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2015| SET 1 - (ECE GATE Exam) - Previous Question Paper Solution

GATE Exam Previous Year Question Paper Solution Electronics and Communication (ECE) - 2015 (SET 1)

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Questions

Question 1 Multiple Choice (Single Answer)

Choose the word most similar in meaning to the given word:

Educe

  1. Exert
  2. Educate
  3. Extract
  4. Extend
Question 2 Multiple Choice (Single Answer)

Choose the appropriate word/phrase, out of the four options given below, to complete the following sentence:

Frogs _______.

  1. croak
  2. roar
  3. hiss
  4. patter
Question 3 Multiple Choice (Single Answer)

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

The principal presented the chief guest with a _______ as token of appreciation.

  1. momento
  2. memento
  3. momentum
  4. moment
Question 4 Multiple Choice (Single Answer)

If log $x(\frac{5}{7}) = - \frac{1}{3}$, then the value of x is

  1. $\frac{343}{125}$
  2. $\frac{125}{343}$
  3. $\frac{-25}{49}$
  4. $\frac{-49}{25}$
Question 5 Multiple Choice (Single Answer)

Humpty Dumpty sits on a wall every day while having lunch. The wall sometimes breaks. A person sitting on the wall falls if the wall breaks.
Which one of the statements below is logically valid and can be inferred from the above sentences?

  1. Humpty Dumpty always falls while having lunch.
  2. Humpty Dumpty does not fall sometimes while having lunch.
  3. Humpty Dumpty never falls during dinner.
  4. When Humpty Dumpty does not sit on the wall, the wall does not break.
Question 6 Multiple Choice (Single Answer)

The following question presents a sentence, part of which is underlined. Beneath the sentence you will find four ways of phrasing the underlined part. Following the requirements of the standard written English, select the answer that produces the most effective sentence.
Tuberculosis, together with its effects, ranks one of the leading causes of death in India.

  1. ranks as one of the leading causes of death
  2. rank as one of the leading causes of death
  3. has the rank of one of the leading causes of death
  4. are one of the leading causes of death
Question 7 Multiple Choice (Single Answer)

Read the following paragraph and choose the correct statement:

Climate change has reduced human security and threatened human well being. An ignored reality of human progress is that human security largely depends upon environmental security. But on the contrary, human progress seems contradictory to environmental security. To keep up both at the required level is a challenge to be addressed by one and all. One of the ways to curb the climate change may be suitable scientific innovations, while the other may be the Gandhian perspective on small scale progress with focus on sustainability.

  1. Human progress and security are positively associated with environmental security.
  2. Human progress is contradictory to environmental security.
  3. Human security is contradictory to environmental security.
  4. Human progress depends upon environmental security.
Question 8 Multiple Choice (Single Answer)

A region of negative differential resistance is observed in the current voltage characteristics of a silicon PN junction if

  1. both the P-region and N-region are heavily doped
  2. the N-region is heavily doped compared to the P-region
  3. the P-region is heavily doped compared to the N-region
  4. an intrinsic silicon region is inserted between the P-region and the N-region
Question 9 Multiple Choice (Single Answer)

A cube of side 3 units is formed using a set of smaller cubes of side 1 unit. Find the proportion of the number of faces of the smaller cubes visible to that of those which are NOT visible.

  1. 1 : 4
  2. 1 : 3
  3. 1 : 2
  4. 2 : 3
Question 10 Multiple Choice (Single Answer)

Operators $\square$,$\diamond$ and $\rightarrow$ are defined by: a $\square$ b = $\frac{a - b}{a + b}$; a $\diamond$ b = $\frac{a + b}{a - b}$; a $\rightarrow$ b = ab.
Find the value of (66 $\square$ 6) $\rightarrow$ (66 $\diamond$ 6).

  1. -2
  2. -1
  3. 1
  4. 2
Question 11 Multiple Choice (Single Answer)

In the given circuit, the values of V1 and V2 respectively are

  1. 5 V and 25 V
  2. 10 V and 30 V
  3. 15 V and 35 V
  4. 0 V and 20 V
Question 12 Multiple Choice (Single Answer)

The polar plot of the transfer function G(s) = $\frac{10(s+1)}{s + 10}$ for $\leq \omega < \infty$ will be in the

  1. first quadrant
  2. second quadrant
  3. third quadrant
  4. fourth quadrant
Question 13 Multiple Choice (Single Answer)

Let z = x + iy be a complex variable. Consider that contour integration is performed along the unit circle in anticlockwise direction. Which of the following statements is NOT TRUE?

  1. The residue of $\frac{z}{z^2 - 1}$ at z = 1 is $\frac{1}{2}$.
  2. $\oint_c z^2 dz = 0$
  3. $\frac{1}{2 \pi i}\oint_c \frac{1}{z} dz = 1$
  4. $\bar{z}$(complex conjugate of z) is an analytical function.
Question 14 Multiple Choice (Single Answer)

For the circuit with ideal diodes shown in the figure, the shape of the output (Vout) for the given sine wave input (Vin) will be

Question 15 Multiple Choice (Single Answer)

In an 8085 microprocessor, the shift registers which store the result of an addition and the overflow bit are

  1. B and F, respectively
  2. A and F, respectively
  3. H and F, respectively
  4. A and C, respectively
Question 16 Multiple Choice (Single Answer)

Negative feedback in a closed-loop control system does not

  1. reduce the overall gain
  2. reduce bandwidth
  3. improve disturbance rejection
  4. reduce sensitivity to parameter variation
Question 17 Multiple Choice (Single Answer)

A function f(x) = 1 - x2 + x3 is defined in the closed interval [-1, 1]. The value of x in the open interval (-1, 1) for which the mean value theorem is satisfied, is

  1. $\frac{-1}{2}$
  2. $\frac{-1}{3}$
  3. $\frac{1}{3}$
  4. $\frac{1}{2}$
Question 18 Multiple Choice (Single Answer)

The result of the convolution x(-t) $\star$$\delta$(- t - t0 ) is

  1. x(t + t0 )
  2. x(t - t0 )
  3. x(- t + t0 )
  4. x(- t - t0 )
Question 19 Multiple Choice (Single Answer)

A sinusoidal signal of 2 kHz frequency is applied to a delta modulator. The sampling rate and step-size $\triangle$ of the delta modulator are 20,000 samples per second and 0.1V, respectively. To prevent slope overload, the maximum amplitude of the sinusoidal signal (in Volts) is

  1. $\frac{1}{2\pi}$
  2. $\frac{1}{\pi}$
  3. $\frac{2}{\pi}$
  4. $\pi$
Question 20 Multiple Choice (Single Answer)

Consider the signal s(t) = m(t)cos (2$\pi$ fc t) +$\hat{m}$ (t) (2$\pi$fc t), where $\hat{m}$ (t) denotes the Hilbert transform of m(t) and the bandwidth of m(t) is very small compared to fc. The signal s(t) is a

  1. high-pass signal
  2. low-pass signal
  3. band-pass signal
  4. double side-band suppressed carrier signal
Question 21 Multiple Choice (Single Answer)

For the discrete-time system shown in the figure, the poles of the system transfer function are located at

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

Consider a straight, infinitely long, current carrying conductor lying on the z-axis. Which of the following plots (in linear scale) qualitatively represents the dependence of $H_{\phi}$ on r , where $H_{\phi}$ is the magnitude of the azimuthal component of magnetic field outside the conductor and r is the radial distance from the conductor?

Question 23 Multiple Choice (Single Answer)

A source emits bit 0 with probability 1/3 and bit 1 with probability 2/3. The emitted bits are communicated to the receiver. The receiver decides for either 0 or 1 based on the received value R. It is given that the conditional density functions of R are

fR/0 (r) = and fR/1 (r) =

The minimum decision error probability is

  1. 0
  2. $\frac{1}{12}$
  3. $\frac{1}{9}$
  4. $\frac{1}{6}$
Question 24 Multiple Choice (Single Answer)

For the NMOSFET in the circuit shown, the threshold voltage is Vth, where Vth > 0. The source voltage Vss is varied from 0 to VDD. Neglecting the channel length modulation, the drain current ID as a function of Vss is represented by

Question 25 Multiple Choice (Single Answer)

The circuit shown in the figure has an ideal op amp. The oscillation frequency and the condition to sustain the oscillations, respectively, are

  1. $\frac{1}{CR}$ and R1 = R2
  2. $\frac{1}{CR}$ and R1 = 4 R2
  3. $\frac{1}{2CR}$ and R1 = R2
  4. $\frac{1}{2CR}$ and R1 = 4 R2
Question 26 Multiple Choice (Single Answer)

The damping ratio of a series RLC circuit can be expressed as

  1. $\frac{R^2C}{2L}$
  2. $\frac{2L}{R^2C}$
  3. $\frac{R}{2}\sqrt{\frac{C}{L}}$
  4. $\frac{2}{R}\sqrt{\frac{L}{C}}$
Question 27 Multiple Choice (Single Answer)

A plant transfer function is given as G(s) = $\bigg(k_p + \frac{K_i}{s} \bigg) \frac{1}{s(s+2)}$. When the plant operates in a unity feedback configuration, the condition for the stability of the closed loop system is

  1. $K_P > \frac{K_I}{2} > 0$
  2. $2K_I > K_P > 0$
  3. $2K_I < K_P$
  4. $2K_I > K_P$
Question 28 Multiple Choice (Single Answer)

A 3-input majority gate is defined by the logic function M(a, b, c) = ab + bc + ca. Which of the following gates is represented by the function $M(\overline{M(a, b, c)}, M(a, b, \bar{c}),c)$?

  1. 3-input NAND gate
  2. 3-input XOR gate
  3. 3-input NOR gate
  4. 3-input XNOR gate
Question 29 Multiple Choice (Single Answer)

A vector $\overrightarrow{P}$ is given by $\overrightarrow{P}$ =$x^3 y^2 \overrightarrow{a}_z$. Which of the following statements is TRUE?

  1. $\overrightarrow{P}$ is solenoidal, but not irrotational.
  2. $\overrightarrow{P}$ is irrotational, but not solenoidal.
  3. $\overrightarrow{P}$ is neither solenoidal nor irrotational.
  4. $\overrightarrow{P}$ is both solenoidal and irrotational.
Question 30 Multiple Choice (Single Answer)

The solution of the differential equation $\frac{d^2 y}{dt^2} + 2 \frac{dy}{dt} + y = 0$ with y(0) = y’ (0) = 1 is

  1. (2 - t) et
  2. (1 + 2t)e -t
  3. (2 + t)e -t
  4. (1 - 2t)et
Question 31 Multiple Choice (Single Answer)

Which of the following graphs describes the function f (x) = e-x (x2 + x + 1)?

Question 32 Multiple Choice (Single Answer)

The pole-zero diagram of a causal and stable discrete-time system is shown in the figure. The zero at the origin has multiplicity 4. The impulse response of the system is h[n]. If h[0] = 1, we can conclude that

  1. h[n] is real for all n
  2. h[n] is purely imaginary for all n
  3. h[n] is real for only even n
  4. h[n] is purely imaginary for only odd n
Question 33 Multiple Choice (Single Answer)

The longitudinal component of the magnetic field inside an air-filled rectangular waveguide made of a perfect electric conductor is given by the following expression:

Hz (x, y, z, t) = 0.1 cos (25$\pi$x) cos (30.3$\pi$y) x cos (12$\pi$ x 109t - $\beta$z)(A/m)

The cross-sectional dimensions of the waveguide are given as a = 0.08 m and b = 0.033 m. The mode of propagation inside the waveguide is

  1. TM12
  2. TM21
  3. TE21
  4. TE12
Question 34 Multiple Choice (Single Answer)

Two sequences [a, b, c] and [A, B, C] are related as:

where $W_3 = e^{j\frac{2 \pi}{3}}$

If another sequence [p, q, r ] is derived as:

Then, the relationship between the sequences [p, q, r ] and [a, b, c] is

  1. [p, q, r ] = [b, a, c]
  2. [p, q, r ] = [b, c, a]
  3. [p, q, r ] = [c, a, b]
  4. [p, q, r ] = [c, b, a]
Question 35 Multiple Choice (Single Answer)

The Boolean expression F(X, Y, Z) = $\bar{X}Y \bar{Z} + X\bar{Y}\bar{Z} + XY\bar{Z} + XYZ$ converted into the canonical product of sum (POS) form is

  1. (X + Y + Z) (X + Y + $\bar{Z}$) (X + Y + $\bar{Z}$) ($\bar{X}$ + Y + $\bar{Z}$)
  2. (X + $\bar{Y}$ + Z) ($\bar{X}$ + Y + $\bar{Z}$) ($\bar{X}$ + $\bar{Y}$ + Z) ($\bar{X}$ + $\bar{Y}$ + $\bar{Z}$)
  3. (X + Y + Z) ($\bar{X}$ + Y + $\bar{Z}$) (X + $\bar{Y}$ + Z) ($\bar{X}$ + $\bar{Y}$ + $\bar{Z}$)
  4. (X + $\bar{Y}$ + $\bar{Z}$) (X + Y + Z) (X + $\bar{Y}$ + Z) (X + Y + Z)
Question 36 Multiple Choice (Single Answer)

Suppose A and B are two independent events with probabilities P(A) $\neq$ 0 and P(B) $\neq$ 0. Let $\bar{A}$ and $\bar{B}$ be their complements. Which of the following statements is FALSE?

  1. P(A $\cap$ B) = P(A) P(B)
  2. P$\Big(\frac{A}{B}\Big)$= P(A)
  3. P(A $\cup$ B) = P(A) + P(B)
  4. $P (\bar{A} \cap \bar{B}) = P(\bar{A}) P(\bar{B})$

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