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2014| SET 2 - (ECE GATE Exam) - Previous Question Paper Solution

GATE Exam Previous Year Question Paper Solution Electronics and Communication (ECE) - 2014 (SET 2)

39 Questions Published
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Questions

Question 1 Multiple Choice (Single Answer)

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

Communication and interpersonal skills are ________ important in their own ways.

  1. Each
  2. Both
  3. All
  4. Either
Question 2 Multiple Choice (Single Answer)

Which of the options given below best completes the following sentence?

She will feel much better if she _________

  1. Will get some rest
  2. Gets some rest
  3. Will be getting some rest
  4. Is getting some rest
Question 3 Multiple Choice (Single Answer)

Find the odd one in the following group.

Q, W, Z, B B, H, K, M W, C, G, J M, S, V, X

  1. Q, W, Z, B
  2. B, H, K, M
  3. W, C, G, J
  4. M, S, V, X
Question 4 Multiple Choice (Single Answer)

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?

  1. The number of red lights is equal to the number of blue lights.
  2. The number of green lights is equal to the number of yellow lights.
  3. The sum of red and green lights is equal to sum of the yellow and blue lights.
  4. The sum of red and blue lights is equal to the sum of green and yellow lights.
Question 5 Multiple Choice (Single Answer)

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?

  1. 4 times the draining rate
  2. 3 times the draining rate
  3. 2.5 times the draining rate
  4. 2 times the draining rate
Question 6 Multiple Choice (Single Answer)

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?

  1. Item 2
  2. Item 3
  3. Item 6
  4. Item 5
Question 7 Multiple Choice (Single Answer)

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 $\rightarrow$ 0.167
2 $\rightarrow$ 0.167
3 $\rightarrow$ 0.152
4 $\rightarrow$ 0.166
5 $\rightarrow$ 0.168
6 $\rightarrow$ 0.180

We call this die

  1. irregular
  2. biased
  3. gaussian
  4. insufficient
Question 8 Multiple Choice (Single Answer)

The value of $\lim\limits_{x \rightarrow \infty}$$\bigg(1 + \frac{1}{x}\bigg)^2$

  1. ln 2
  2. 1.0
  3. e
  4. $\infty$
Question 9 Multiple Choice (Single Answer)

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

  1. in series with a current source
  2. in parallel with a voltage source
  3. in series with a voltage source
  4. in parallel with a current source
Question 10 Multiple Choice (Single Answer)

Choose the most appropriate pair of words from the options given below to complete the following sentence.

She could not _________ the thought of _________ the election to her bitter rival.

  1. Bear, loosing
  2. Bare, loosing
  3. Bear, losing
  4. Bare, losing
Question 11 Multiple Choice (Single Answer)

For 0 $\leq$ t < $\infty$, the maximum value of the function f(t) = e–t – 2e–2t occurs at

  1. t = loge 4
  2. t = loge 2
  3. t = 0
  4. t = loge 8
Question 12 Multiple Choice (Single Answer)

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

  1. low pressure chemical vapour deposition
  2. low energy sputtering
  3. low temperature dry oxidation
  4. low energy ion-implantation
Question 13 Multiple Choice (Single Answer)

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

  1. Voltage shunt feedback
  2. Current series feedback
  3. Current shunt feedback
  4. Voltage series feedback
Question 14 Multiple Choice (Single Answer)

An increase in the base recombination of a BJT will increase

  1. the common emitter dc current gain b
  2. the breakdown voltage BVCEO
  3. the unity-gain cut-off frequency fT
  4. none of these
Question 15 Multiple Choice (Single Answer)

In the differential amplifier shown in the figure, the magnitudes of the common mode and differential-mode gains are ACM and Ad, respectively. If the resistance RE is increased, then

  1. ACM increases
  2. common-mode rejection ratio increases
  3. Ad increases
  4. common-mode rejection ratio decreases
Question 16 Multiple Choice (Single Answer)

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

  1. 2(n – 1)
  2. n/2
  3. 2n
  4. 2(n–1)
Question 17 Multiple Choice (Single Answer)

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

  1. M = X $\oplus$ Y, N = XY
  2. M = XY, N = X $\oplus$ Y
  3. M = $\bar{X}$ Y, N = X $\oplus$ Y
  4. M = X$\bar{Y}$, N = $\overline{X \oplus Y}$
Question 18 Multiple Choice (Single Answer)

Let x[n] = x[-n]. Let X(z) be the z-transform of x[n]. If 0.5 + j0.25 is a zero of X(z), which one of the following must also be a zero of X(z)?

  1. 0.5 - j0.25
  2. 1/(0.5 + j0.25)
  3. 1/(0.5 - j0.25)
  4. 2 + j4
Question 19 Multiple Choice (Single Answer)

An FIR system is described by the system function

H(z) = 1 + $\frac{7}{2}$ z–1 + $\frac{3}{2}$ z–2

The system is

  1. maximum phase
  2. minimum phase
  3. mixed phase
  4. zero phase
Question 20 Multiple Choice (Single Answer)

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

  1. n0 = 1.5 x 106 cm–3, p0 = 1.5 x 105 cm-3
  2. n0 = 1.5 x 1010 cm–3, p0 = 1.5 x 1015 cm-3
  3. n0 = 2.25 x 1015 cm–3, p0 = 1.5 x 1010 cm-3
  4. n0 = 2.25 x 1015 cm–3, p0 = 1 x 105 cm-3
Question 21 Multiple Choice (Single Answer)

For the following system,

when X1(s) = 0, the transfer function $\frac{Y(s)}{X_2(s)}$ s

  1. $\frac{s + 1}{s^2}$
  2. $\frac{1}{s + 1}$
  3. $\frac{s + 2}{s(s + 1)}$
  4. $\frac{s + 1}{s(s + 2)}$
Question 22 Multiple Choice (Single Answer)

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

  1. E = + 8$\hat{y}$, H = - 4$\hat{z}$
  2. E = - 2$\hat{y}$, H = - 3$\hat{z}$
  3. E = + 2$\hat{z}$, H = + 2$\hat{y}$
  4. E = - 3$\hat{y}$, H = + 4$\hat{z}$
Question 23 Multiple Choice (Single Answer)

The capacity of a band-limited additive white Gaussian noise (AWGN) channel is given by C = Wlog2 $\bigg( 1 + \frac{P}{\sigma^2 W} \bigg)$ bits per second (bps), where W is the channel bandwidth, P is the average power received and $\sigma$2 is the one sided power spectral density of the AWGN. For a fixed $\frac{P}{\sigma^2}$ = 1000 the channel capacity (in kbps) with infinite bandwidth (W $\rightarrow$ 3) is approximately

  1. 1.44
  2. 1.08
  3. 0.72
  4. 0.36
Question 24 Multiple Choice (Single Answer)

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

  1. 01110....
  2. 01010....
  3. 00110....
  4. 01100....
Question 25 Multiple Choice (Single Answer)

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

  1. 0.625
  2. 0.75
  3. 1.125
  4. 1.5
Question 26 Multiple Choice (Single Answer)

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


  1. W1
  2. W2
  3. W3
  4. W4
Question 27 Multiple Choice (Single Answer)

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

  1. MVI A, F8H
  2. IN F8H
  3. OUT F8H
  4. LDA F8F8H
Question 28 Multiple Choice (Single Answer)

The diode in the circuit shown has Von = 0.7 Volts but is ideal otherwise. If Vi = 5 sin (wt) Volts, the minimum and maximum values of Vo (in Volts) are, respectively,

  1. - 5 and 2.7
  2. 2.7 and 5
  3. - 5 and 3.85
  4. 1.3 and 5
Question 29 Multiple Choice (Single Answer)

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?

  1. I (t) = $\frac{5}{3}$ (1 – e–t/r), T = $\frac{2}{3}$ m sec
  2. I (t) = $\frac{5}{2}$ (1 – e–t/r), T = $\frac{2}{3}$ m sec
  3. I (t) = $\frac{5}{3}$ (1 – e–t/r), T = 3 m sec
  4. I (t) = $\frac{5}{2}$ (1 – e–t/r), T = 3 m sec
Question 30 Multiple Choice (Single Answer)

The system of linear equations

$\begin{bmatrix}
\ 2 & 1 & 3 \
\ 3 & 0 & 1 \
\ 1 & 2 & 5 \
\end{bmatrix}$$\begin{bmatrix}
\ a \
\ b \
\ c \
\end{bmatrix}$$\begin{bmatrix}
\ 5 \
\ -4 \
\ 14 \
\end{bmatrix}$

  1. a unique solution
  2. infinitely many solutions
  3. no solution
  4. exactly two solutions
Question 31 Multiple Choice (Single Answer)

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

  1. ey cos (x)
  2. e–y sin (x)
  3. – ey sin(x)
  4. – e–y sin (x)
Question 32 Multiple Choice (Single Answer)

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

$\begin{bmatrix}
\ . \
\ X_1 \
\ . \
X_2 \
\end{bmatrix}$= $\begin{bmatrix}
\ -1 & 0 \
\ 0 & -2 \
\end{bmatrix}$$\begin{bmatrix}
\ X_1 \
\ X_2 \
\end{bmatrix}$

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

  1. x1 (t) = - 1, x2 (t) = 2
  2. x1 (t) = – e-t, x2 (t) = 2 e-t
  3. x1 (t) = - e-t, x2 (t) = – e-2t
  4. x1 (t) = - e-t, x2 (t) = – 2 e-t
Question 33 Multiple Choice (Single Answer)

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

The corresponding system is

  1. always controllable
  2. always observable
  3. always stable
  4. always unstable
Question 34 Multiple Choice (Single Answer)

If the electric field of a plane wave is $\overrightarrow{E}$ (z, t) = x3 cos (wt - kz + 30o) – y4 sin (wt - kz + 45o) (mV/m), the polarization state of the plane wave is

  1. left elliptical
  2. left circular
  3. right elliptical
  4. right circular
Question 35 Multiple Choice (Single Answer)

The input-output relationship of a causal stable LTI system is given as Y[n] = $\alpha$y[n – 1] + $\beta$x[n]

If the impulse response h6n@ of this system satisfies the condition $\sum_{n=0}^\infty h$[n] = 2, the relationship between a and b is

  1. a = 1 - $\beta$/2
  2. a = 1 + $\beta$/2
  3. a = 2$\beta$
  4. a = - 2$\beta$
Question 36 Multiple Choice (Single Answer)

When a silicon diode having a doping concentration of NA = 9 x 10 cm16 on p-side and ND = 1 x 1016 cm-3 on n-side is reverse biased, the total depletion width is found to be 3 $\mu$m. Given that the permittivity of silicon is 1.04 x 10-12 F/cm, the depletion width on the p-side and the maximum electric field in the depletion region, respectively, are

  1. 2.7 $\mu$m and 2.3 x 105 V/cm
  2. 0.3 $\mu$m and 4.15 x 105 V/cm
  3. 0.3 $\mu$m and 0.42 x 105 V/cm
  4. 2.1 $\mu$m and 0.42 x 105 V/cm
Question 37 Multiple Choice (Single Answer)

Coherent orthogonal binary FSK modulation is used to transmit two equiprobable symbol waveforms s1 (t) = acos 2$\pi$f1 t and s2 (t) = $\alpha$cos 2$\pi$f2 t, where $\alpha$ = 4 mV. Assume an AWGN channel with two sided noise power spectral density $\frac{N_0}{2}$ = 0.5 x 10 W/Hz. Using an optimal receiver and the relation Q (v) = $\frac{1}{\sqrt{2 \pi}} \int\limits_v^\infty$$e^{-u^2/2}$ du, the bit error probability for a data rate of 500 kbps is

  1. Q (2)
  2. Q (2 $\sqrt{2}$)
  3. Q (4)
  4. Q (4 $\sqrt{2}$)
Question 38 Multiple Choice (Single Answer)

If the characteristic equation of the differential equation $\frac{d^2 y}{dx^2} + 2 \alpha \frac{dy}{dx} + y = 0$ has two equal roots, then the values of a are

  1. $\pm$ 1
  2. 0, 0
  3. $\pm$ j
  4. $\pm$ 1/2

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