Electronics And Communication - ECE 2014 GATE Paper (Practice Test) - GATE

A regular die has six sides with numbers 1 to 6 marked on its sides. If a very large number of
throws show the following frequencies of occurrence: 1→0.167; 2→0.167; 3→0.152; 4→
0.166; 5→0.168; 6 →0.180. We call this die

Fill in the missing number in the series.
2   3   6   15   ___   15 7.5    630

Q. No. 6 – 10 Carry One Mark Each

Q.

Find the odd one in the following group
Q,W,Z,B           B,H,K,M           W,C,G,J                  M,S,V,X

Lights of four colors (red, blue, green, yellow) are hung on a ladder. On every step of the
ladder there are two lights. If one of the lights is red, the other light on that step will always
be blue. If one of the lights on a step is green, the other light on that step will always be
yellow. Which of the following statements is not necessarily correct?

sum of eight consecutive odd numbers is 656. The average of four consecutive even
numbers is 87. What is the sum of the smallest odd number and second largest even number?

The total exports and revenues from the exports of a country are given in the two charts
shown below. The pie chart for exports shows the quantity of each item exported as a
percentage of the total quantity of exports. The pie chart for the revenues shows the
percentage of the total revenue generated through export of each item. The total quantity of
exports of all the items is 500 thousand tonnes and the total revenues are 250 crore rupees.
Which item among the following has generated the maximum revenue per kg?

It takes 30 minutes to empty a half-full tank by draining it at a constant rate. It is decided to
simultaneously pump water into the half-full tank while draining it. What is the rate at which
water has to be pumped in so that it gets fully filled in 10 minutes?

Q. No. 11 – 35 Carry One Mark Each

Q.

The determinant of matrix A is 5 and the determinant of matrix B is 40. The determinant of
matrix AB is ________.

Let X be a random variable which is uniformly chosen from the set of positive odd numbers
less than 100. The expectation E[X]is __________.

For 0 t < ∞, the maximum value of the function f(t) =e^-t -  2e^-2t  occurs at

The value of  

If the characteristic equation of the differential equation

has two equal roots, then the values of α are

Norton’s theorem states that a complex network connected to a load can be replaced with an
equivalent impedance

In the figure shown, the ideal switch has been open for a long time. If it is closed at t=0, then
the magnitude of the current (in mA) through the 4k? resistor at t = 0+ is _______.

A silicon bar is doped with donor impurities N_D = 2.25 x 10¹⁵ atoms / cm³. Given the intrinsic
carrier concentration of silicon at T = 300 K is n_i = 1.5 x 1010 cm-3. Assuming complete
impurity ionization, the equilibrium electron and hole concentrations are

An increase in the base recombination of a BJT will increase

In CMOS technology, shallow P-well or N-well regions can be formed using

The feedback topology in the amplifier circuit (the base bias circuit is not shown for
simplicity) in the figure is

In the differential amplifier shown in the figure, the magnitudes of the common-mode and
differential-mode gains are A_cm and A_d, respectively. If the resistance R_E is increased, then

A cascade connection of two voltage amplifiers A1 and A2 is shown in the figure. The openloop
gain A_v0, input resistance R_in, and output resistance RO for A1 and A2 are as follows:

For an n-variable Boolean function, the maximum number of prime implicants is

The number of bytes required to represent the decimal number 1856357 in packed BCD
(Binary Coded Decimal) form is __________ .

In a half-subtractor circuit with X and Y as inputs, the Borrow (M) and Difference (N = X - Y)
are given by

An FIR system is described by the system function

Let x[n] = x[-n]. Let X(z) be the z-transform of x[n]. If 0.5 + j 0.25 is a zero o X(z), which
one of the following must also be a zero of X(z).

Consider the periodic square wave in the figure shown.

The ratio of the power in the 7^th harmonic to the power in the 5^th harmonic for this waveform
is closest in value to _______.

The natural frequency of an undamped second-order system is 40 rad/s. If the system is
damped with a damping ratio 0.3, the damped natural frequency in rad/s is ________.

For the following sytem

When X₁( s) = 0 , the transfer function 

The capacity of a band-limited additive white Gaussian noise (AWGN) channel is given by  bits per second (bps), where W is the channel bandwidth, P is the
average power received and σ² is the one-sided power spectral density of the AWGN. For a
fixed P/σ² =1000. the channel capacity (in kbps) with infinite bandwidth (W→∞) is
approximately

Consider sinusoidal modulation in an AM system. Assuming no overmodulation, the
modulation index (μ) when the maximum and minimum values of the envelope,
respectively, are 3 V and 1 V, is ________.

To maximize power transfer, a lossless transmission line is to be matched to a resistive load
impedance via a λ / 4 transformer as shown.

The characteristic impedance (in?) of the λ / 4 transformer is _________.

Which one of the following field patterns represents a TEM wave travelling in the positive x direction?

Q. No. 36 – 65 Carry Two Marks Each

Q.

The system of linear equations

The maximum value of the determinant among all 2×2 real symmetric matrices with trace 14
is ________.

A series LCR circuit is operated at a frequency different from its resonant frequency. The operating frequency is such that the current leads the supply voltage. The magnitude of current is half the value at resonance. If the values of L, C and R are 1 H, 1 F and 1?? ,
respectively, the operating angular frequency (in rad/s) is ________.

Imp : you should answer only the numneric value

In the h-parameter model of the 2-port network given in the figure shown, the value of h22 (in
S) is _____ .

Imp : you should answer only the numneric value

In the figure shown, the capacitor is initially uncharged. Which one of the following
expressions describes the current I(t) (in mA) for t > 0?

In the magnetically coupled circuit shown in the figure, 56 % of the total flux emanating from one coil links the other coil. The value of the mutual inductance (in H) is ______ .

Assume electronic charge q = 1.6×10^-19 C, kT/q = 25 mV and electron mobility  μ_n = 1000 cm²/V-s. If the concentration gradient of electrons injected into a P-type silicon sample is 1×10²¹/cm⁴, the magnitude of electron diffusion current density (in A/cm²) is _________.

Consider an abrupt PN junction (at T = 300 K) shown in the figure. The depletion region
width Xn on the N-side of the junction is 0.2 μm and the permittivity of silicon ( ε_si )  is
1.044×10^-12 F/cm. At the junction, the approximate value of the peak electric field (in kV/cm)
is _________.

Imp : you should answer only the numneric value

When a silicon diode having a doping concentration of N_A = 9 × 10¹⁶ cm^-3 on p-side and N_D = 1 × 10¹⁶ cm^-3 on n-side is reverse biased, the total depletion width is found to be 3μm . Given that the permittivity of silicon is 1.04 × 10^–12 F/cm, the depletion width on the p-side and the
maximum electric field in the depletion region, respectively, are

The diode in the circuit shown has V_on = 0.7 Volts but is ideal otherwise.
If V_i = 5sin (ωt) Volts, the minimum and maximum values of V_O (in Volts) are, respectively

For the n-channel MOS transistor shown in the figure, the threshold voltage V_Th is 0.8 V.
Neglect channel length modulation effects. When the drain voltage V_D = 1.6 V, the drain
current I_D was found to be 0.5 mA. If V_D is adjusted to be 2 V by changing the values of R
and V_DD, the new value of ID (in mA) is

For the MOSFETs shown in the figure, the threshold voltage |V_t| = 2V and

. The value of ID (in mA) is ________.

In the circuit shown, choose the correct timing diagram of the output (y) from the given
waveforms W1, W2, W3 and W4.

The outputs of the two flip-flops Q1, Q2 in the figure shown are initialized to 0,0. The
sequence generated at Q1 upon application of clock signal is

For the 8085 microprocessor, the interfacing circuit to input 8-bit digital data (DI₀ – DI₇)
from an external device is shown in the figure. The instruction for correct data transfer is

Consider a discrete-time signal

If y[n] is the convolution of x[n] with itself, the value of y[4] is _________.

The input-output relationship of a causal stable LTI system is given as

y[n] = αy[n −1] + βx[n]

If the impulse response h[n] of this system satisfies the condition relationship between α and β is

The value of the integral  is ______________________

Imp : you should answer only the numneric value

An unforced liner time invariant (LTI) system is represented by

If the initial conditions are x₁(0) = 1 and x₂(0) = -1, the solution of the state equation is

The Bode asymptotic magnitude plot of a minimum phase system is shown in the figure

If the system is connected in a unity negative feedback configuration, the steady state error of
the closed loop system, to a unit ramp input, is_________.

Consider the state space system expressed by the signal flow diagram shown in the figure.

The corresponding system is

The input to a 1-bit quantizer is a random variable X with pdf  f_x ⁽x) = 2e^−2x for x0 and
 f_x(x) = 0 for x < 0 , for x < 0 For outputs to be of equal probability, the quantizer threshold
should be _____.

Coherent orthogonal binary FSK modulation is used to transmit two equiprobable symbol  waveforms

where α = 4mV. Assume an AWGN channel with two-sided noise power spectral density  N₀/2=0.5 x 10^-12 W/Hz. Using an optimal receiver and the relation  du the bit error probability for a data
rate of 500 kbps is

The power spectral density of a real stationary random process .X(t) is given by

In the figure, M(f) is the Fourier transform of the message signal .m(t) where A = 100 Hz and
B = 40 Hz. Given v(t) = cos (2πf_ct) and w(t ) = cos( 2π (f_c + A) t) , where f_c > A The cutoff
frequencies of both the filters are F_c

The bandwidth of the signal at the output of the modulator (in Hz) is _____.

Imp : you should answer only the numneric value

If the electric field of a plane wave is

the polarization state of the plane wave is

In the transmission line shown, the impedance Zin (in ohms) between node A and the ground
is _________.

Imp : you should answer only the numneric value

For a rectangular waveguide of internal dimensions a × b(a > b) , the cut-off frequency for
the TE₁₁ mode is the arithmetic mean of the cut-off frequencies for TE₁₀ mode and TE₂₀
mode. If a = √5 cm, the value of b (in cm) is _____.

The real part of an analytic function f(z) where z =.x + jy is given by e^-y cos(x). The
imaginary part of f(z) is