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2014| SET 1 - (ECE GATE Exam) - Previous Question Paper Solution

GATE Exam Previous Year Question Paper Solution Electronics and Communication (ECE) - 2014 (SET 1)

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Questions

Question 1 Multiple Choice (Single Answer)

Find the odd one from the following group:

W, E, K, O I, Q, W, A F, N, T, X N, V, B, D

  1. W, E, K, O
  2. I, Q, W, A
  3. F, N, T, X
  4. N, V, B, D
Question 2 Multiple Choice (Single Answer)

For matrices of same dimension M, N and scalar c, which one of these properties DOES NOT ALWAYS hold?

  1. (MT)T = M
  2. (cM)T = c(M)T
  3. (M+ N)T = MT + NT
  4. MN = NM
Question 3 Multiple Choice (Single Answer)

Choose the most appropriate word from the options given below to complete the following sentence.

Many ancient cultures attributed disease to supernatural causes. However, modern science has largely helped __________ such notions.

  1. impel
  2. dispel
  3. propel
  4. repel
Question 4 Multiple Choice (Single Answer)

In the ac equivalent circuit shown in the figure, if iin is the input current and RF is very larger, the type of feedback is

  1. voltage-voltage feedback
  2. voltage-current feedback
  3. current-voltage feedback
  4. current-current feedback
Question 5 Multiple Choice (Single Answer)

The statistics of runs scored in a series by four batsmen are provided in the following table. Who is the most consistent batsman of these four?

   
Batsman Average Standard Deviation
K 31.2 5.21
L 46.0 6.35
M 54.4 6.22
N 17.9 5.90
  1. K
  2. L
  3. M
  4. N
Question 6 Multiple Choice (Single Answer)

The exports and imports (in crores of Rs.) of a country from 2000 to 2007 are given in the following bar chart. If the trade deficit is defined as excess of imports over exports, in which year is the trade deficit 1/5th of the exports?

  1. 2005
  2. 2004
  3. 2007
  4. 2006
Question 7 Multiple Choice (Single Answer)

If fixed positive charges are present in the gate oxide of an n-channel enhancement type MOSFET, it will lead to

  1. a decrease in the threshold voltage
  2. channel length modulation
  3. an increase in substrate leakage current
  4. an increase in accumulation capacitance
Question 8 Multiple Choice (Single Answer)

A good current buffer has

  1. low input impedance and low output impedance
  2. low input impedance and high output impedance
  3. high input impedance and low output impedance
  4. high input impedance and high output impedance
Question 9 Multiple Choice (Single Answer)

The Boolean expression $(X + Y)(X + \bar{Y}) + \overline{(X \bar{Y}) + \bar{X}}$ simplifies to

  1. X
  2. Y
  3. XY
  4. X + Y
Question 10 Multiple Choice (Single Answer)

C is a closed path in the z-plane by |z| = 3. The value of the integral $\oint_c \bigg(\frac{z^2 - z + 4j}{z + 2j}\bigg)dz$ is

  1. - 4$\pi$ (1 + j2)
  2. 4$\pi$ (3 - j2)
  3. - 4$\pi$ (3 + j2)
  4. 4$\pi$ (1 - j2)
Question 11 Multiple Choice (Single Answer)

The force on a point charge +q kept at a distance d from the surface of an infinite grounded metal plate in a medium of permittivity e is

  1. 0
  2. $\frac{q^2}{16\pi ed^2}$ away from the plate
  3. $\frac{q^2}{16\pi ed^2}$ towards the plate
  4. $\frac{q^2}{4\pi ed^2}$ towards the plate
Question 12 Multiple Choice (Single Answer)

A two-port network has scattering parameters given by [S] = $\begin{bmatrix}
\ s_{11} & s_{12} \
\ s_{21} & s_{22} \
\end{bmatrix}$. If the port-2 of the two port is short circuited, the s11 parameter for the resultant one port network is

  1. $\frac{s_{11}-s_{11}s_{22}+S_{12}s_{21}}{1 + s_{22}}$
  2. $\frac{S_{11} + s_{11}s_{22} - s_{12}s_{21}}{1 + s_{22}}$
  3. $\frac{S_{11} + s_{11}s_{22} - s_{12}s_{21}}{1 + s_{22}}$
  4. $\frac{S_{11} - s_{11}s_{22} + s_{12}s_{21}}{1 - s_{22}}$
Question 13 Multiple Choice (Single Answer)

In the following circuit employing pass transistor logic, all NMOS transistors are identical with a threshold voltage of 1V. Ignoring the body-effect, the output voltages at P, Q and R are,

  1. 4 V, 3 V, 2 V
  2. 5 V, 5 V, 5 V
  3. 4 V, 4 V, 4 V
  4. 5 V, 4 V, 3 V
Question 14 Multiple Choice (Single Answer)

A 230 V rms source supplies power to two loads connected in parallel. The first load draws 10 kW at 0.8 leading power factor and the second one draws 10 kVA at 0.8 lagging power factor. The complex power delivered by the source is

  1. (18 + j1.5) kVA
  2. (18 - j1.5) kVA
  3. (20 + j1.5) kVA
  4. (20 - j1.5) kVA
Question 15 Multiple Choice (Single Answer)

For a function g(t), it is given that $\int\limits_{-\infty}^{+ \infty}$g(t) e-jwt dt = we-2w2 for any real value w. if y(t) = $\int\limits_{-\infty}^{t}$g(T), then $\int\limits_{-\infty}^{+\infty}$y(t) dt is

  1. 0
  2. - j
  3. $-\frac{j}{2}$
  4. $\frac{j}{2}$
Question 16 Multiple Choice (Single Answer)

A discrete time signal x[n] = sin ($\pi^2$ n), n being an integer, is

  1. periodic with period $\pi$
  2. periodic with period $\pi^2$
  3. periodic with period $\frac{\pi}{2}$
  4. not periodic
Question 17 Multiple Choice (Single Answer)

In the circuit shown, the op-amp has finite input impedance, infinite voltage gain and zero input offset voltage. The output voltage Vout is

  1. – I2 (R1 + R2)
  2. I2 R2
  3. I1 R2
  4. – I1(R1 + R2)
Question 18 Multiple Choice (Single Answer)

The doping concentrations on the p-side and n-side of a silicon diode are 1 x 1016 cm-3 and 1 x 1017 cm-3, respectively. A forward bias of 0.3 V is applied to the diode. At T = 300 K, the intrinsic carrier concentration of silicon ni = 1.5 x 1010 cm-3 and $\frac{kT}{q}$ = 26 m V. The electron concentration at the edge of the depletion region on the p-side is

  1. 2.3 x 109 cm-3
  2. 1 x 1016 cm-3
  3. 1 x 1017 cm-3
  4. 2.25 x 106 cm-3
Question 19 Multiple Choice (Single Answer)

The digital logic shown in the figure satisfies the given state diagram when Q1 is connected to input A of the XOR gate.


Suppose the XOR gate is replaced by an XNOR gate. Which one of the following options preserves the state diagram?

  1. Input A is connected to $\overline{Q_2}$
  2. Input A is connected to $\overline{Q_2}$
  3. Input A is connected to $\overline{Q_1}$ and S is complemented
  4. Input A is connected to $\overline{Q_1}$
Question 20 Multiple Choice (Single Answer)

A system is described by the following differential equation, where u(t) is the input to the system and y(t) is the output of the system.
$\begin{matrix}
\ . \
\ y \
\end{matrix}$ (t) + 5y(t) = u(t)
when y(0) = 1 and u(t) is a unit step function, y(t) is

  1. 0.2 + 0.8e-5t
  2. 0.2 - 0.2e-5t
  3. 0.8 + 0.2e-5t
  4. 0.8 - 0.8e-5t
Question 21 Multiple Choice (Single Answer)

Consider the Boolean function, F(w, x, y, z) = wy + xy + $\bar{w}$xyz + $\bar{w}$$\bar{x}$y + xz + $\overline{XYZ}$. Which one of the following is the complete set of essential prime implicants?

  1. w, y, xz, $\overline{XZ}$
  2. w, y, xz
  3. y, $\overline{XYZ}$
  4. y, xz, $\overline{XZ}$
Question 22 Multiple Choice (Single Answer)

Let x [n] = $\bigg(- \frac{1}{9} \bigg)^n$ u (n) – $\bigg(- \frac{1}{3} \bigg)^n$ u (– n – 1). The Region of Convergence (ROC) of the z-transform of x [n]

  1. is |z| > $\frac{1}{9}$
  2. is |z| < $\frac{1}{3}$
  3. is $\frac{1}{3}$ > |z| > $\frac{1}{9}$
  4. Does not exist
Question 23 Multiple Choice (Single Answer)

For the following feedback system G(s) = $\bigg( \frac{1}{(s + 1)(s+2)} \bigg)$. The 2% settling time of the step response is required to be less than 2 seconds.


Which one of the following compensators C(s) achieves this?

  1. 3$\bigg( \frac{1}{s + 5} \bigg)$
  2. 5$\bigg( \frac{0.03}{s} + 1\bigg)$
  3. 2(s + 4)
  4. 4$\bigg( \frac{s +8}{s + 3} \bigg)$
Question 24 Multiple Choice (Single Answer)

Let X be a real-valued random variable with E[X] and E[X2] denoting the mean values of X and X2, respectively. The relation which always holds true is

  1. (E[X])2 > E[X2]
  2. (E[X])2 $\geq$ (E[X])2
  3. E[X2] = (E[X])2
  4. E[X2] > (E[X])2
Question 25 Multiple Choice (Single Answer)

Consider the state space model of a system, as given below:

$\begin{bmatrix}
\ . \
\ x_1 \
\ . \
\ x_2 \
\ . \
\ x_3 \
\end{bmatrix}$ = $\begin{bmatrix}
\ -1 & 1 & 0 \
\ 0 & -1 & 0 \
\ 0 & 0 &-2 \
\end{bmatrix}$$\begin{bmatrix}
\ x_1 \
\ x_2 \
\ x_3 \
\end{bmatrix}$ + $\begin{bmatrix}
\ 0 \
\ 4 \
\ 0 \
\end{bmatrix}$ u; y = $\begin{bmatrix}
\ 1 & 1 & 1\
\end{bmatrix}$$\begin{bmatrix}
\ x_1 \
\ x_2 \
\ x_3 \
\end{bmatrix}$

The system is

  1. controllable and observable
  2. uncontrollable and observable
  3. uncontrollable and unobservable
  4. controllable and unobservable
Question 26 Multiple Choice (Single Answer)

For a parallel plate transmission line, let v be the speed of propagation and Z be the characteristic impedance. Neglecting fringe effects, a reduction of the spacing between the plates by a factor of two results in

  1. halving of v and no change in Z
  2. no changes in v and halving of Z
  3. no change in both v and Z
  4. halving of both v and Z
Question 27 Multiple Choice (Single Answer)

The Taylor series expansion of 3 sinx + 2 cos x is

  1. 2 + 3x – x2 – $\frac{x^3}{2}$ + ………
  2. 2 – 3x + x2 – $\frac{x^3}{2}$ + ………
  3. 2 + 3x + x2 + $\frac{x^3}{2}$ + ………
  4. 2 + 3x – x2 + $\frac{x^3}{2}$ + ………
Question 28 Multiple Choice (Single Answer)

The output F in the digital logic circuit shown in the figure is

  1. F = $\overline{X}$YZ + X$\overline{Y}$Z
  2. F = $\overline{X}$Y$\overline{Z}$ + X$\overline{YZ}$
  3. F = $\overline{XY}$Z + XYZ
  4. F = $\overline{XYZ}$ + XYZ
Question 29 Multiple Choice (Single Answer)

Consider the feedback system shown in the figure. The Nyquist plot of G(s) is also shown. Which one of the following conclusions is correct?

  1. G(s) is an all pass filter
  2. G(s) is a strictly proper transfer function
  3. G(s) is a stable and minimum phase transfer function
  4. The closed-loop system is unstable for sufficiently large and positive k
Question 30 Multiple Choice (Single Answer)

Consider a random process X(t) = $\sqrt{2}$ sin(2$\pi$t + $\varphi$), where the random phase $\varphi$ is uniformly distributed in the interval [0, 2$\pi$]. The auto-correlation E[X(t1) X(t2)] is

  1. cos(2$\pi$ (t1 + t2))
  2. sin(2$\pi$ (t1 – t2))
  3. sin(2$\pi$ (t1 + t2))
  4. cos(2$\pi$ (t1 – t2))

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