Electronics and Communication Gate 2016 Set-2 Questions with Answer

Ques 14 GATE 2016 SET-2

An ideal band-pass channel 500 Hz - 2000 Hz is deployed for communication. A modem is designed to transmit bits at the rate of 4800 bits/s using 16-QAM. The roll-off factor of a pulse with a raised cosine spectrum that utilizes the entire frequency band is

(0.25) is the correct answer.

Ques 15 GATE 2016 SET-2

A binary communication system makes use of the symbols "zero" and "one". There are channel errors. Consider the following events:
x₀: a "zero" is transmitted
x₁: a "one" is transmitted
y₀: a "zero" is received
y₁: a "one" is received
The following probabilities are given: P(x₀)=1/2, P(y₀|x₀)=3/4 and P(y₀|x₁)=1/2. The information in bits that you obtain when you learn which symbol has been received (while you know that a "zero" has been transmitted) is

(0.81) is the correct answer.

Ques 16 GATE 2016 SET-2

Consider the time-varying vector I=x̂15cos(ωt)+ŷ5sin(ωt) in Cartesian coordinates, where ω>0 is a constant. When the vector magnitude |I| is at its minimum value, the angle θ that I makes with the x axis (in degrees, such that 0≤θ≤180) is

(90) is the correct answer.

Ques 17 GATE 2016 SET-2

A uniform and constant magnetic field B=ẑB exists in the ẑ direction in vacuum. A particle of mass m with a small charge q is introduced into this region with an initial velocity v=x̂v_x+ẑv_z. Given that B, m, q, v_x and v_z are all non-zero, which one of the following describes the eventual trajectory of the particle?

Helical motion in the ẑ direction.

Circular motion in the xy plane.

Linear motion in the ẑ direction.

Linear motion in the x̂ direction.

(a) is the correct answer.

Ques 18 GATE 2016 SET-2

Let the electric field vector of a plane electromagnetic wave propagating in a homogenous medium be expressed as E=x̂E_xe^-j(ωt-βz), where the propagation constant β is a function of the angular frequency ω. Assume that β(ω) and E_x are known and are real. From the information available, which one of the following CANNOT be determined?

The type of polarization of the wave.

The group velocity of the wave.

The phase velocity of the wave.

The power flux through the z=0 plane.

(d) is the correct answer.

Ques 19 GATE 2016 SET-2

Light from free space is incident at an angle θ_i to the normal of the facet of a step-index large core optical fibre. The core and cladding refractive indices are n₁=1.5 and n₂=1.4 respectively.

The maximum value of θ_i (in degrees) for which the incident light will be guided in the core of the fibre is

(32.5) is the correct answer.

Ques 20 GATE 2016 SET-2

The parallel-plate capacitor shown in the figure has movable plates. The capacitor is charged so that the energy stored in it is E when the plate separation is d. The capacitor is then isolated electrically and the plates are moved such that the plate separation becomes 2d. At this new plate separation, what is the energy stored in the capacitor, neglecting fringing effects?

√2E

E/2

(a) is the correct answer.

Ques 21 GATE 2016 SET-2

A lossless microstrip transmission line consists of a trace of width w. It is drawn over a practically infinite ground plane and is separated by a dielectric slab of thickness t and relative permittivity ε_r>1. The inductance per unit length and the characteristic impedance of this line are L and Z₀, respectively.

Which one of the following inequalities is always satisfied?

Z₀>√(Lt/(ε₀ε_rw))

Z₀<√(Lt/(ε₀ε_rw))

Z₀>√(Lw/(ε₀ε_rt))

Z₀<√(Lw/(ε₀ε_rt))

(b) is the correct answer.

Ques 22 GATE 2016 SET-2

A microwave circuit consisting of lossless transmission lines T₁ and T₂ is shown in the figure. The plot shows the magnitude of the input reflection coefficient Γ as a function of frequency f. The phase velocity of the signal in the transmission lines is 2×10⁸ m/s.

The length L (in meters) of T₂ is

(0.1) is the correct answer.

Ques 23 GATE 2016 SET-2

A positive charge q is placed at x=0 between two infinite metal plates placed at x=-d and at x=+d respectively. The metal plates lie in the yz plane. The charge is at rest at t=0, when a voltage +V is applied to the plate at -d and voltage -V is applied to the plate at x=+d. Assume that the quantity of the charge q is small enough that it does not perturb the field set up by the metal plates.

The time that the charge q takes to reach the right plate is proportional to

d/V

√d/V

d/√V

√(d/V)

Ques 24 GATE 2016 SET-2

Assume that the diode in the figure has V_on=0.7 V, but is otherwise ideal.

The magnitude of the current i₂ (in mA) is equal to

(0.25) is the correct answer.

Ques 25 GATE 2016 SET-2

Resistor R₁ in the circuit below has been adjusted so that I₁=1 mA. The bipolar transistors Q1 and Q2 are perfectly matched and have very high current gain, so their base currents are negligible. The supply voltage V_cc is 6 V. The thermal voltage kT/q is 26 mV.

The value of R₂ (in Ω) for which I₂=100 μA is

(589) is the correct answer.

Ques 26 GATE 2016 SET-2

Which one of the following statements is correct about an ac-coupled common-emitter amplifier operating in the mid-band region?

The device parasitic capacitances behave like open circuits, whereas coupling and bypass capacitances behave like short circuits.

The device parasitic capacitances, coupling capacitances and bypass capacitances behave like open circuits.

The device parasitic capacitances, coupling capacitances and bypass capacitances behave like short circuits.

The device parasitic capacitances behave like short circuits, whereas coupling and bypass capacitances behave like open circuits.

(a) is the correct answer.

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