the waveform.

Question 2

In an 8085 microprocessor, the contents of the accumulator and the carry flag are A7 (in hex) and 0, respectively. If the instruction RLC is executed, then the contents of the accumulator (in hex) and the carry flag, respectively, will be

Accepted Answer

4F and 1. A7 = 1010 0111. RLC rotates left: the MSB (1) goes to carry and to the LSB, giving 0100 1111 = 4F with carry = 1. Correct option is 3 (4F and 1), not stored option 1 (4E and 1).

Question 3

The minimum number of 2-input NAND gates required to implement a 2-input XOR gate is

Accepted Answer

4. A 2-input XOR gate can be constructed using 4 2-input NAND gates by combining them in a specific configuration that utilizes the properties of NAND gates to achieve the desired output of the XOR function.

Question 4

The block diagram of a feedback control system is shown in the figure. The overall closed-loop gain G of the system is

Accepted Answer

G = G1G2 / (1 + G1G2 + G1G2H1). The correct option accounts for the contributions of both the forward path gains and the feedback loop, accurately representing the overall closed-loop gain by including all relevant terms in the denominator.

Question 5

For the unity feedback control system shown in the figure, the open-loop transfer function G(s) is given as G(s) = 2 / (s(s+1)). The steady state error e_ss due to a unit step input is

Accepted Answer

0. The steady state error for a unity feedback system with a type 1 system (one integrator in the open-loop transfer function) is zero for a unit step input, as the system can perfectly track the input due to its ability to eliminate steady state error.

Question 6

A binary baseband digital communication system employs the signal

p(t) = { 1/√Tₛ, 0 ≤ t ≤ Tₛ
 { 0, otherwise

for transmission of bits. The graphical representation of the matched filter output y(t) for this signal will be

Accepted Answer

(C) A triangular waveform from t = 0 to 2Tₛ with peak value 1 at t = Tₛ. The correct option describes the output of the matched filter for a rectangular pulse input, which results in a triangular waveform due to the convolution of the pulse shape with itself. The peak occurs at the midpoint of the pulse duration, specifically at Tₛ, and the waveform extends from 0 to 2Tₛ, reflecting the integration of the signal over time.

Question 7

If a right-handed circularly polarized wave is incident normally on a plane perfect conductor, then the reflected wave will be

Accepted Answer

(B) left-handed circularly polarized. When a right-handed circularly polarized wave reflects off a perfect conductor, the phase of the electric field component reverses, resulting in a left-handed circularly polarized wave.

Question 8

Faraday's law of electromagnetic induction is mathematically described by which one of the following equations?

Accepted Answer

(C) ∇ × E = −∂B/∂t. Option (C) correctly represents Faraday's law of electromagnetic induction, which states that a changing magnetic field over time induces an electric field. This relationship is fundamental in electromagnetism and is mathematically expressed through the curl of the electric field being equal to the negative rate of change of the magnetic field.

Question 9

A second-order linear time-invariant system is described by the following state equations
(d/dt) x1(t) + 2 x1(t) = 3 u(t)
(d/dt) x2(t) + x2(t) = u(t)
where x1(t) and x2(t) are the two state variables and u(t) denotes the input. If the output c(t) = x1(t), then the system is

Accepted Answer

controllable but not observable. With x1' = -2x1 + 3u, x2' = -x2 + u, the controllability matrix has full rank 2 (both states driven by u), but with c = x1 the observability matrix has rank 1 (x2 is hidden). So the system is controllable but not observable, option 0, not stored option 1.

Question 10

A wide sense stationary random process X(t) passes through the LTI system shown in the figure. If the autocorrelation function of X(t) is R_X(τ), then the autocorrelation function R_Y(τ) of the output Y(t) is equal to

Accepted Answer

2R_X(τ) + R_X(τ - T₀) + R_X(τ + T₀). The correct option reflects the properties of the autocorrelation function when a wide sense stationary process passes through a linear time-invariant (LTI) system, where the output's autocorrelation is influenced by the input's autocorrelation at different time shifts, specifically incorporating contributions from both positive and negative shifts of T₀.

GATE Technical: Electronics and Communication Engineering (Set 3) questions with solutions

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