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GATE EC 2014 Set 3

All 65 solved GATE EC 2014 Set 3 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 26Medium 38Hard 1

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65 of 65 questions

General Aptitude (GA)

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

    Question

    "India is a country of rich heritage and cultural diversity."
    Which one of the following facts best supports the claim made in the above sentence?
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    Question

    The value of one U.S. dollar is 65 Indian Rupees today, compared to 60 last year. The Indian Rupee has
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    Question

    'Advice' is
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    Question

    The next term in the series 81, 54, 36, 24, ... is
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    Question

    In which of the following options will the expression P<MP < M be definitely true?
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    Question

    Find the next term in the sequence: 7G, 11K, 13M, ___
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    Question

    The multi-level hierarchical pie chart shows the population of animals in a reserve forest. The correct conclusions from this information are:
    (i) Butterflies are birds
    (ii) There are more tigers in this forest than red ants
    (iii) All reptiles in this forest are either snakes or crocodiles
    (iv) Elephants are the largest mammals in this forest
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    Question

    A man can row at 88 km per hour in still water. If it takes him thrice as long to row upstream, as to row downstream, then find the stream velocity in km per hour.
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    Question

    A firm producing air purifiers sold 200200 units in 20122012. 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 20122012. The expenditure on labour in 20122012 is Rs. 4,50,0004,50,000. In 20132013, the raw material expenses increased by 30%30\% and all other expenses increased by 20%20\%. If the company registered a profit of Rs. 1010 lakhs in 20122012, at what price (in Rs.) was each air purifier sold?
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    Question

    A batch of one hundred bulbs is inspected by testing four randomly chosen bulbs. The batch is rejected if even one of the bulbs is defective. A batch typically has five defective bulbs. The probability that the current batch is accepted is
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ELECTRONICS AND COMMUNICATION ENGINEERING – EC

55
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    Question

    The maximum value of the function f(x)=ln⁡(1+x)−xf(x) = \ln(1 + x) - x (where x>−1x > -1) occurs at x = \text{______}.
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    Question

    Which ONE of the following is a linear non-homogeneous differential equation, where xx and yy are the independent and dependent variables respectively?
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    Question

    Match the application to appropriate numerical method.
    ApplicationNumerical Method
    P1: Numerical integrationM1: Newton-Raphson Method
    P2: Solution to a transcendental equationM2: Runge-Kutta Method
    P3: Solution to a system of linear equationsM3: Simpson’s 1/3-rule
    P4: Solution to a differential equationM4: Gauss Elimination Method
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    Question

    An unbiased coin is tossed an infinite number of times. The probability that the fourth head appears at the tenth toss is
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    Question

    If z=xyln⁡(xy)z = xy \ln(xy), then
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    Question

    A series RC circuit is connected to a DC voltage source at time t=0t = 0. The relation between the source voltage VsV_s, the resistance RR, the capacitance CC, and the current i(t)i(t) is given below:Vs=Ri(t)+1C∫0ti(u)duV_s = R i(t) + \frac{1}{C} \int_0^t i(u) duWhich one of the following represents the current i(t)i(t)?
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    Question

    In the figure shown, the value of the current II (in Amperes) is __________.
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    Question

    In MOSFET fabrication, the channel length is defined during the process of
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    Question

    A thin P-type silicon sample is uniformly illuminated with light which generates excess carriers. The recombination rate is directly proportional to
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    Question

    At T=300 KT = 300\text{ K}, the hole mobility of a semiconductor μp=500 cm2/V-s\mu_p = 500\text{ cm}^2/\text{V-s} and kTq=26 mV\frac{kT}{q} = 26\text{ mV}. The hole diffusion constant DpD_p in cm2/s\text{cm}^2/\text{s} is ________
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    Question

    The desirable characteristics of a transconductance amplifier are
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    Question

    In the circuit shown, the PNP transistor has ∣VBE∣=0.7 V|V_{BE}| = 0.7\text{ V} and β=50\beta = 50. Assume that RB=100 kΩR_B = 100\text{ k}\Omega. For V0V_0 to be 5 V5\text{ V}, the value of RCR_C (in kΩ\text{k}\Omega) is _______
    A circuit diagram showing a PNP transistor with emitter connected to $V_{EE} = 10\text{ V}$, base connected to ground through $R_B$, and collector connected to ground through $R_C$. $V_0$ is the collector voltage.
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    Question

    The figure shows a half-wave rectifier. The diode D is ideal. The average steady-state current (in Amperes) through the diode is approximately ____________.
    Half-wave rectifier circuit with an ideal diode D, a load resistor R = 100 $\Omega$, a filter capacitor C = 4 mF, and an AC input source $10 \sin \omega t$ with $f = 50$ Hz.
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    Question

    An analog voltage in the range 0 to 8 V is divided in 16 equal intervals for conversion to 4-bit digital output. The maximum quantization error (in V) is _________
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    Question

    The circuit shown in the figure is a
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    Question

    Consider the multiplexer based logic circuit shown in the figure.
    A logic circuit consisting of two cascaded 2:1 multiplexers. The first MUX has inputs W and its complement, with select line S1. Its output is fed to the second MUX, which also receives the complement of that output. The second MUX has select line S2 and produces output F.
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    Question

    Let x(t)=cos⁡(10πt)+cos⁡(30πt)x(t) = \cos(10\pi t) + \cos(30\pi t) be sampled at 20 Hz and reconstructed using an ideal low-pass filter with cut-off frequency of 20 Hz. The frequency/frequencies present in the reconstructed signal is/are
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    Question

    For an all-pass system H(z)=(z−1−b)(1−az−1)H(z) = \frac{(z^{-1} - b)}{(1 - az^{-1})}, where ∣H(e−jω)∣=1|H(e^{-j\omega})| = 1, for all ω\omega. If Re(a)≠0,Im(a)≠0\text{Re}(a) \neq 0, \text{Im}(a) \neq 0, then b equals
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    Question

    A modulated signal is y(t)=m(t)cos⁡(40000πt)y(t) = m(t) \cos(40000\pi t), where the baseband signal m(t)m(t) has frequency components less than 5 kHz only. The minimum required rate (in kHz) at which y(t)y(t) should be sampled to recover m(t)m(t) is _______.
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    Question

    Consider the following block diagram in the figure.
    A feedforward block diagram with input R(s) and output C(s). R(s) branches into three paths: one to block G1, one to a first summer, and one to a second summer. The output of G1 goes to the first summer. The output of the first summer goes to block G2. The output of G2 goes to the second summer, which produces C(s).
    The transfer function C(s)R(s)\frac{C(s)}{R(s)} is
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    Question

    The input −3e2tu(t)-3e^{2t}u(t), where u(t)u(t) is the unit step function, is applied to a system with transfer function s−2s+3\frac{s-2}{s+3}. If the initial value of the output is −2-2, then the value of the output at steady state is _______.
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    Question

    The phase response of a passband waveform at the receiver is given byϕ(f)=−2πα(f−fc)−2πβfc\phi(f) = -2\pi\alpha(f - f_c) - 2\pi\beta f_cwhere fcf_c is the centre frequency, and α\alpha and β\beta are positive constants. The actual signal propagation delay from the transmitter to receiver is
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    Question

    Consider an FM signal f(t)=cos⁡[2πfct+β1sin⁡2πf1t+β2sin⁡2πf2t]f(t) = \cos[2\pi f_c t + \beta_1 \sin 2\pi f_1 t + \beta_2 \sin 2\pi f_2 t]. The maximum deviation of the instantaneous frequency from the carrier frequency fcf_c is
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    Question

    Consider an air filled rectangular waveguide with a cross-section of 5 cm×3 cm5\text{ cm} \times 3\text{ cm}. For this waveguide, the cut-off frequency (in MHz) of TE21TE_{21} mode is _________.
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    Question

    In the following figure, the transmitter Tx sends a wideband modulated RF signal via a coaxial cable to the receiver Rx. The output impedance ZTZ_T of Tx, the characteristic impedance Z0Z_0 of the cable and the input impedance ZRZ_R of Rx are all real.
    A block diagram showing a transmitter, coaxial cable, and receiver connected in series.
    Which one of the following statements is TRUE about the distortion of the received signal due to impedance mismatch?
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    Question

    The maximum value of f(x)=2x3−9x2+12x−3f(x) = 2x^3 - 9x^2 + 12x - 3 in the interval 0≤x≤30 \le x \le 3 is __________
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    Which one of the following statements is NOT true for a square matrix A?
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    Question

    A fair coin is tossed repeatedly till both head and tail appear at least once. The average number of tosses required is ______ .
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    Question

    Let X1,X2X_1, X_2, and X3X_3 be independent and identically distributed random variables with the uniform distribution on [0,1][0, 1]. The probability P{X1+X2≤X3}P\{X_1+ X_2 \leq X_3\} is ________.
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    Question

    Consider the building block called ‘Network N’ shown in the figure.
    Let C=100μFC = 100 \mu F and R=10kΩR = 10 k\Omega.
    Circuit diagram of Network N containing a capacitor C and resistor R

    Two such blocks are connected in cascade, as shown in the figure.
    Two Network N blocks connected in cascade with input V1(s) and output V3(s)

    The transfer function V3(s)V1(s)\frac{V_3(s)}{V_1(s)} of the cascaded network is
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    Question

    In the circuit shown in the figure, the value of node voltage V2V_2 is
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    Question

    In the circuit shown in the figure, the angular frequency ω\omega (in rad/s), at which the Norton equivalent impedance as seen from terminals b-b' is purely resistive, is _________.
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    Question

    For the Y-network shown in the figure, the value of R1R_1 (in Ω\Omega) in the equivalent Δ\Delta-network is ____.
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    Question

    The donor and accepter impurities in an abrupt junction silicon diode are 1×1016 cm−31 \times 10^{16} \text{ cm}^{-3} and 5×1018 cm−35 \times 10^{18} \text{ cm}^{-3}, respectively. Assume that the intrinsic carrier concentration in silicon ni=1.5×1010 cm−3n_i = 1.5 \times 10^{10} \text{ cm}^{-3} at 300 K, kTq=26 mV\frac{kT}{q} = 26 \text{ mV} and the permittivity of silicon ϵsi=1.04×10−12 F/cm\epsilon_{si} = 1.04 \times 10^{-12} \text{ F/cm}. The built-in potential and the depletion width of the diode under thermal equilibrium conditions, respectively, are
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    Question

    The slope of the IDI_D vs. VGSV_{GS} curve of an n-channel MOSFET in linear regime is 10−3Ω−110^{-3} \Omega^{-1} at VDS=0.1 VV_{DS} = 0.1 \text{ V}. For the same device, neglecting channel length modulation, the slope of the ID\sqrt{I_D} vs. VGSV_{GS} curve (in A/V\sqrt{\text{A}}/\text{V}) under saturation regime is approximately _________.
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    Question

    An ideal MOS capacitor has boron doping-concentration of 1015 cm−310^{15} \text{ cm}^{-3} in the substrate. When a gate voltage is applied, a depletion region of width 0.5 \mum0.5 \text{ \mu m} is formed with a surface (channel) potential of 0.2 V0.2 \text{ V}. Given that ϵ0=8.854×10−14 F/cm\epsilon_0 = 8.854 \times 10^{-14} \text{ F/cm} and the relative permittivities of silicon and silicon dioxide are 12 and 4, respectively, the peak electric field (in V/μ\mu m) in the oxide region is ____________.
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    Question

    In the circuit shown, the silicon BJT has β=50\beta = 50. Assume VBE=0.7 VV_{BE} = 0.7\text{ V} and VCE(sat)=0.2 VV_{CE(sat)} = 0.2\text{ V}. Which one of the following statements is correct?
    BJT circuit with Vcc=10V, Rc, Rb=50k, Vin=5V
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    Question

    Assuming that the Op-amp in the circuit shown is ideal, VoV_o is given by
    Op-amp circuit with resistors R, 3R, 2R, R and inputs V1, V2
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    Question

    For the MOSFET M1M_1 shown in the figure, assume W/L=2W/L = 2, VDD=2.0 VV_{DD} = 2.0\text{ V}, μnCox=100 μA/V2\mu_n C_{ox} = 100\text{ }\mu\text{A/V}^2 and VTH=0.5 VV_{TH} = 0.5\text{ V}. The transistor M1M_1 switches from saturation region to linear region when VinV_{in} (in Volts) is__________.
    MOSFET circuit diagram with resistor R=10k and supply VDD
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    If WLWL is the Word Line and BLBL the Bit Line, an SRAM cell is shown in
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    Question

    In the circuit shown, WW and YY are MSBs of the control inputs. The output FF is given by
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    Question

    If XX and YY are inputs and the Difference (D=X−YD = X - Y) and the Borrow (BB) are the outputs, which one of the following diagrams implements a half-subtractor?
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    Question

    Let H1(z)=(1−pz−1)−1H_1(z) = (1 - pz^{-1})^{-1}, H2(z)=(1−qz−1)−1H_2(z) = (1 - qz^{-1})^{-1}, H(z)=H1(z)+rH2(z)H(z) = H_1(z) + r H_2(z). The quantities p,q,rp, q, r are real numbers. Consider p=12,q=−14,∣r∣<1p = \frac{1}{2}, q = -\frac{1}{4}, |r| < 1. If the zero of H(z)H(z) lies on the unit circle, then r=________r = \_\_\_\_\_\_\_\_
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    Question

    Let h(t)h(t) denote the impulse response of a causal system with transfer function 1s+1\frac{1}{s+1}. Consider the following three statements.
    S1: The system is stable.
    S2: h(t+1)h(t)\frac{h(t+1)}{h(t)} is independent of tt for t>0t > 0.
    S3: A non-causal system with the same transfer function is stable.
    For the above system,
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    Question

    The z-transform of the sequence x[n]x[n] is given by X(z)=1(1−2z−1)2X(z) = \frac{1}{(1-2z^{-1})^2}, with the region of convergence ∣z∣>2|z| > 2. Then, x[2]x[2] is ________.
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    The steady state error of the system shown in the figure for a unit step input is _______.
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    Question

    The state equation of a second-order linear system is given byx˙(t)=Ax(t),x(0)=x0\dot{\mathbf{x}}(t) = \mathbf{Ax}(t), \quad \mathbf{x}(0) = \mathbf{x}_0For x0=[1−1]\mathbf{x}_0 = \begin{bmatrix} 1 \\ -1 \end{bmatrix}, x(t)=[e−t−e−t]\mathbf{x}(t) = \begin{bmatrix} e^{-t} \\ -e^{-t} \end{bmatrix} and for x0=[01]\mathbf{x}_0 = \begin{bmatrix} 0 \\ 1 \end{bmatrix}, x(t)=[e−t−e−2t−e−t+2e−2t]\mathbf{x}(t) = \begin{bmatrix} e^{-t} - e^{-2t} \\ -e^{-t} + 2e^{-2t} \end{bmatrix}.
    When x0=[35]\mathbf{x}_0 = \begin{bmatrix} 3 \\ 5 \end{bmatrix}, x(t)\mathbf{x}(t) is
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    Question

    In the root locus plot shown in the figure, the pole/zero marks and the arrows have been removed. Which one of the following transfer functions has this root locus?
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    Question

    Let X(t)X(t) be a wide sense stationary (WSS) random process with power spectral density SX(f)S_X(f). If Y(t)Y(t) is the process defined as Y(t)=X(2t−1)Y(t) = X(2t - 1), the power spectral density SY(f)S_Y(f) is
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    A real band-limited random process X(t)X(t) has two-sided power spectral density SX(f)={10−6(3000−∣f∣) Watts/Hzfor ∣f∣≤3 kHz0otherwiseS_X(f) = \begin{cases} 10^{-6}(3000-|f|) \text{ Watts/Hz} & \text{for } |f| \leq 3 \text{ kHz} \\ 0 & \text{otherwise} \end{cases} where ff is the frequency expressed in Hz. The signal X(t)X(t) modulates a carrier cos⁡16000πt\cos 16000 \pi t and the resultant signal is passed through an ideal band-pass filter of unity gain with centre frequency of 8 kHz and band-width of 2 kHz. The output power (in Watts) is ________.
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    In a PCM system, the signal m(t)={sin⁡(100πt)+cos⁡(100πt)} Vm(t) = \{\sin(100\pi t) + \cos(100\pi t)\} \text{ V} is sampled at the Nyquist rate. The samples are processed by a uniform quantizer with step size 0.75 V. The minimum data rate of the PCM system in bits per second is ________.
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    A binary random variable XX takes the value of 1 with probability 1/31/3. XX is input to a cascade of 2 independent identical binary symmetric channels (BSCs) each with crossover probability 1/21/2. The output of BSCs are the random variables Y1Y_1 and Y2Y_2 as shown in the figure.
    Cascade of two binary symmetric channels
    The value of H(Y1)+H(Y2)H(Y_1) + H(Y_2) in bits is _____.
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    Given the vector A=(cos⁡x)(sin⁡y)a^x+(sin⁡x)(cos⁡y)a^y\mathbf{A} = (\cos x)(\sin y)\hat{a}_x + (\sin x)(\cos y)\hat{a}_y, where a^x,a^y\hat{a}_x, \hat{a}_y denote unit vectors along x,yx,y directions, respectively. The magnitude of curl of A\mathbf{A} is ________
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    A region shown below contains a perfect conducting half-space and air. The surface current K⃗s\vec{K}_s on the surface of the perfect conductor is K⃗s=x^2\vec{K}_s = \hat{x}2 amperes per meter. The tangential H⃗\vec{H} field in the air just above the perfect conductor is
    A coordinate system showing air for $y > 0$ and a perfect conductor for $y < 0$. A surface current $\vec{K}_s$ is indicated on the boundary at $y=0$ along the $x$-axis.
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    Assume that a plane wave in air with an electric field E⃗=10cos⁡(ωt−3x−3z)a^y\vec{E} = 10 \cos(\omega t - 3x - \sqrt{3}z) \hat{a}_y V/m is incident on a non-magnetic dielectric slab of relative permittivity 3 which covers the region z>0z > 0. The angle of transmission in the dielectric slab is ________ degrees.
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