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GATE EC 2014 Set 4

All 65 solved GATE EC 2014 Set 4 questions in exam order. Open a question, commit to an answer, and learn from the step-by-step solution. One question at a time.

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Questions

65

Paper marks

100

Question formats

2

MCQ · NAT

Revision mode

Self-paced

No timer. Focus on understanding.

Difficulty mixEasy 27Medium 33Hard 5

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65 of 65 questions

General Aptitude (GA)

10
  1. Think it through. Then check your answer.

    Question

    Which of the following options is the closest in meaning to the word underlined in the sentence below?
    In a democracy, everybody has the freedom to disagree with the government.
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    Question

    After the discussion, Tom said to me, 'Please revert!'. He expects me to _________.
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    Question

    While receiving the award, the scientist said, "I feel vindicated". Which of the following is closest in meaning to the word ‘vindicated’?
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    Question

    Let f(x,y)=xnym=Pf(x, y) = x^n y^m = P. If xx is doubled and yy is halved, the new value of ff is
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    Question

    In a sequence of 12 consecutive odd numbers, the sum of the first 5 numbers is 425. What is the sum of the last 5 numbers in the sequence?
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    Question

    Find the next term in the sequence: 13M, 17Q, 19S, ___
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    Question

    If ‘KCLFTSB’ stands for ‘best of luck’ and ‘SHSWDG’ stands for ‘good wishes’, which of the following indicates ‘ace the exam’?
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    Question

    Industrial consumption of power doubled from 2000-2001 to 2010-2011. Find the annual rate of increase in percent assuming it to be uniform over the years.
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    Question

    A firm producing air purifiers sold 200 units in 2012. The following pie chart presents the share of raw material, labour, energy, plant & machinery, and transportation costs in the total manufacturing cost of the firm in 2012. The expenditure on labour in 2012 is Rs. 4,50,000. In 2013, the raw material expenses increased by 30% and all other expenses increased by 20%. What is the percentage increase in total cost for the company in 2013?
    Pie chart showing cost distribution for 2012: Transportation 10%, Labour 15%, Raw Material 20%, Energy 25%, Plant and machinery 30%
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    Question

    A five digit number is formed using the digits 1, 3, 5, 7 and 9 without repeating any of them. What is the sum of all such possible five digit numbers?
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ELECTRONICS AND COMMUNICATION ENGINEERING – EC

55
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    Question

    The series ∑n=0∞1n!\sum_{n=0}^{\infty} \frac{1}{n!} converges to
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    Question

    The magnitude of the gradient for the function f(x,y,z)=x2+3y2+z3f(x, y, z) = x^2 + 3y^2 + z^3 at the point (1,1,1)(1,1,1) is ________.
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    Question

    Let XX be a zero mean unit variance Gaussian random variable. E[∣X∣]E[|X|] is equal to ________.
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    Question

    If aa and bb are constants, the most general solution of the differential equation d2xdt2+2dxdt+x=0\frac{d^2x}{dt^2} + 2\frac{dx}{dt} + x = 0 is
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    Question

    The directional derivative of f(x,y)=xy2(x+y)f(x, y) = \frac{xy}{\sqrt{2}}(x + y) at (1,1)(1, 1) in the direction of the unit vector at an angle of π4\frac{\pi}{4} with y-axis, is given by ______ .
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    Question

    The circuit shown in the figure represents a
    Circuit diagram showing a dependent current source controlled by an input current $I_i$
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    Question

    The magnitude of current (in mA) through the resistor R2R_2 in the figure shown is_______.
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    Question

    At T=300 KT = 300\text{ K}, the band gap and the intrinsic carrier concentration of GaAs are 1.42 eV1.42\text{ eV} and 106 cm−310^6\text{ cm}^{-3}, respectively. In order to generate electron hole pairs in GaAs, which one of the wavelength (λC\lambda_C) ranges of incident radiation, is most suitable? (Given that: Plank’s constant is 6.62×10−34 J-s6.62 \times 10^{-34}\text{ J-s}, velocity of light is 3×1010 cm/s3 \times 10^{10}\text{ cm/s} and charge of electron is 1.6×10−19 C1.6 \times 10^{-19}\text{ C})
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    Question

    In the figure, ln⁡(ρi)\ln(\rho_i) is plotted as a function of 1/T1/T, where ρi\rho_i is the intrinsic resistivity of silicon, TT is the temperature, and the plot is almost linear.
    plot of ln(rho_i) vs 1/T
    The slope of the line can be used to estimate
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    Question

    The cut-off wavelength (in μ\mu m) of light that can be used for intrinsic excitation of a semiconductor material of bandgap Eg=1.1E_g = 1.1 eV is ________
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    Question

    If the emitter resistance in a common-emitter voltage amplifier is not bypassed, it will
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    Question

    Two silicon diodes, with a forward voltage drop of 0.7 V, are used in the circuit shown in the figure. The range of input voltage ViV_i for which the output voltage Vo=ViV_o = V_i, is
    Circuit diagram with two diodes and voltage sources
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    Question

    The circuit shown represents
    Op-amp circuit with resistors and capacitors
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    Question

    For a given sample-and-hold circuit, if the value of the hold capacitor is increased, then
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    Question

    In the circuit shown in the figure, if C=0C = 0, the expression for YY is
    Logic gate circuit with inputs A, B, and C
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    Question

    The output (Y) of the circuit shown in the figure is
    CMOS logic circuit with PMOS and NMOS transistors
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    Question

    A Fourier transform pair is given by(23)nu[n+3]↔FTAe−j6πf1−(23)e−j2πf\left(\frac{2}{3}\right)^n u[n+3] \xleftrightarrow{FT} \frac{A e^{-j6\pi f}}{1 - \left(\frac{2}{3}\right) e^{-j2\pi f}}where u[n]u[n] denotes the unit step sequence. The values of AA is _________.
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    Question

    A real-valued signal x(t)x(t) limited to the frequency band ∣f∣≤W2|f| \leq \frac{W}{2} is passed through a linear time invariant system whose frequency response isH(f)={e−j4πf,∣f∣≤W20,∣f∣>W2H(f) = \begin{cases} e^{-j4\pi f}, & |f| \leq \frac{W}{2} \\ 0, & |f| > \frac{W}{2} \end{cases}The output of the system is
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    Question

    The sequence x[n]=0.5nu[n]x[n] = 0.5^n u[n], where u[n]u[n] is the unit step sequence, is convolved with itself to obtain y[n]y[n]. Then ∑n=−∞+∞y[n]\sum_{n=-\infty}^{+\infty} y[n] is _______.
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    Question

    In a Bode magnitude plot, which one of the following slopes would be exhibited at high frequencies by a 4th4^{th} order all-pole system?
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    Question

    For the second order closed-loop system shown in the figure, the natural frequency (in rad/s) is
    Block diagram of a unity negative feedback system with forward path transfer function $G(s) = \frac{4}{s(s+4)}$
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    Question

    If calls arrive at a telephone exchange such that the time of arrival of any call is independent of the time of arrival of earlier or future calls, the probability distribution function of the total number of calls in a fixed time interval will be
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    Question

    In a double side-band (DSB) full carrier AM transmission system, if the modulation index is doubled, then the ratio of total sideband power to the carrier power increases by a factor of ______.
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    Question

    For an antenna radiating in free space, the electric field at a distance of 1 km is found to be 12 mV/m. Given that intrinsic impedance of the free space is 120πΩ120\pi \Omega, the magnitude of average power density due to this antenna at a distance of 2 km from the antenna (in nW/m2nW/m^2) is ____.
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    Question

    Match Column A with Column B.
    Column AColumn B
    1. Point electromagnetic sourceP. Highly directional
    2. Dish antennaQ. End fire
    3. Yagi-Uda antennaR. Isotropic
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    Question

    With initial values y(0)=y′(0)=1y(0) = y'(0) = 1, the solution of the differential equation d2ydx2+4dydx+4y=0\frac{d^2y}{dx^2} + 4\frac{dy}{dx} + 4y = 0 at x=1x = 1 is _____.
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    Question

    Parcels from sender S to receiver R pass sequentially through two post-offices. Each post-office has a probability 15\frac{1}{5} of losing an incoming parcel, independently of all other parcels. Given that a parcel is lost, the probability that it was lost by the second post-office is_________.
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    Question

    The unilateral Laplace transform of f(t)f(t) is 1s2+s+1\frac{1}{s^2+s+1}. Which one of the following is the unilateral Laplace transform of g(t)=t⋅f(t)g(t) = t \cdot f(t)?
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    Question

    For a right angled triangle, if the sum of the lengths of the hypotenuse and a side is kept constant, in order to have maximum area of the triangle, the angle between the hypotenuse and the side is
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    Question

    The steady state output of the circuit shown in the figure is given by y(t)=A(ω)sin⁡(ωt+ϕ(ω))y(t) = A(\omega) \sin(\omega t + \phi(\omega)). If the amplitude ∣A(ω)∣=0.25|A(\omega)| = 0.25, then the frequency ω\omega is
    RC circuit with input $\sin(\omega t)$ and output $y(t)$
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    Question

    In the circuit shown in the figure, the value of vo(t)v_o(t) (in Volts) for t→∞t \to \infty is _____
    A circuit diagram with current sources, resistors, and an inductor.
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    Question

    The equivalent resistance in the infinite ladder network shown in the figure, is ReR_e.
    An infinite ladder network with resistors.
    The value of Re/RR_e/R is _____
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    Question

    For the two-port network shown in the figure, the impedance (ZZ) matrix (in Ω\Omega) is
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    Question

    Consider a silicon sample doped with ND=1×1015/cm3N_D = 1 \times 10^{15}/\text{cm}^3 donor atoms. Assume that the intrinsic carrier concentration ni=1.5×1010/cm3n_i = 1.5 \times 10^{10}/\text{cm}^3. If the sample is additionally doped with NA=1×1018/cm3N_A = 1 \times 10^{18}/\text{cm}^3 acceptor atoms, the approximate number of electrons/cm3\text{cm}^3 in the sample, at T=300T=300 K, will be ______.
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    Question

    Consider two BJTs biased at the same collector current with area A1=0.2μm×0.2μmA_1 = 0.2 \mu\text{m} \times 0.2 \mu\text{m} and A2=300μm×300μmA_2 = 300 \mu\text{m} \times 300 \mu\text{m}. Assuming that all other device parameters are identical, kT/q=26 mVkT/q = 26 \text{ mV}, the intrinsic carrier concentration is 1×1010 cm−31 \times 10^{10} \text{ cm}^{-3}, and q=1.6×10−19 Cq = 1.6 \times 10^{-19} \text{ C}, the difference between the base-emitter voltages (in mV) of the two BJTs (i.e., VBE1−VBE2V_{BE1} - V_{BE2}) is _____.
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    Question

    An N-type semiconductor having uniform doping is biased as shown in the figure.
    A block of N-type semiconductor with a potential $V$ applied to the left terminal and the right terminal grounded.
    If ECE_C is the lowest energy level of the conduction band, EVE_V is the highest energy level of the valence band and EFE_F is the Fermi level, which one of the following represents the energy band diagram for the biased N-type semiconductor?
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    Question

    Consider the common-collector amplifier in the figure (bias circuitry ensures that the transistor operates in forward active region, but has been omitted for simplicity). Let ICI_C be the collector current, VBEV_{BE} be the base-emitter voltage and VTV_T be the thermal voltage. Also, gmg_m and ror_o are the small-signal transconductance and output resistance of the transistor, respectively. Which one of the following conditions ensures a nearly constant small signal voltage gain for a wide range of values of RER_E?
    common-collector amplifier circuit
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    Question

    A BJT in a common-base configuration is used to amplify a signal received by a 50 Ω\Omega antenna. Assume kT/q=25kT/q = 25 mV. The value of the collector bias current (in mA) required to match the input impedance of the amplifier to the impedance of the antenna is________.
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    Question

    For the common collector amplifier shown in the figure, the BJT has high β\beta, negligible VCE(sat)V_{CE(sat)}, and VBE=0.7V_{BE} = 0.7 V. The maximum undistorted peak-to-peak output voltage vov_o (in Volts) is _______.
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    Question

    An 8-to-1 multiplexer is used to implement a logical function YY as shown in the figure. The output YY is given by
    8-to-1 multiplexer circuit diagram
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    Question

    A 16-bit ripple carry adder is realized using 16 identical full adders (FA) as shown in the figure. The carry-propagation delay of each FA is 12 ns and the sum-propagation delay of each FA is 15 ns. The worst case delay (in ns) of this 16-bit adder will be __________.
    16-bit ripple carry adder diagram
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    Question

    An 8085 microprocessor executes “STA 1234H” with starting address location 1FFEH (STA copies the contents of the Accumulator to the 16-bit address location). While the instruction is fetched and executed, the sequence of values written at the address pins A15−A8A_{15} - A_8 is
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    Question

    A stable linear time invariant (LTI) system has a transfer function H(s)=1s2+s−6H(s) = \frac{1}{s^2+s-6}. To make this system causal it needs to be cascaded with another LTI system having a transfer function H1(s)H_1(s). A correct choice for H1(s)H_1(s) among the following options is
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    Question

    A causal LTI system has zero initial conditions and impulse response h(t)h(t). Its input x(t)x(t) and output y(t)y(t) are related through the linear constant-coefficient differential equationd2y(t)dt2+αdy(t)dt+α2y(t)=x(t).\frac{d^2y(t)}{dt^2} + \alpha \frac{dy(t)}{dt} + \alpha^2 y(t) = x(t).Let another signal g(t)g(t) be defined asg(t)=α2∫0th(τ)dτ+dh(t)dt+αh(t).g(t) = \alpha^2 \int_0^t h(\tau) d\tau + \frac{dh(t)}{dt} + \alpha h(t).If G(s)G(s) is the Laplace transform of g(t)g(t), then the number of poles of G(s)G(s) is _____.
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    Question

    The NN-point DFT XX of a sequence x[n]x[n], 0≤n≤N−10 \leq n \leq N - 1 is given by X[k]=1N∑n=0N−1x[n]e−j2πNnk,0≤k≤N−1.X[k] = \frac{1}{\sqrt{N}} \sum_{n=0}^{N-1} x[n]e^{-j \frac{2\pi}{N} nk}, 0 \leq k \leq N - 1.Denote this relation as X=DFT(x)X = DFT(x). For N=4N = 4, which one of the following sequences satisfies DFT(DFT(x))=xDFT(DFT(x)) = x?
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    Question

    The state transition matrix ϕ(t)\phi(t) of a system [x˙1x˙2]=[0100][x1x2]\begin{bmatrix} \dot{x}_1 \\ \dot{x}_2 \end{bmatrix} = \begin{bmatrix} 0 & 1 \\ 0 & 0 \end{bmatrix} \begin{bmatrix} x_1 \\ x_2 \end{bmatrix} is
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    Question

    Consider a transfer function Gp(s)=ps2+3ps−2s2+(3+p)s+(2−p)G_p(s) = \frac{ps^2+3ps-2}{s^2+(3+p)s+(2-p)} with pp a positive real parameter. The maximum value of pp until which GpG_p remains stable is ________.
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    Question

    The characteristic equation of a unity negative feedback system is 1+KG(s)=01 + KG(s) = 0. The open loop transfer function G(s)G(s) has one pole at 0 and two poles at -1. The root locus of the system for varying K is shown in the figure.
    Root locus plot showing a pole at the origin and a double pole at -1, with a constant damping ratio line $\xi = 0.5$ intersecting the locus at point A.
    The constant damping ratio line, for ξ=0.5\xi = 0.5, intersects the root locus at point A. The distance from the origin to point A is given as 0.5. The value of KK at point A is ________.
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    Question

    Consider a communication scheme where the binary valued signal X satisfies P{X = +1} = 0.75 and P{X = -1} = 0.25. The received signal Y = X + Z, where Z is a Gaussian random variable with zero mean and variance σ2\sigma^2. The received signal Y is fed to the threshold detector. The output of the threshold detector X^\hat{X} is:X^={+1,Y>τ−1,Y<τ\hat{X} = \begin{cases} +1, & Y > \tau \\ -1, & Y < \tau \end{cases}.
    To achieve a minimum probability of error P{X^≠X\hat{X} \neq X}, the threshold τ\tau should be
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    Question

    Consider the Z-channel given in the figure. The input is 00 or 11 with equal probability.
    Z-channel diagram showing transition probabilities from input 0, 1 to output 0, 1
    If the output is 00, the probability that the input is also 00 equals ______________
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    An MM-level PSK modulation scheme is used to transmit independent binary digits over a band-pass channel with bandwidth 100100 kHz. The bit rate is 200200 kbps and the system characteristic is a raised-cosine spectrum with 100%100\% excess bandwidth. The minimum value of MM is ________.
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    Consider a discrete-time channel Y=X+ZY = X + Z, where the additive noise ZZ is signal-dependent. In particular, given the transmitted symbol X∈{−a,+a}X \in \{-a, +a\} at any instant, the noise sample ZZ is chosen independently from a Gaussian distribution with mean βX\beta X and unit variance. Assume a threshold detector with zero threshold at the receiver.
    When β=0\beta = 0, the BER was found to be Q(a)=1×10−8Q(a) = 1 \times 10^{-8}.
    (Q(v)=12π∫v∞e−u2/2duQ(v) = \frac{1}{\sqrt{2\pi}} \int_{v}^{\infty} e^{-u^2/2} du, and for v>1v > 1, use Q(v)≈e−v2/2Q(v) \approx e^{-v^2/2})
    When β=−0.3\beta = -0.3, the BER is closest to
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    Question

    The electric field (assumed to be one-dimensional) between two points A and B is shown. Let ψA\psi_A and ψB\psi_B be the electrostatic potentials at A and B, respectively. The value of ψB−ψA\psi_B - \psi_A in Volts is ________.
    Electric field vs distance graph
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    Given F⃗=za^x+xa^y+ya^z\vec{F} = z\hat{a}_x + x\hat{a}_y + y\hat{a}_z. If SS represents the portion of the sphere x2+y2+z2=1x^2 + y^2 + z^2 = 1 for z≥0z \geq 0, then ∫S∇×F⃗⋅ds⃗\int_S \nabla \times \vec{F} \cdot d\vec{s} is ______________.
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    If E⃗=−(2y3−3yz2)x^−(6xy2−3xz2)y^+(6xyz)z^\vec{E} = -(2y^3 - 3yz^2)\hat{x} - (6xy^2 - 3xz^2)\hat{y} + (6xyz)\hat{z} is the electric field in a source free region, a valid expression for the electrostatic potential is
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