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GATE EC 2014 Set 2

All 65 solved GATE EC 2014 Set 2 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 24Medium 39Hard 2

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65 of 65 questions

General Aptitude (GA)

10
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    Question

    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.
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    Question

    Which of the options given below best completes the following sentence?
    She will feel much better if she ________________.
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    Question

    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.
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    Question

    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→0.167;2→0.167;3→0.152;4→0.166;5→0.168;6→0.1801 \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
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    Question

    Fill in the missing number in the series.
    2 3 6 15 _____ 157.5 630
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    Question

    Find the odd one in the following group
    Q,W,Z,B B,H,K,M W,C,G,J M,S,V,X
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    Question

    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?
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    Question

    The sum of eight consecutive odd numbers is 656. The average of four consecutive even numbers is 87. What is the sum of the smallest odd number and second largest even number?
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    Question

    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?
    Pie charts showing Exports and Revenues percentages for Items 1 through 6
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    Question

    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?
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ELECTRONICS AND COMMUNICATION ENGINEERING – EC

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    Question

    The determinant of matrix A is 5 and the determinant of matrix B is 40. The determinant of matrix AB is __________
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    Question

    Let X be a random variable which is uniformly chosen from the set of positive odd numbers less than 100. The expectation, E[X], is __________
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    Question

    For 0≤t<∞0 \leq t < \infty, the maximum value of the function f(t)=e−t−2e−2tf(t) = e^{-t} - 2 e^{-2t} occurs at
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    Question

    The value of lim⁡x→∞(1+1x)x\lim_{x \to \infty} \left( 1 + \frac{1}{x} \right)^xis
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    Question

    If the characteristic equation of the differential equation d2ydx2+2αdydx+y=0\frac{d^2y}{dx^2} + 2 \alpha \frac{dy}{dx} + y = 0has two equal roots, then the values of α\alpha are
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    Question

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

    In the figure shown, the ideal switch has been open for a long time. If it is closed at t=0t = 0, then the magnitude of the current (in mA) through the 4 kΩ4\text{ k}\Omega resistor at t=0+t = 0^+ is _______.
    A circuit diagram with a 10V DC source, a 5 k$\Omega$ resistor, a 10 $\mu$F capacitor, a 4 k$\Omega$ resistor, a switch that closes at $t=0$, a 1 k$\Omega$ resistor, and a 1 mH inductor.
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    Question

    A silicon bar is doped with donor impurities ND=2.25×1015 atoms / cm3N_D = 2.25 \times 10^{15}\text{ atoms / cm}^3. Given the intrinsic carrier concentration of silicon at T=300 KT = 300\text{ K} is ni=1.5×1010 cm−3n_i = 1.5 \times 10^{10}\text{ cm}^{-3}. Assuming complete impurity ionization, the equilibrium electron and hole concentrations are
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    Question

    An increase in the base recombination of a BJT will increase
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    Question

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

    The feedback topology in the amplifier circuit ( the base bias circuit is not shown for simplicity) in the figure is
    BJT amplifier circuit with feedback resistor RE at the emitter
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    Question

    In the differential amplifier shown in the figure, the magnitudes of the common-mode and differential-mode gains are AcmA_{cm} and AdA_d, respectively. If the resistance RER_E is increased, then
    Differential amplifier circuit with current source I0 and emitter resistance RE
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    Question

    A cascade connection of two voltage amplifiers A1 and A2 is shown in the figure. The open-loop gain Av0A_{v0}, input resistance RinR_{in}, and output resistance RoR_o for A1 and A2 are as follows:
    A1: Av0=10,Rin=10 kΩ,Ro=1 kΩA_{v0} = 10, R_{in} = 10\text{ k}\Omega, R_o = 1\text{ k}\Omega.
    A2: Av0=5,Rin=5 kΩ,Ro=200 ΩA_{v0} = 5, R_{in} = 5\text{ k}\Omega, R_o = 200\text{ }\Omega.
    The approximate overall voltage gain vout/vinv_{out}/v_{in} is __________.
    Cascade connection of two voltage amplifiers A1 and A2 with input $v_{in}$, output $v_{out}$, and a load resistor $R_L = 1\text{ k}\Omega$
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    Question

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

    The number of bytes required to represent the decimal number 1856357 in packed BCD (Binary Coded Decimal) form is __________ .
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    Question

    In a half-subtractor circuit with XX and YY as inputs, the Borrow (MM) and Difference (N=X−YN = X - Y) are given by
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    Question

    An FIR system is described by the system functionH(z)=1+72z−1+32z−2H(z) = 1 + \frac{7}{2} z^{-1} + \frac{3}{2} z^{-2}The system is
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    Question

    Let x[n]=x[−n]x[n] = x[-n]. Let X(z)X(z) be the zz-transform of x[n]x[n]. If 0.5+j0.250.5 + j 0.25 is a zero of X(z)X(z), which one of the following must also be a zero of X(z)X(z).
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    Question

    Consider the periodic square wave in the figure shown.
    periodic square wave with amplitude 1 from 0 to 1 and -1 from 1 to 2, period T=2
    The ratio of the power in the 7th7^{th} harmonic to the power in the 5th5^{th} harmonic for this waveform is closest in value to _______.
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    Question

    The natural frequency of an undamped second-order system is 4040 rad/s. If the system is damped with a damping ratio 0.30.3, the damped natural frequency in rad/s is ________.
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    Question

    For the following system,
    block diagram of a control system with two summers and two blocks s/(s+1) and 1/s
    when X1(s)=0X_1(s) = 0, the transfer function Y(s)X2(s)\frac{Y(s)}{X_2(s)} is
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    Question

    The capacity of a band-limited additive white Gaussian noise (AWGN) channel is given by C=Wlog⁡2(1+Pσ2W)C = W \log_2 \left( 1 + \frac{P}{\sigma^2 W} \right) bits per second (bps), where WW is the channel bandwidth, PP is the average power received and σ2\sigma^2 is the one-sided power spectral density of the AWGN.
    For a fixed Pσ2=1000\frac{P}{\sigma^2} = 1000, the channel capacity (in kbps) with infinite bandwidth (W→∞W \to \infty) is approximately
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    Question

    Consider sinusoidal modulation in an AM system. Assuming no overmodulation, the modulation index (μ\mu) when the maximum and minimum values of the envelope, respectively, are 3 V and 1 V, is ________.
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    Question

    To maximize power transfer, a lossless transmission line is to be matched to a resistive load impedance via a λ/4\lambda/4 transformer as shown.
    A lossless transmission line connected to a $\lambda/4$ transformer which is then connected to a resistive load $Z_L = 100\ \Omega$. The input impedance looking into the transformer is $Z_{in} = 50\ \Omega$.
    The characteristic impedance (in Ω\Omega) of the λ/4\lambda/4 transformer is _________.
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    Which one of the following field patterns represents a TEM wave travelling in the positive xx direction?
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    Question

    The system of linear equations(213301125)(abc)=(5−414)\begin{pmatrix} 2 & 1 & 3 \\ 3 & 0 & 1 \\ 1 & 2 & 5 \end{pmatrix} \begin{pmatrix} a \\ b \\ c \end{pmatrix} = \begin{pmatrix} 5 \\ -4 \\ 14 \end{pmatrix}has
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    Question

    The real part of an analytic function f(z)f(z) where z=x+jyz = x + jy is given by e−ycos⁡(x)e^{-y}\cos(x). The imaginary part of f(z)f(z) is
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    The maximum value of the determinant among all 2×22 \times 2 real symmetric matrices with trace 14 is ________.
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    If r⃗=xa^x+ya^y+za^z\vec{r} = x\hat{a}_x + y\hat{a}_y + z\hat{a}_z and ∣r⃗∣=r|\vec{r}| = r, then div(r2∇(ln⁡r))=______.\text{div}(r^2 \nabla(\ln r)) = \_\_\_\_\_\_.
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    Question

    A series LCR circuit is operated at a frequency different from its resonant frequency. The operating frequency is such that the current leads the supply voltage. The magnitude of current is half the value at resonance. If the values of LL, CC and RR are 1 H, 1 F and 1 Ω\Omega, respectively, the operating angular frequency (in rad/s) is ________.
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    Question

    In the h-parameter model of the 2-port network given in the figure shown, the value of h22h_{22} (in S) is ______ .
    Circuit diagram of a 2-port network with a bridge-like configuration of resistors with values 3 $\Omega$ and 2 $\Omega$
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    Question

    In the figure shown, the capacitor is initially uncharged. Which one of the following expressions describes the current I(t)I(t) (in mA) for t>0t > 0?
    RC circuit diagram with a 5V DC source, a 1 k$\Omega$ series resistor $R_1$, and a parallel combination of a 2 k$\Omega$ resistor $R_2$ and a 1 $\mu$F capacitor $C$
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    Question

    In the magnetically coupled circuit shown in the figure, 56 % of the total flux emanating from one coil links the other coil. The value of the mutual inductance (in H) is ______ .
    Magnetically coupled circuit showing two inductors $L_1 = 4\text{ H}$ and $L_2 = 5\text{ H}$ with mutual inductance $M$
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    Question

    Assume electronic charge q=1.6×10−19 Cq = 1.6 \times 10^{-19}\text{ C}, kT/q=25 mVkT/q = 25\text{ mV} and electron mobility μn=1000 cm2/V-s\mu_n = 1000\text{ cm}^2/\text{V-s}. If the concentration gradient of electrons injected into a P-type silicon sample is 1×1021/cm41 \times 10^{21}/\text{cm}^4, the magnitude of electron diffusion current density (in A/cm2\text{A/cm}^2) is _________.
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    Question

    Consider an abrupt PN junction (at T=300 KT = 300\text{ K}) shown in the figure. The depletion region width XnX_n on the N-side of the junction is 0.2 μm0.2\text{ }\mu\text{m} and the permittivity of silicon (ϵsi\epsilon_{si}) is 1.044×10−12 F/cm1.044 \times 10^{-12}\text{ F/cm}. At the junction, the approximate value of the peak electric field (in kV/cm\text{kV/cm}) is _________.
    Diagram of an abrupt PN junction showing $P^+$-region with $N_A \gg N_D$ and $N$-region with $N_D = 10^{16}/\text{cm}^3$, and depletion width $X_n$
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    Question

    When a silicon diode having a doping concentration of NA=9×1016 cm−3N_A = 9 \times 10^{16}\text{ cm}^{-3} on p-side and ND=1×1016 cm−3N_D = 1 \times 10^{16}\text{ cm}^{-3} on n-side is reverse biased, the total depletion width is found to be 3 μm3\text{ }\mu\text{m}. Given that the permittivity of silicon is 1.04×10−12 F/cm1.04 \times 10^{-12}\text{ F/cm}, the depletion width on the p-side and the maximum electric field in the depletion region, respectively, are
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    Question

    The diode in the circuit shown has Von=0.7V_{on} = 0.7 Volts but is ideal otherwise. If Vi=5sin⁡(ωt)V_i = 5 \sin(\omega t) Volts, the minimum and maximum values of VoV_o (in Volts) are, respectively,
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    Question

    For the n-channel MOS transistor shown in the figure, the threshold voltage VTHV_{TH} is 0.80.8 V. Neglect channel length modulation effects. When the drain voltage VD=1.6V_D = 1.6 V, the drain current IDI_D was found to be 0.50.5 mA. If VDV_D is adjusted to be 22 V by changing the values of RR and VDDV_{DD}, the new value of IDI_D (in mA) is
    N-channel MOSFET circuit with gate tied to drain
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    Question

    For the MOSFETs shown in the figure, the threshold voltage ∣Vt∣=2|V_t| = 2 V and 12μnCox(WL)=0.1\frac{1}{2} \mu_n C_{ox} \left(\frac{W}{L}\right) = 0.1 mA/V2^2. The value of IDI_D (in mA) is _______.
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    In the circuit shown, choose the correct timing diagram of the output (y) from the given waveforms W1, W2, W3 and W4.
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    The outputs of the two flip-flops Q1Q_1, Q2Q_2 in the figure shown are initialized to 0, 0. The sequence generated at Q1Q_1 upon application of clock signal is
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    Question

    For the 8085 microprocessor, the interfacing circuit to input 8-bit digital data (DI0–DI7DI_0 – DI_7) from an external device is shown in the figure. The instruction for correct data transfer is
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    Consider a discrete-time signal x[n]={nfor 0≤n≤100otherwisex[n] = \begin{cases} n & \text{for } 0 \le n \le 10 \\ 0 & \text{otherwise} \end{cases}If y[n]y[n] is the convolution of x[n]x[n] with itself, the value of y[4]y[4] is _________.
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    The input-output relationship of a causal stable LTI system is given asy[n]=αy[n−1]+βx[n]y[n] = \alpha y[n-1] + \beta x[n]If the impulse response h[n]h[n] of this system satisfies the condition ∑n=0∞h[n]=2\sum_{n=0}^{\infty} h[n] = 2, the relationship between α\alpha and β\beta is
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    The value of the integral ∫−∞∞sinc2(5t)dt\int_{-\infty}^{\infty} \text{sinc}^2(5t) dt is ________.
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    Question

    An unforced linear time invariant (LTI) system is represented by[x1˙x2˙]=[10−1−2][x1x2]\begin{bmatrix} \dot{x_1} \\ \dot{x_2} \end{bmatrix} = \begin{bmatrix} 1 & 0 \\ -1 & -2 \end{bmatrix} \begin{bmatrix} x_1 \\ x_2 \end{bmatrix}If the initial conditions are x1(0)=1x_1(0) = 1 and x2(0)=−1x_2(0) = -1, the solution of the state equation is
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    Question

    The Bode asymptotic magnitude plot of a minimum phase system is shown in the figure. If the system is connected in a unity negative feedback configuration, the steady state error of the closed loop system, to a unit ramp input, is_________.
    Bode asymptotic magnitude plot showing magnitude $|G(j\omega)|$ in dB versus frequency $\omega$ in rad/s on a log scale. The plot starts at 26.02 dB at 0.1 rad/s and has an initial slope of -20 dB/decade.
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    Question

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

    The corresponding system is
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    Question

    The input to a 1-bit quantizer is a random variable XX with pdf fX(x)=2e−2xf_X(x) = 2e^{-2x} for x≥0x \geq 0 and fX(x)=0f_X(x) = 0 for x<0x < 0. For outputs to be of equal probability, the quantizer threshold should be _____.
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    Question

    Coherent orthogonal binary FSK modulation is used to transmit two equiprobable symbol waveforms s1(t)=αcos⁡2πf1ts_1(t) = \alpha \cos 2\pi f_1 t and s2(t)=αcos⁡2πf2ts_2(t) = \alpha \cos 2\pi f_2 t, where α=4\alpha = 4 mV. Assume an AWGN channel with two-sided noise power spectral density N02=0.5×10−12\frac{N_0}{2} = 0.5 \times 10^{-12} W/Hz. Using an optimal receiver and the relation Q(v)=12π∫v∞e−u2/2duQ(v) = \frac{1}{\sqrt{2\pi}} \int_v^\infty e^{-u^2/2} du, the bit error probability for a data rate of 500 kbps is
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    Question

    The power spectral density of a real stationary random process X(t)X(t) is given bySX(f)={1W,∣f∣≤W0,∣f∣>WS_X(f) = \begin{cases} \frac{1}{W}, & |f| \leq W \\ 0, & |f| > W \end{cases}The value of the expectation E[πX(t)X(t−14W)]E \left[ \pi X(t) X \left( t - \frac{1}{4W} \right) \right] is_________.
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    Question

    In the figure, M(f)M(f) is the Fourier transform of the message signal m(t)m(t) where A=100A = 100 Hz and B=40B = 40 Hz. Given v(t)=cos⁡(2πfct)v(t) = \cos(2\pi f_c t) and w(t)=cos⁡(2π(fc+A)t)w(t) = \cos(2\pi (f_c + A)t), where fc>Af_c > A. The cutoff frequencies of both the filters are fcf_c.
    Block diagram of a modulator and the spectrum of message signal M(f)
    The bandwidth of the signal at the output of the modulator (in Hz) is _____.
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    If the electric field of a plane wave is E⃗(z,t)=x^3cos⁡(ωt−kz+30∘)−y^4sin⁡(ωt−kz+45∘)\vec{E}(z,t) = \hat{x} 3 \cos(\omega t - kz + 30^\circ) - \hat{y} 4 \sin(\omega t - kz + 45^\circ) (mV/m), the polarization state of the plane wave is
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    In the transmission line shown, the impedance ZinZ_{in} (in ohms) between node A and the ground is _________.
    Transmission line circuit with a parallel resistor and a half-wavelength line
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    Question

    For a rectangular waveguide of internal dimensions a×ba \times b (a>ba > b), the cut-off frequency for the TE11TE_{11} mode is the arithmetic mean of the cut-off frequencies for TE10TE_{10} mode and TE20TE_{20} mode. If a=5a = \sqrt{5} cm, the value of bb (in cm) is _____.
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