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GATE 2015 ECE - Technical Section Questions

Electronics and Communication Engineering technical questions from GATE 2015 exam covering signals & systems, communications, digital electronics, control systems, electromagnetic theory, and semiconductor physics

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Questions

Question 1 Multiple Choice (Single Answer)

Directions: Carry One Mark Each.

The electric field of a uniform plane electromagnetic wave is

$\overrightarrow{E} = (\overrightarrow{a_z} + j4 \overrightarrow{a_y})exp[j(2 \pi \times 10^7 t - 0.2z)]$

The polarization of the wave is

  1. right handed circular
  2. right handed elliptical
  3. left handed circular
  4. left handed elliptical
Question 2 Multiple Choice (Single Answer)

Directions: Carry One Mark Each.

By performing cascading and/or summing/differencing operations using transfer function blocks G1(s) and G2(s), one cannot realise a transfer function of the form

  1. G1(s)G2(s)
  2. $\frac{G_1(s)}{G_2(s)}$
  3. G1(s)$\bigg( \frac{1}{G_1(s)} + G_2(s) \bigg)$
  4. G1(s)$\bigg( \frac{1}{G_1(s)} - G_2(s) \bigg)$
Question 3 Multiple Choice (Single Answer)

Directions: Carry One Mark Each.

An electric bus has on-board instruments that report the total electricity consumed since the start of the trip as well as the total distance covered. During a single day of operation, the bus travels on stretches M, N, O and P, in that order. The cumulative distance travelled and the corresponding electricity consumption are shown in the table below.

 Stretch| Cumulative distance (km)| Electricity used (kWh) |
| M| 20|12|
| N| 45| 25|
| O| 75| 45|
| P| 100| 57|

Which of the following is the stretch where the electricity consumption per km is the minimum?

  1. M
  2. N
  3. O
  4. P
Question 4 Multiple Choice (Single Answer)

In the figure shown, the output Y is required to be Y = AB + $\overline{CD}$.

The gates G1 and G2 must respectively be

  1. NOR and OR
  2. OR and NAND
  3. NAND and OR
  4. AND and NAND
Question 5 Multiple Choice (Single Answer)

Directions: Carry One Mark Each.

Let the signal f(t) = 0 be outside the intervals T1 and T2, where T1 and T2 are finite. Furthermore, |f(t)| < $\infty$. The region of convergence (ROC) of the signal’s bilateral Laplace transform F(s) is

  1. a parallel strip containing the j$\Omega$ axis
  2. a parallel strip not containing the j$\Omega$ axis
  3. the entire s-plane
  4. a half plane containing the j$\Omega$ axis
Question 6 Multiple Choice (Single Answer)

Directions: Carry One Mark Each.

The bilateral Laplace transform of a function , is

  1. $\frac{a-b}{s}$
  2. $\frac{e^2(a -b)}{I^S}$
  3. $\frac{e^{-as}- e^{-bs}}{s}$
  4. $\frac{e^{s(a - b)}}{s}$
Question 7 Multiple Choice (Single Answer)

Directions: Carry One Mark Each.

The value of x for which all the eigen values of the matrix given below are real is

$\begin{bmatrix}
\ 10 & 5+j & 4 \
\ x & 20 & 2 \
\ 4 & 2 & -10 \
\end{bmatrix}$

  1. 5 + j
  2. 5 – j
  3. 1 – 5j
  4. 1 + 5j
Question 8 Multiple Choice (Single Answer)

Directions: Carry One Mark Each.

The general solution of the differential equation $\frac{dy}{dx} = \frac{1 + cos 2y}{1 - cos 2x}$ is

  1. tan y – cos x = c (c is a constant)
  2. tan x – cot y = c (c is a constant)
  3. tan y + cot x = c (c is a constant)
  4. tan x + cot y = c (c is a constant)
Question 9 Multiple Choice (Single Answer)

Directions: Carry One Mark Each.

The 2-port admittance matrix of the circuit shown is given by

  1. $\begin{bmatrix} \ 0.3 & 0.2 \\ \ 0.2 & 0.3 \\ \end{bmatrix}$
  2. $\begin{bmatrix} \ 15 & 5 \\ \ 5 & 15 \\ \end{bmatrix}$
  3. $\begin{bmatrix} \ 3.33 & 5 \\ \ 5 & 3.33 \\ \end{bmatrix}$
  4. $\begin{bmatrix} \ 0.3 & 0.4 \\ \ 0.4 & 0.3 \\ \end{bmatrix}$
Question 10 Multiple Choice (Single Answer)

Directions: Carry One Mark Each.

The magnitude and phase of the complex Fourier series coefficients ak of a periodic signal x(t) are shown in the figure. Choose the correct answer from the given options.

Notation: C is the set of complex numbers, R is the set of purely real numbers and P is the set of purely imaginary numbers.

  1. x(t) $\epsilon$ R
  2. x(t) $\epsilon$ P
  3. x(t) $\epsilon$ (C – R)
  4. The information given is not sufficient to draw any conclusion about x(t).
Question 11 Multiple Choice (Single Answer)

Directions: Carry One Mark Each.

In an 8085 microprocessor, which of the following instructions change(s) the content of the accumulator?

  1. MOV B and M
  2. PCHL
  3. RNZ
  4. SBI BE (H)
Question 12 Multiple Choice (Single Answer)

Directions: Carry One Mark Each.

If the circuit shown has to function as a clamping circuit, which one of the following conditions should be satisfied for sinusoidal signal of period T?

  1. RC << T
  2. RC = 0.35 T
  3. RC $\approx$ T
  4. RC >> T
Question 13 Multiple Choice (Single Answer)

Directions: Carry One Mark Each.

For the signal flow graph shown in the figure, the value of $\frac{C(s)}{R(s)}$ is

  1. $\frac{1}{1 - G_1G_2H_1 - G_3G_4H_2 - G_2G_3H_3 + G_1G_2G_3G_4H_1H_2}$
  2. $\frac{G_1G_2G_3G_4}{1 + G_1G_2H_1 + G_3G_4H_2 + G_2G_3H_3 + G_1G_2G_3G_4H_1H_2}$
  3. $\frac{1}{1 + G_1G_2H_1 + G_3G_4H_2 + G_2G_3H_3 + G_1G_2G_3G_4H_1H_2}$
  4. $\frac{1}{1 - G_1G_2H_1 - G_3G_4H_2 - G_2G_3H_3 + G_1G_2G_3G_4H_1H_2}$
Question 14 Multiple Choice (Single Answer)

Directions: Carry Two Marks Each.

Let X $\epsilon$ P{0, 1} and Y $\epsilon$ {0, 1} be two independent binary random variables. If P(X = 0) = p and P(Y = 0) = q, then P(X + Y $\geq$ 1) is equal to

  1. pq + (1 – p) (1 – q)
  2. pq
  3. p(1 – q)
  4. 1 – pq
Question 15 Multiple Choice (Single Answer)

Directions: Carry Two Marks Each.

An LC tank circuit consists of an ideal capacitor C that is connected in parallel with a coil of inductance L having an internal resistance R. The resonant frequency of the tank circuit is

  1. $\frac{1}{2 \pi \sqrt{LC}}$
  2. $\frac{1}{2 \pi \sqrt{LC}}\sqrt{1 - R^2 \frac{C}{L}}$
  3. $\frac{1}{2 \pi \sqrt{LC}}\sqrt{1 - \frac{L}{R^2 C}}$
  4. $\frac{1}{2 \pi \sqrt{LC}}\sqrt{1 - R^2 \frac{C}{L}}$
Question 16 Multiple Choice (Single Answer)

Directions: Carry Two Marks Each.

The figure shows a binary counter with synchronous clear input. With the decoding logic shown, the counter works as a

  1. mod-2 counter
  2. mod-4 counter
  3. mod-5 counter
  4. mod-6 counter
Question 17 Multiple Choice (Single Answer)

Directions: Carry Two Marks Each.

The state variable representation of a system is given as

The response y(t) is

  1. sin (t)
  2. 1 - et
  3. 1 - cos(t)
  4. 0
Question 18 Multiple Choice (Single Answer)

Directions: Carry Two Marks Each.

is an independent and identically distributed (i, i, d) random process with Xn equally likely to be +1 or –1. is another random process obtained as Yn = Xn + 0.5 Xn – 1. The autocorrelation function of is another random process obtained as Yn = Xn + 0.5 Xn – 1. The autocorrelation function of denoted by Ry[k] is

Question 19 Multiple Choice (Single Answer)

Directions: Carry Two Marks Each.

Consider the differential equation $\frac{ds}{dt}$ = 10 – 0.2x with initial condition x(0) = 1. The response x(t) for t > 0 is

  1. 2 – e–0.2t
  2. 2 – e0.2t
  3. 50 – 49e–0.2t
  4. 50 – 49e0.2t
Question 20 Multiple Choice (Single Answer)

Directions: Carry Two Marks Each.

Input x(t) and output y(t) of an LTI system are related by the differentiation equation y’’(t) – y’(t) – 6y(t) = x(t). If the system is neither casual nor stable, the impulse response h(t) of the system is

  1. $ \frac{1}{5}e^{3t}u(-t*) +\frac{1}{5}e^{-2t}u(-t)$
  2. $- \frac{1}{5}e^{3t}u(-t) +\frac{1}{5}e^{-2t}u(-t)$
  3. $\frac{1}{5}e^{3t}u^*(-t) -\frac{1}{5}e^{-2t}u(t)$
  4. $- \frac{1}{5}e^{3t}u(-t) -\frac{1}{5}e^{-2t}u(t)$
Question 21 Multiple Choice (Single Answer)

Directions: Carry Two Marks Each.

A zero mean white Gaussian noise having power spectral density of $\frac{N_o}{2}$ is passed through an LTI filter whose impulse response h(t) is shown in the figure. The variance of the filtered noise at t = 4 is

  1. $\frac{3}{2}A^2 N_o$
  2. $\frac{3}{4}A^2 N_o$
  3. A2No
  4. $\frac{1}{2}A^2 N_o$
Question 22 Multiple Choice (Single Answer)

Directions: Carry Two Marks Each.

A function of Boolean variables X, Y and Z is expressed in terms of the minterms as

$F(X, Y, Z) = \sum(1, 2, 5, 6, 7)$

Which of the following products of sums given below is equal to the function F(X, Y, Z)?

  1. $(\bar{X} + \bar{Y}+ \bar{Z}).(\bar{X} + Y + Z).(X + \bar{Y}+\bar{Z})$
  2. $(X + Y + Z).(X + \bar{Y} + \bar{Z}).(\bar{X} + Y + Z)$
  3. $(\bar{X} + \bar{Y} + Z).(\bar{X} + y + \bar{Z}). (X + \bar{Y}+ Z).(X + Y + \bar{Z}).(X + Y + Z)$
  4. $( X + y + \bar{Z}) . (\bar{X} + Y + Z). (\bar{X} + Y + \bar{Z}).(\bar{X} + \bar{Y}+ \bar{Z})$
Question 23 Multiple Choice (Single Answer)

Directions: Carry Two Marks Each.

Consider a binary, digital communication system which uses pulses g(t) and –g(t) for transmitting bits over an AWGN channel. If the receiver uses a matched filter, which of the following pulses will give the minimum probability of bit error?

  1. (A)
  2. (B)
  3. (C)
  4. (D)
Question 24 Multiple Choice (Single Answer)

Directions: Carry Two Marks Each.

A 1-to-8 demultiplexer with data input Din, address inputs S0, S1 and S2 (with S0 as the LSB) and $\overline{y}_o$ to $\overline{y}_7$ as the eight demultiplexed output, is to be designed using two 2 - to - 4 decoders (with enable input $\bar{E}$ and address input A0 and A1). As shown in the figure, Din, S0, S1 and S2 are to be connected to P, Q, R and S, but not necessarily in this order. The respective input connections to P, Q, R and S terminals should be

  1. S2, Din, S0 and S1
  2. S1, Din, S0 and S2
  3. Din, S0, S1 and S2
  4. Din, S2, S0 and S1
Question 25 Multiple Choice (Single Answer)

Directions: Carry Two Marks Each.

The output of a standard second-order system for a unit step input is given as y(t) = 1 – $\frac{2}{\sqrt{3}}$e–t cos$\Big( \sqrt{3t} - \frac{\pi}{6} \Big)$. The transfer function of the system is

  1. $\frac{2}{(s+2)(s + \sqrt{3})}$
  2. $\frac{1}{s^2 + 2s + 1}$
  3. $\frac{3}{s^2 + 2s + 3}$
  4. $\frac{4}{s^2 + 2s + 4}$
Question 26 Multiple Choice (Single Answer)

Directions: Carry Two Marks Each.

The electric field of a plane wave that is propagating in a lossless non-magnetic medium is given by

E(z, t) = ax 5 cos(2$\pi$ x 109 t + $\beta$z) + ay3 cos x (2$\pi$ x 109t + $\beta$z - $\frac{\pi}{2}$)

The polarization is

  1. right hand circular
  2. left hand elliptical
  3. right hand elliptical
  4. linear
Question 27 Multiple Choice (Single Answer)

Directions: Carry Two Marks Each.

The energy band diagram and electron density profile n(x) in a semiconductor are shown in the figure. Assume that n(x) = 105 e$\Big( \frac{q \alpha x}{kT} \Big)$cm–3, with $\alpha$ = 0.1 V/cm and x expressed in cm. Given$\frac{kT}{q}$= 0.026 V, Dn = 36 cm2 s–1, and$\frac{D}{\mu}$=$\frac{kT}{q}$. The electron current density (in A/cm2) at x = 0 is

  1. – 4.4 x 10–2
  2. – 2.2 x 10–2
  3. 0
  4. 2.2 x 10–2
Question 28 Multiple Choice (Single Answer)

Directions: Carry One Mark Each.

The signal cos(10$\pi$t + $\frac{\pi}{4}$) is ideally sampled at a sampling frequency of 15 Hz. The sampled signal is passed through a filter with impulse response $\bigg( \frac{sin (\pi t)}{\pi t} \bigg)$cos$\bigg( 40 \pi t - \frac{\pi}{2} \bigg)$. The filter output is

  1. $\frac{15}{2}$cos$\bigg( 40 \pi t - \frac{\pi}{4} \bigg)$
  2. $\frac{15}{2}\bigg( \frac{sin (\pi t)}{\pi t} \bigg)cos\bigg( 10 \pi t + \frac{\pi}{4} \bigg)$
  3. $\frac{15}{2}cos\bigg( 10 \pi t - \frac{\pi}{4} \bigg)$
  4. $\frac{15}{2}\bigg( \frac{sin (\pi t)}{\pi t} \bigg)cos\bigg( 10 \pi t - \frac{\pi}{2} \bigg)$
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