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GATE EC 2015 Set 2

All 65 solved GATE EC 2015 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 18Medium 43Hard 4

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65 of 65 questions

General Aptitude (GA)

10
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    Question

    Choose the appropriate word/phrase, out of the four options given below, to complete the following sentence:
    Dhoni, as well as the other team members of Indian team, _________ present on the occasion.
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    Question

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

    What is the adverb for the given word below?
    Misogynous
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    Question

    An electric bus has onboard instruments that report the total electricity consumed since the start of the trip as well as the total distance covered. During a single day of operation, the bus travels on stretches M, N, O, and P, in that order. The cumulative distances travelled and the corresponding electricity consumption are shown in the Table below:
    StretchCumulative distance (km)Electricity used (kWh)
    M2012
    N4525
    O7545
    P10057
    The stretch where the electricity consumption per km is minimum is
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    Question

    Ram and Ramesh appeared in an interview for two vacancies in the same department. The probability of Ram's selection is 1/61/6 and that of Ramesh is 1/81/8. What is the probability that only one of them will be selected?
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    Question

    In the following sentence certain parts are underlined and marked P, Q, and R. One of the parts may contain certain error or may not be acceptable in standard written communication. Select the part containing an error. Choose D as your answer if there is no error.
    The student corrected all the errors that the instructor marked on the answer book.
    PQR\quad\quad\quad\quad\quad\text{P}\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\text{Q}\quad\quad\quad\quad\quad\quad\quad\quad\text{R}
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    Question

    Given below are two statements followed by two conclusions. Assuming these statements to be true, decide which one logically follows.
    Statements:
    I. All film stars are playback singers.
    II. All film directors are film stars.
    Conclusions:
    I. All film directors are playback singers.
    II. Some film stars are film directors.
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    Question

    A tiger is 50 leaps of its own behind a deer. The tiger takes 5 leaps per minute to the deer's 4. If the tiger and the deer cover 8 metre and 5 metre per leap respectively, what distance in metres will the tiger have to run before it catches the deer?
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    Question

    If a2+b2+c2=1a^2 + b^2 + c^2 = 1, then ab+bc+acab + bc + ac lies in the interval
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    Question

    Lamenting the gradual sidelining of the arts in school curricula, a group of prominent artists wrote to the Chief Minister last year, asking him to allocate more funds to support arts education in schools. However, no such increase has been announced in this year’s Budget. The artists expressed their deep anguish at their request not being approved, but many of them remain optimistic about funding in the future.
    Which of the statement(s) below is/are logically valid and can be inferred from the above statements?
    (i) The artists expected funding for the arts to increase this year.
    (ii) The Chief Minister was receptive to the idea of increasing funding for the arts.
    (iii) The Chief Minister is a prominent artist.
    (iv) Schools are giving less importance to arts education nowadays.
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Electronics and Communication Engineering

55
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    Question

    The bilateral Laplace transform of a function f(t)={1if a≤t≤b0otherwisef(t) = \begin{cases} 1 & \text{if } a \leq t \leq b \\ 0 & \text{otherwise} \end{cases} is
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    Question

    The value of xx for which all the eigen-values of the matrix given below are real is[105+j4x20242−10]\begin{bmatrix} 10 & 5+j & 4 \\ x & 20 & 2 \\ 4 & 2 & -10 \end{bmatrix}
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    Question

    Let f(z)=az+bcz+df(z) = \frac{az+b}{cz+d}. If f(z1)=f(z2)f(z_1) = f(z_2) for all z1≠z2z_1 \neq z_2, a=2a = 2, b=4b = 4 and c=5c = 5, then dd should be equal to ________.
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    Question

    The general solution of the differential equation dydx=1+cos⁡2y1−cos⁡2x\frac{dy}{dx} = \frac{1 + \cos 2y}{1 - \cos 2x} is
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    Question

    The magnitude and phase of the complex Fourier series coefficients aka_k of a periodic signal x(t)x(t) are shown in the figure. Choose the correct statement from the four choices given. Notation: CC is the set of complex numbers, RR is the set of purely real numbers, and PP is the set of purely imaginary numbers.
    Magnitude and phase plots of Fourier series coefficients $a_k$
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    Question

    The voltage (VcV_c) across the capacitor (in Volts) in the network shown is ______.
    A series RLC circuit with an AC source of $100\text{ V, } 50\text{ Hz}$, a resistor with $80\text{ V}$ across it, an inductor with $40\text{ V}$ across it, and a capacitor with voltage $V_c$ across it.
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    Question

    In the circuit shown, the average value of the voltage VabV_{ab} (in Volts) in steady state condition is ______.
    A circuit containing an AC source $5\pi \sin(5000t)$, a $1\text{ k}\Omega$ resistor, a $1\text{ }\mu\text{F}$ capacitor, a $1\text{ mH}$ inductor, a $2\text{ k}\Omega$ resistor, and a $5\text{ V}$ DC source. $V_{ab}$ is the voltage across the capacitor.
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    Question

    The 2-port admittance matrix of the circuit shown is given by
    A $\pi$-network circuit with a $5\text{ }\Omega$ series resistor and two $10\text{ }\Omega$ shunt resistors.
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    Question

    An n-type silicon sample is uniformly illuminated with light which generates 102010^{20} electron-hole pairs per cm3\text{cm}^3 per second. The minority carrier lifetime in the sample is 1μs1 \mu\text{s}. In the steady state, the hole concentration in the sample is approximately 10x10^x, where xx is an integer. The value of xx is ______.
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    Question

    A piece of silicon is doped uniformly with phosphorous with a doping concentration of 1016/cm310^{16}/\text{cm}^3. The expected value of mobility versus doping concentration for silicon assuming full dopant ionization is shown below. The charge of an electron is 1.6×10−19 C1.6 \times 10^{-19} \text{ C}. The conductivity (in S cm−1\text{S cm}^{-1}) of the silicon sample at 300 K300 \text{ K} is ______.
    Graph of Hole and Electron Mobility in Silicon at 300 K
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    Question

    If the circuit shown has to function as a clamping circuit, then which one of the following conditions should be satisfied for the sinusoidal signal of period TT?
    Diode clamping circuit diagram
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    Question

    In the circuit shown, V0=VoAV_0 = V_{oA} for switch SW in position AA and V0=VoBV_0 = V_{oB} for SW in position BB. Assume that the opamp is ideal. The value of VoBVoA\frac{V_{oB}}{V_{oA}} is ________.
    Operational amplifier circuit with a switch SW and multiple resistors
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    Question

    In the bistable circuit shown, the ideal opamp has saturation levels of ±5 V\pm 5\text{ V}. The value of R1R_1 (in kΩ\text{k}\Omega) that gives a hysteresis width of 500 mV500\text{ mV} is ________.
    Non-inverting Schmitt trigger circuit using an operational amplifier
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    Question

    In the figure shown, the output YY is required to be Y=AB+CˉDˉY = A B + \bar{C} \bar{D}. The gates G1 and G2 must be, respectively,
    Logic gate circuit with inputs A, B, C, D and output Y
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    Question

    In an 8085 microprocessor, which one of the following instructions changes the content of the accumulator?
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    Question

    A mod-nn counter using a synchronous binary up-counter with synchronous clear input is shown in the figure. The value of nn is ________.
    A 4-bit binary counter circuit with a NAND gate feedback to the synchronous CLEAR input
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    Question

    Let the signal f(t)=0f(t) = 0 outside the interval [T1,T2][T_1, T_2], where T1T_1 and T2T_2 are finite. Furthermore, ∣f(t)∣<∞|f(t)| < \infty. The region of convergence (RoC) of the signal's bilateral Laplace transform F(s)F(s) is
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    Question

    Two causal discrete-time signals x[n]x[n] and y[n]y[n] are related as y[n]=∑m=0nx[m]y[n] = \sum_{m=0}^{n} x[m]. If the zz-transform of y[n]y[n] is 2z(z−1)2\frac{2}{z(z-1)^2}, the value of x[2]x[2] is ______.
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    Question

    By performing cascading and/or summing/differencing operations using transfer function blocks G1(s)G_1(s) and G2(s)G_2(s), one CANNOT realize a transfer function of the form
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    Question

    For the signal flow graph shown in the figure, the value of C(s)R(s)\frac{C(s)}{R(s)} is
    Signal flow graph with nodes R(s), X1, X2, X3, X4, X5, C(s) and gains G1, G2, G3, G4 and feedback loops H1, H2, H3
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    Question

    A unity negative feedback system has an open-loop transfer function G(s)=Ks(s+10)G(s) = \frac{K}{s(s+10)}. The gain KK for the system to have a damping ratio of 0.25 is ________.
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    Question

    A sinusoidal signal of amplitude AA is quantized by a uniform quantizer. Assume that the signal utilizes all the representation levels of the quantizer. If the signal to quantization noise ratio is 31.8 dB, the number of levels in the quantizer is ________.
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    Question

    The signal cos⁡(10πt+π4)\cos\left(10\pi t + \frac{\pi}{4}\right) is ideally sampled at a sampling frequency of 15 Hz. The sampled signal is passed through a filter with impulse response (sin⁡(πt)πt)cos⁡(40πt−π2)\left(\frac{\sin(\pi t)}{\pi t}\right) \cos\left(40\pi t - \frac{\pi}{2}\right). The filter output is
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    Question

    In a source free region in vacuum, if the electrostatic potential ϕ=2x2+y2+cz2\phi = 2x^2 + y^2 + cz^2, the value of constant cc must be ___________.
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    Question

    The electric field of a uniform plane electromagnetic wave isE⃗=(a⃗x+j4a⃗y)exp⁡[j(2π×107t−0.2z)]\vec{E} = (\vec{a}_x + j4\vec{a}_y) \exp[j(2\pi \times 10^7 t - 0.2z)]The polarization of the wave is
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    Question

    Consider the differential equation dxdt=10−0.2x\frac{dx}{dt} = 10 - 0.2x with initial condition x(0)=1x(0) = 1. The response x(t)x(t) for t>0t > 0 is
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    Question

    The value of the integral ∫−∞∞12cos⁡(2πt)sin⁡(4πt)4πtdt\int_{-\infty}^{\infty} 12 \cos(2\pi t) \frac{\sin(4\pi t)}{4\pi t} dt is _______.
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    Question

    If CC denotes the counterclockwise unit circle, the value of the contour integral 12πj∮CRe{z}dz\frac{1}{2\pi j} \oint_C \text{Re}\{z\} dzis _______.
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    Question

    Let the random variable XX represent the number of times a fair coin needs to be tossed till two consecutive heads appear for the first time. The expectation of XX is _______.
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    Question

    An LC tank circuit consists of an ideal capacitor CC connected in parallel with a coil of inductance LL having an internal resistance RR. The resonant frequency of the tank circuit is
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    Question

    In the circuit shown, the Norton equivalent resistance (in Ω\Omega) across terminals a-b is
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    Question

    In the circuit shown, the initial voltages across the capacitors C1C_1 and C2C_2 are 1 V1 \text{ V} and 3 V3 \text{ V}, respectively. The switch is closed at time t=0t = 0. The total energy dissipated (in Joules) in the resistor RR until steady state is reached, is
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    Question

    A dc voltage of 10 V10 \text{ V} is applied across an n-type silicon bar having a rectangular cross-section and a length of 1 cm1 \text{ cm} as shown in figure.
    A rectangular n-Si bar of length 1 cm connected to a 10 V DC source
    The donor doping concentration NDN_D and the mobility of electrons μn\mu_n are 1016 cm−310^{16} \text{ cm}^{-3} and 1000 cm2V−1s−11000 \text{ cm}^2\text{V}^{-1}\text{s}^{-1}, respectively. The average time (in μs\mu\text{s}) taken by the electrons to move from one end of the bar to other end is _________.
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    Question

    In a MOS capacitor with an oxide layer thickness of 10 nm10\text{ nm}, the maximum depletion layer thickness is 100 nm100\text{ nm}. The permittivities of the semiconductor and the oxide layer are ϵs\epsilon_s and ϵox\epsilon_{ox} respectively. Assuming ϵs/ϵox=3\epsilon_s/\epsilon_{ox} = 3, the ratio of the maximum capacitance to the minimum capacitance of this MOS capacitor is ___________.
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    Question

    The energy band diagram and the electron density profile n(x)n(x) in a semiconductor are shown in the figures. Assume that n(x)=1015e(qαxkT) cm−3n(x) = 10^{15} e^{\left(\frac{q \alpha x}{k T}\right)} \text{ cm}^{-3}, with α=0.1 V/cm\alpha = 0.1 \text{ V/cm} and xx expressed in cm. Given kTq=0.026 V\frac{k T}{q} = 0.026 \text{ V}, Dn=36 cm2s−1D_n = 36 \text{ cm}^2\text{s}^{-1}, and Dμ=kTq\frac{D}{\mu} = \frac{k T}{q}. The electron current density (in A/cm2\text{A/cm}^2) at x=0x = 0 is
    Energy band diagram and electron density profile
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    Question

    A function of Boolean variables X, Y and Z is expressed in terms of the min-terms as
    F(X, Y, Z) = Σ (1, 2, 5, 6, 7)
    Which one of the product of sums given below is equal to the function F(X, Y, Z)?
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    Question

    The figure shows a binary counter with synchronous clear input. With the decoding logic shown, the counter works as a
    A 3-bit binary counter with outputs Q0, Q1, Q2. The CLK input is shown. The CLR input is connected to the output of an OR gate. The inputs to the OR gate are Q1 and Q2.
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    Question

    A 1-to-8 demultiplexer with data input DinD_{in}, address inputs S0S_0, S1S_1, S2S_2 (with S0S_0 as the LSB) and Y0Y_0 to Y7Y_7 as the eight demultiplexed outputs, is to be designed using two 2-to-4 decoders (with enable input E and address inputs A0A_0 and A1A_1) as shown in the figure. DinD_{in}, S0S_0, S1S_1 and S2S_2 are to be connected to P, Q, R and S, but not necessarily in this order. The respective input connections to P, Q, R, and S terminals should be
    Circuit diagram of a 1-to-8 demultiplexer implemented with two 2-to-4 decoders and logic gates.
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    Question

    Let the random variable XX represent the number of times a fair coin needs to be tossed till two consecutive heads appear for the first time. The expectation of XX is _______.
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    Question

    An LCLC tank circuit consists of an ideal capacitor CC connected in parallel with a coil of inductance LL having an internal resistance RR. The resonant frequency of the tank circuit is
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    Question

    In the circuit shown, the Norton equivalent resistance (in Ω\Omega) across terminals a-b is _______.
    Circuit diagram with a dependent voltage source $4I$ in series with a $2\Omega$ resistor, a parallel $2\Omega$ resistor, and a parallel $4\Omega$ resistor through which current $I$ flows, connected to terminals a-b.
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    Question

    In the circuit shown, the initial voltages across the capacitors C1C_1 and C2C_2 are 1 V1\text{ V} and 3 V3\text{ V}, respectively. The switch is closed at time t=0t = 0. The total energy dissipated (in Joules) in the resistor RR until steady state is reached, is _______.
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    Question

    A dc voltage of 10 V10\text{ V} is applied across an n-type silicon bar having a rectangular cross-section and a length of 1 cm1\text{ cm} as shown in figure. The donor doping concentration NDN_D and the mobility of electrons μn\mu_n are 1016 cm−310^{16}\text{ cm}^{-3} and 1000 cm2V−1s−11000\text{ cm}^2\text{V}^{-1}\text{s}^{-1}, respectively. The average time (in μs\mu\text{s}) taken by the electrons to move from one end of the bar to other end is _______.
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    Question

    In a MOS capacitor with an oxide layer thickness of 10 nm10\text{ nm}, the maximum depletion layer thickness is 100 nm100\text{ nm}. The permittivities of the semiconductor and the oxide layer are ϵs\epsilon_s and ϵox\epsilon_{ox} respectively. Assuming ϵs/ϵox=3\epsilon_s/\epsilon_{ox} = 3, the ratio of the maximum capacitance to the minimum capacitance of this MOS capacitor is _______.
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    Question

    Let x(t)=αs(t)+s(−t)x(t) = \alpha s(t) + s(-t) with s(t)=βe−4tu(t)s(t) = \beta e^{-4t} u(t), where u(t)u(t) is unit step function. If the bilateral Laplace transform of x(t)x(t) isX(s)=16s2−16,−4<Re{s}<4;X(s) = \frac{16}{s^2 - 16}, \quad -4 < \text{Re}\{s\} < 4;then the value of β\beta is _______.
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    Question

    The state variable representation of a system is given asx˙=[010−1]x;x(0)=[10]\dot{x} = \begin{bmatrix} 0 & 1 \\ 0 & -1 \end{bmatrix} x; \quad x(0) = \begin{bmatrix} 1 \\ 0 \end{bmatrix}y=[01]xy = \begin{bmatrix} 0 & 1 \end{bmatrix} xThe response y(t)y(t) is
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    The output of a standard second-order system for a unit step input is given asy(t)=1−23e−tcos⁡(3t−π6).y(t) = 1 - \frac{2}{\sqrt{3}} e^{-t} \cos\left(\sqrt{3}t - \frac{\pi}{6}\right).The transfer function of the system is
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    Question

    The transfer function of a mass-spring-damper system is given byG(s)=1Ms2+Bs+KG(s) = \frac{1}{Ms^2 + Bs + K}The frequency response data for the system are given in the following table.
    ω\omega in rad/s∣G(jω)∣|G(j\omega)| in dBarg⁡(G(jω))\arg (G(j\omega)) in deg
    0.01-18.5-0.2
    0.1-18.5-1.3
    0.2-18.4-2.6
    1-16-16.9
    2-11.4-89.4
    3-21.5-151
    5-32.8-167
    10-45.3-174.5
    The unit step response of the system approaches a steady state value of ____________.
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    The diode in the circuit given below has VON=0.7 VV_{ON} = 0.7\text{ V} but is ideal otherwise. The current (in mA) in the 4 kΩ4\text{ k}\Omega resistor is ______.
    A bridge circuit with a 1mA current source, resistors of 2k, 3k, 4k, 6k, and a center branch containing a diode and a 1k resistor.
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    {Xn}n=−∞n=∞\{X_n\}_{n=-\infty}^{n=\infty} is an independent and identically distributed (i.i.d.) random process with XnX_n equally likely to be +1+1 or −1-1. {Yn}n=−∞n=∞\{Y_n\}_{n=-\infty}^{n=\infty} is another random process obtained as Yn=Xn+0.5Xn−1Y_n = X_n + 0.5 X_{n-1}. The autocorrelation function of {Yn}n=−∞n=∞\{Y_n\}_{n=-\infty}^{n=\infty}, denoted by RY[k]R_Y[k], is
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    {Xn}n=−∞n=∞\{X_n\}_{n=-\infty}^{n=\infty} is an independent and identically distributed (i.i.d.) random process with XnX_n equally likely to be +1+1 or −1-1. {Yn}n=−∞n=∞\{Y_n\}_{n=-\infty}^{n=\infty} is another random process obtained as Yn=Xn+0.5Xn−1Y_n = X_n + 0.5 X_{n-1}. The autocorrelation function of {Yn}n=−∞n=∞\{Y_n\}_{n=-\infty}^{n=\infty}, denoted by RY[k]R_Y[k], is
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    Question

    Consider a binary, digital communication system which uses pulses g(t)g(t) and −g(t)-g(t) for transmitting bits over an AWGN channel. If the receiver uses a matched filter, which one of the following pulses will give the minimum probability of bit error?
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    An air-filled rectangular waveguide of internal dimensions a cm×b cma\text{ cm} \times b\text{ cm} (a>ba > b) has a cutoff frequency of 6 GHz6\text{ GHz} for the dominant TE10TE_{10} mode. For the same waveguide, if the cutoff frequency of the TM11TM_{11} mode is 15 GHz15\text{ GHz}, the cutoff frequency of the TE01TE_{01} mode in GHz is ______.
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    Two half-wave dipole antennas placed as shown in the figure are excited with sinusoidally varying currents of frequency 3 MHz3\text{ MHz} and phase shift of π/2\pi/2 between them (the element at the origin leads in phase). If the maximum radiated E⃗\vec{E}-field at the point PP in the xx-yy plane occurs at an azimuthal angle of 60∘60^\circ, the distance dd (in meters) between the antennas is _______.
    A diagram showing two antennas on the x-axis, one at the origin and one at distance d. Point P is at an angle 60 degrees from the x-axis. OP >> d.
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    The electric field of a plane wave propagating in a lossless non-magnetic medium is given by the following expressionE(z,t)=ax5cos⁡(2π×109t+βz)+ay3cos⁡(2π×109t+βz−π2)\mathbf{E}(z, t) = \mathbf{a}_x 5 \cos(2\pi \times 10^9 t + \beta z) + \mathbf{a}_y 3 \cos\left(2\pi \times 10^9 t + \beta z - \frac{\pi}{2}\right)The type of the polarization is
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