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GATE EC 2014 Set 1

All 65 solved GATE EC 2014 Set 1 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 23Medium 37Hard 5

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65 of 65 questions

General Aptitude (GA)

10
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    Question

    Choose the most appropriate phrase from the options given below to complete the following sentence.
    The aircraft ________________ take off as soon as its flight plan was filed.
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    Question

    Read the statements:
    All women are entrepreneurs.
    Some women are doctors.
    Which of the following conclusions can be logically inferred from the above statements?
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    Question

    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.
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    Question

    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?
    BatsmanAverageStandard deviation
    K31.25.21
    L46.06.35
    M54.46.22
    N17.95.90
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    Question

    What is the next number in the series?12 \quad 35 \quad 81 \quad 173 \quad 357 \quad \text{____}
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    Question

    Find the odd one from the following group:W,E,K,OI,Q,W,AF,N,T,XN,V,B,DW,E,K,O \quad I,Q,W,A \quad F,N,T,X \quad N,V,B,D
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    Question

    For submitting tax returns, all resident males with annual income below Rs 10 lakh should fill up Form P and all resident females with income below Rs 8 lakh should fill up Form Q. All people with incomes above Rs 10 lakh should fill up Form R, except non residents with income above Rs 15 lakhs, who should fill up Form S. All others should fill Form T. An example of a person who should fill Form T is
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    Question

    A train that is 280 metres long, travelling at a uniform speed, crosses a platform in 60 seconds and passes a man standing on the platform in 20 seconds. What is the length of the platform in metres?
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    Question

    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 1/5th1/5^{th} of the exports?
    Bar chart showing Exports and Imports from 2000 to 2007
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    Question

    You are given three coins: one has heads on both faces, the second has tails on both faces, and the third has a head on one face and a tail on the other. You choose a coin at random and toss it, and it comes up heads. The probability that the other face is tails is
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ELECTRONICS AND COMMUNICATION ENGINEERING – EC

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    Question

    For matrices of same dimension MM, NN and scalar cc, which one of these properties DOES NOT ALWAYS hold?
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    Question

    In a housing society, half of the families have a single child per family, while the remaining half have two children per family. The probability that a child picked at random, has a sibling is _____
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    Question

    CC is a closed path in the zz-plane given by ∣z∣=3|z| = 3. The value of the integral ∮C(z2−z+4jz+2j)dz\oint_C \left( \frac{z^2-z+4j}{z+2j} \right) dz is
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    Question

    A real (4×4)(4 \times 4) matrix AA satisfies the equation A2=IA^2 = I, where II is the (4×4)(4 \times 4) identity matrix. The positive eigen value of AA is _________.
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    Question

    Let X1,X2,X_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 is the largest}P\{X_1 \text{ is the largest}\} is ________
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    Question

    For maximum power transfer between two cascaded sections of an electrical network, the relationship between the output impedance Z1Z_1 of the first section to the input impedance Z2Z_2 of the second section is
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    Question

    Consider the configuration shown in the figure which is a portion of a larger electrical network
    A resistor network with three resistors $R$ forming a triangle, and currents $i_1, i_2, i_3, i_4, i_5, i_6$ as shown.
    For R=1 ΩR = 1\ \Omega and currents i1=2 A,i4=−1 A,i5=−4 Ai_1 = 2\ \text{A}, i_4 = -1\ \text{A}, i_5 = -4\ \text{A}, which one of the following is TRUE?
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    Question

    When the optical power incident on a photodiode is 10μW10\mu\text{W} and the responsivity is 0.8 A/W0.8\text{ A/W}, the photocurrent generated (in μA\mu\text{A}) is ________.
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    Question

    In the figure, assume that the forward voltage drops of the PN diode D1D_1 and Schottky diode D2D_2 are 0.7 V0.7\text{ V} and 0.3 V0.3\text{ V}, respectively. If ON denotes conducting state of the diode and OFF denotes non-conducting state of the diode, then in the circuit,
    diode circuit
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    Question

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

    A good current buffer has
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    Question

    In the ac equivalent circuit shown in the figure, if iini_{in} is the input current and RFR_F is very large, the type of feedback is
    AC equivalent circuit of a two-stage MOSFET amplifier with feedback resistor $R_F$
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    Question

    In the low-pass filter shown in the figure, for a cut-off frequency of 5 kHz, the value of R2R_2 (in kΩ\Omega) is _____________.
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    Question

    In the following circuit employing pass transistor logic, all NMOS transistors are identical with a threshold voltage of 1 V1\text{ V}. Ignoring the body-effect, the output voltages at PP, QQ and RR are,
    Pass transistor logic circuit with three NMOS transistors in series, gates connected to 5V, input at 5V
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    Question

    The Boolean expression (X+Y)(X+Yˉ)+XYˉ+Xˉ‾(X + Y) (X + \bar{Y}) + \overline{X\bar{Y} + \bar{X}} simplifies to
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    Question

    Five JK flip-flops are cascaded to form the circuit shown in Figure. Clock pulses at a frequency of 1 MHz1 \text{ MHz} are applied as shown. The frequency (in  kHz\text{ kHz}) of the waveform at Q3Q_3 is __________ .
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    Question

    A discrete-time signal x[n]=sin⁡(π2n)x[n] = \sin(\pi^2 n), nn being an integer, is
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    Question

    Consider two real valued signals, x(t)x(t) band-limited to [−500 Hz,500 Hz][-500 \text{ Hz}, 500 \text{ Hz}] and y(t)y(t) band-limited to [−1 kHz,1 kHz][-1 \text{ kHz}, 1 \text{ kHz}]. For z(t)=x(t)⋅y(t)z(t) = x(t) \cdot y(t), the Nyquist sampling frequency (in kHz) is ______.
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    Question

    A continuous, linear time-invariant filter has an impulse response h(t)h(t) described byh(t)={3for 0≤t≤30otherwiseh(t) = \begin{cases} 3 & \text{for } 0 \leq t \leq 3 \\ 0 & \text{otherwise} \end{cases}When a constant input of value 5 is applied to this filter, the steady state output is _____.
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    Question

    The forward path transfer function of a unity negative feedback system is given by G(s)=K(s+2)(s−1)G(s) = \frac{K}{(s + 2)(s - 1)}. The value of KK which will place both the poles of the closed-loop system at the same location, is ______.
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    Question

    Consider the feedback system shown in the figure. The Nyquist plot of G(s)G(s) is also shown. Which one of the following conclusions is correct?
    📷 Figure: Feedback system block diagram and Nyquist plot
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    Question

    In a code-division multiple access (CDMA) system with N=8N = 8 chips, the maximum number of users who can be assigned mutually orthogonal signature sequences is ________
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    Question

    In the circuit shown in the figure, the value of capacitor CC (in mF) needed to have critically damped response i(t)i(t) is ________.
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    Question

    A two-port network has scattering parameters given by [S]=[s11s12s21s22][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 s11s_{11} parameter for the resultant one-port network is
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    Question

    The force on a point charge +q+q kept at a distance dd from the surface of an infinite grounded metal plate in a medium of permittivity ϵ\epsilon is
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    The Taylor series expansion of 3sin⁡x+2cos⁡x3 \sin x + 2 \cos x is
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    Question

    For a function g(t)g(t), it is given that ∫−∞+∞g(t)e−jωtdt=ωe−2ω2\int_{-\infty}^{+\infty} g(t)e^{-j\omega t} dt = \omega e^{-2\omega^2} for any real value ω\omega. If y(t)=∫−∞tg(τ)dτy(t) = \int_{-\infty}^{t} g(\tau) d\tau, then ∫−∞+∞y(t)dt\int_{-\infty}^{+\infty} y(t)dt is
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    Question

    The volume under the surface z(x,y)=x+yz(x, y) = x + y and above the triangle in the xx-yy plane defined by {0≤y≤x and 0≤x≤12}\{0 \leq y \leq x \text{ and } 0 \leq x \leq 12\} is _________.
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    Question

    Consider the matrixJ6=[000001000010000100001000010000100000]J_6 = \begin{bmatrix} 0 & 0 & 0 & 0 & 0 & 1 \\ 0 & 0 & 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 & 0 & 0 \\ 1 & 0 & 0 & 0 & 0 & 0 \end{bmatrix}which is obtained by reversing the order of the columns of the identity matrix I6I_6.
    Let P=I6+αJ6P = I_6 + \alpha J_6, where α\alpha is a non-negative real number. The value of α\alpha for which det⁡(P)=0\det(P) = 0 is ________.
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    Question

    A Y-network has resistances of 10Ω10\Omega each in two of its arms, while the third arm has a resistance of 11Ω11\Omega. In the equivalent Δ\Delta-network, the lowest value (in Ω\Omega) among the three resistances is ________.
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    Question

    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
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    Question

    A periodic variable xx is shown in the figure as a function of time. The root-mean-square (rms) value of xx is _________.
    Graph of a periodic signal x(t) with a ramp from 0 to 1 over T/2 and zero for the remaining T/2
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    Question

    In the circuit shown in the figure, the value of capacitor CC (in mF) needed to have critically damped response i(t)i(t) is________.
    Series RLC circuit with R = 40 Ω, L = 4 H, and capacitor C
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    A BJT is biased in forward active mode. Assume VBE=0.7 VV_{BE} = 0.7\text{ V}, kT/q=25 mVkT/q = 25\text{ mV} and reverse saturation current IS=10−13 AI_S = 10^{-13}\text{ A}. The transconductance of the BJT (in mA/V) is __________.
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    The doping concentrations on the p-side and n-side of a silicon diode are 1×1016 cm−31 \times 10^{16}\text{ cm}^{-3} and 1×1017 cm−31 \times 10^{17}\text{ cm}^{-3}, respectively. A forward bias of 0.3 V0.3\text{ V} is applied to the diode. At T=300 KT = 300\text{ K}, the intrinsic carrier concentration of silicon ni=1.5×1010 cm−3n_i = 1.5 \times 10^{10}\text{ cm}^{-3} and kTq=26 mV\frac{kT}{q} = 26\text{ mV}. The electron concentration at the edge of the depletion region on the p-side is
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    A depletion type N-channel MOSFET is biased in its linear region for use as a voltage controlled resistor. Assume threshold voltage VTH=−0.5 VV_{TH} = -0.5\text{ V}, VGS=2.0 VV_{GS} = 2.0\text{ V}, VDS=5 VV_{DS} = 5\text{ V}, W/L=100W/L = 100, Cox=10−8 F/cm2C_{ox} = 10^{-8}\text{ F/cm}^2 and μn=800 cm2/V-s\mu_n = 800\text{ cm}^2/\text{V-s}. The value of the resistance of the voltage controlled resistor (in Ω\Omega) is __________.
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    Question

    In the voltage regulator circuit shown in the figure, the op-amp is ideal. The BJT has VBE=0.7 VV_{BE} = 0.7\text{ V} and β=100\beta = 100, and the zener voltage is 4.7 V4.7\text{ V}. For a regulated output of 9 V9\text{ V}, the value of RR (in Ω\Omega) is _______.
    A voltage regulator circuit featuring an ideal op-amp, a BJT, a Zener diode, and several resistors.
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    In the circuit shown, the op-amp has finite input impedance, infinite voltage gain and zero input offset voltage. The output voltage VoutV_{out} is
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    Question

    For the amplifier shown in the figure, the BJT parameters are VBE=0.7 VV_{BE} = 0.7\text{ V}, β=200\beta = 200, and thermal voltage VT=25 mVV_T = 25\text{ mV}. The voltage gain (vo/viv_o/v_i) of the amplifier is _______ .
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    The output F in the digital logic circuit shown in the figure is
    A digital logic circuit with three inputs X, Y, Z and one output F. An XOR gate takes inputs X and Y. An XNOR gate takes inputs Y and Z. An AND gate takes the outputs of the XOR and XNOR gates to produce the final output F.
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    Consider the Boolean function, F(w,x,y,z)=wy+xy+wˉxyz+wˉxˉy+xz+xˉyˉzˉF(w, x, y, z) = wy + xy + \bar{w}xyz + \bar{w}\bar{x}y + xz + \bar{x}\bar{y}\bar{z}. Which one of the following is the complete set of essential prime implicants?
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    Question

    The digital logic shown in the figure satisfies the given state diagram when Q1 is connected to input A of the XOR gate.
    A digital logic circuit with two D flip-flops and an XOR gate, and its corresponding state diagram.
    Suppose the XOR gate is replaced by an XNOR gate. Which one of the following options preserves the state diagram?
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    Let x[n]=(−19)nu(n)−(−13)nu(−n−1)x[n] = \left(-\frac{1}{9}\right)^n u(n) - \left(-\frac{1}{3}\right)^n u(-n - 1). The Region of Convergence (ROC) of the z-transform of x[n]x[n] is
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    Consider a discrete time periodic signal x[n]=sin⁡(πn5)x[n] = \sin\left(\frac{\pi n}{5}\right). Let aka_k be the complex Fourier series coefficients of x[n]x[n]. The coefficients {ak}\{a_k\} are non-zero when k=Bm±1k = Bm \pm 1, where mm is any integer. The value of BB is ______.
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    A system is described by the following differential equation, where u(t)u(t) is the input to the system and y(t)y(t) is the output of the system.y˙(t)+5y(t)=u(t)\dot{y}(t) + 5y(t) = u(t)When y(0)=1y(0) = 1 and u(t)u(t) is a unit step function, y(t)y(t) is
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    Question

    Consider the state space model of a system, as given below[x˙1x˙2x˙3]=[−1100−1000−2][x1x2x3]+[040]u;y=[111][x1x2x3].\begin{bmatrix} \dot{x}_1 \\ \dot{x}_2 \\ \dot{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; \quad y = [1 \quad 1 \quad 1] \begin{bmatrix} x_1 \\ x_2 \\ x_3 \end{bmatrix}.The system is
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    Question

    The phase margin in degrees of G(s)=10(s+0.1)(s+1)(s+10)G(s) = \frac{10}{(s+0.1)(s+1)(s+10)} calculated using the asymptotic Bode plot is ________.
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    Question

    For the following feedback system G(s)=1(s+1)(s+2)G(s) = \frac{1}{(s+1)(s+2)}. The 2%-settling time of the step response is required to be less than 2 seconds.
    Feedback system block diagram with compensator C(s) and plant G(s) in a unity negative feedback loop
    Which one of the following compensators C(s)C(s) achieves this?
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    Let XX be a real-valued random variable with E[X]E[X] and E[X2]E[X^2] denoting the mean values of XX and X2X^2, respectively. The relation which always holds true is
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    Consider a random process X(t)=2sin⁡(2πt+ϕ)X(t) = \sqrt{2}\sin(2\pi t + \phi), where the random phase ϕ\phi is uniformly distributed in the interval [0,2π][0, 2\pi]. The auto-correlation E[X(t1)X(t2)]E[X(t_1)X(t_2)] is
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    Question

    Let Q(γ)Q(\sqrt{\gamma}) be the BER of a BPSK system over an AWGN channel with two-sided noise power spectral density N0/2N_0/2. The parameter γ\gamma is a function of bit energy and noise power spectral density.
    A system with two independent and identical AWGN channels with noise power spectral density N0/2N_0/2 is shown in the figure. The BPSK demodulator receives the sum of outputs of both the channels.
    Block diagram of a BPSK system where the modulator output is split into two parallel AWGN channels, summed together, and then fed into a BPSK demodulator
    If the BER of this system is Q(bγ)Q(b\sqrt{\gamma}), then the value of bb is _____.
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    A fair coin is tossed repeatedly until a ‘Head’ appears for the first time. Let LL be the number of tosses to get this first ‘Head’. The entropy H(L) in bits is ________.
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    In spherical coordinates, let a^θ,a^ϕ\hat{a}_\theta, \hat{a}_\phi denote unit vectors along the θ,ϕ\theta, \phi directions.E=100rsin⁡θcos⁡(ωt−βr)a^θV/m\mathbf{E} = \frac{100}{r} \sin \theta \cos(\omega t - \beta r) \hat{a}_\theta V/mandH=0.265rsin⁡θcos⁡(ωt−βr)a^ϕA/m\mathbf{H} = \frac{0.265}{r} \sin \theta \cos(\omega t - \beta r) \hat{a}_\phi A/mrepresent the electric and magnetic field components of the EM wave at large distances rr from a dipole antenna, in free space. The average power (W) crossing the hemispherical shell located at r=1km,0≤θ≤π/2r = 1km, 0 \leq \theta \leq \pi/2 is ________
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    For a parallel plate transmission line, let vv be the speed of propagation and ZZ be the characteristic impedance. Neglecting fringe effects, a reduction of the spacing between the plates by a factor of two results in
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    Question

    The input impedance of a λ8\frac{\lambda}{8} section of a lossless transmission line of characteristic impedance 50 Ω50\ \Omega is found to be real when the other end is terminated by a load ZL(=R+jX) ΩZ_L (= R + jX)\ \Omega. If XX is 30 Ω30\ \Omega, the value of RR (in Ω\Omega) is _______
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