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GATE EC 2015 Set 3

All 65 solved GATE EC 2015 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 20Medium 43Hard 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.
    If the athlete had wanted to come first in the race, he ________________ several hours every day.
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    Question

    Choose the most suitable one word substitute for the following expression:
    Connotation of a road or way
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    Question

    Choose the correct verb to fill in the blank below:
    Let us ________________.
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    Question

    Find the missing sequence in the letter series below:
    A, CD, GHI, ?, UVWXY
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    Question

    If x>y>1x > y > 1, which of the following must be true?
    i. ln⁡x>ln⁡y\ln x > \ln y
    ii. ex>eye^x > e^y
    iii. yx>xyy^x > x^y
    iv. cos⁡x>cos⁡y\cos x > \cos y
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    Question

    Ram and Shyam shared a secret and promised to each other that it would remain between them. Ram expressed himself in one of the following ways as given in the choices below. Identify the correct way as per standard English.
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    Question

    In the following question, the first and the last sentence of the passage are in order and numbered 1 and 6. The rest of the passage is split into 4 parts and numbered as 2, 3, 4, and 5. These 4 parts are not arranged in proper order. Read the sentences and arrange them in a logical sequence to make a passage and choose the correct sequence from the given options.
    1.On Diwali, the family rises early in the morning.
    2.The whole family, including the young and the old enjoy doing this.
    3.Children let off fireworks later in the night with their friends.
    4.At sunset, the lamps are lit and the family performs various rituals.
    5.Father, mother, and children visit relatives and exchange gifts and sweets.
    6.Houses look so pretty with lighted lamps all around.
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    Question

    From a circular sheet of paper of radius 30 cm, a sector of 10% area is removed. If the remaining part is used to make a conical surface, then the ratio of the radius and height of the cone is _______.
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    Question

    log⁡tan⁡1∘+log⁡tan⁡2∘+⋯+log⁡tan⁡89∘\log \tan 1^\circ + \log \tan 2^\circ + \dots + \log \tan 89^\circ is....
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    Question

    Ms. X will be in Bagdogra from 01/05/2014 to 20/05/2014 and from 22/05/2014 to 31/05/2014. On the morning of 21/05/2014, she will reach Kochi via Mumbai.
    Which one of the statements below is logically valid and can be inferred from the above sentences?
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Electronics and Communication Engineering

55
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    Question

    For A=[1tan⁡x−tan⁡x1]A = \begin{bmatrix} 1 & \tan x \\ -\tan x & 1 \end{bmatrix}, the determinant of ATA−1A^T A^{-1} is
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    Question

    The contour on the xx-yy plane, where the partial derivative of x2+y2x^2 + y^2 with respect to yy is equal to the partial derivative of 6y+4x6y + 4x with respect to xx, is
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    Question

    If CC is a circle of radius rr with centre z0z_0, in the complex zz-plane and if nn is a non-zero integer, then ∮Cdz(z−z0)n+1\oint_C \frac{dz}{(z-z_0)^{n+1}} equals
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    Question

    Consider the function g(t)=e−tsin⁡(2πt)u(t)g(t) = e^{-t} \sin(2\pi t) u(t) where u(t)u(t) is the unit step function. The area under g(t)g(t) is ________.
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    Question

    The value of ∑n=0∞n(12)n\sum_{n=0}^{\infty} n \left(\frac{1}{2}\right)^n is ________.
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    Question

    For the circuit shown in the figure, the Thevenin equivalent voltage (in Volts) across terminals a-b is ________.
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    Question

    In the circuit shown, the voltage VxV_x (in Volts) is ________.
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    Question

    At very high frequencies, the peak output voltage V0V_0 (in Volts) is ________.
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    Question

    Which one of the following processes is preferred to form the gate dielectric (SiO2SiO_2) of MOSFETs?
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    Question

    If the base width in a bipolar junction transistor is doubled, which one of the following statements will be TRUE?
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    Question

    In the circuit shown in the figure, the BJT has a current gain (β\beta) of 50. For an emitter-base voltage VEB=600 mVV_{EB} = 600\text{ mV}, the emitter-collector voltage VECV_{EC} (in Volts) is ______.
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    Question

    In the circuit shown using an ideal opamp, the 3-dB cut-off frequency (in Hz) is _______.
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    Question

    In the circuit shown, assume that diodes D1D_1 and D2D_2 are ideal. In the steady state condition, the average voltage VabV_{ab} (in Volts) across the 0.5 μF0.5\text{ }\mu\text{F} capacitor is _______.
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    Question

    The circuit shown consists of J-K flip-flops, each with an active low asynchronous reset (Rd‾\overline{R_d} input). The counter corresponding to this circuit is
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    Question

    In the circuit shown, diodes D₁, D₂ and D₃ are ideal, and the inputs E₁, E₂ and E₃ are "0 V" for logic '0' and "10 V" for logic '1'. What logic gate does the circuit represent?
    A circuit diagram with three inputs E1, E2, E3 connected to the anodes of three diodes D1, D2, D3 respectively. The cathodes are joined together and connected to a 10V source through a 1kΩ resistor. The output Vo is taken from the common cathode point.
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    Question

    Which one of the following 8085 microprocessor programs correctly calculates the product of two 8-bit numbers stored in registers B and C?
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    Question

    The impulse response of an LTI system can be obtained by
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    Question

    Consider a four-point moving average filter defined by the equation y[n]=∑i=03αix[n−i]y[n] = \sum_{i=0}^{3} \alpha_i x[n-i]. The condition on the filter coefficients that results in a null at zero frequency is
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    Question

    Consider the Bode plot shown in the figure. Assume that all the poles and zeros are real-valued.
    Bode magnitude plot showing a bandpass characteristic with slopes of +40 dB/dec and -40 dB/dec. The gain is 0 dB at $f_L$ and $f_H$, and 40 dB between 300 Hz and 900 Hz.
    The value of fH−fLf_H - f_L (in Hz) is ___________.
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    Question

    The phase margin (in degrees) of the system G(s)=10s(s+10)G(s) = \frac{10}{s(s+10)} is ___________.
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    Question

    The transfer function of a first-order controller is given asGc(s)=K(s+a)s+bG_c(s) = \frac{K(s + a)}{s + b}where KK, aa and bb are positive real numbers. The condition for this controller to act as a phase lead compensator is
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    Question

    The modulation scheme commonly used for transmission from GSM mobile terminals is
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    Question

    A message signal m(t)=Amsin⁡(2πfmt)m(t) = A_m \sin(2\pi f_m t) is used to modulate the phase of a carrier Accos⁡(2πfct)A_c \cos(2\pi f_c t) to get the modulated signal y(t)=Accos⁡(2πfct+m(t))y(t) = A_c \cos(2\pi f_c t + m(t)). The bandwidth of y(t)y(t)
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    Question

    The directivity of an antenna array can be increased by adding more antenna elements, as a larger number of elements
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    Question

    A coaxial cable is made of two brass conductors. The spacing between the conductors is filled with Teflon (ϵr′=2.1,tan⁡δ=0\epsilon_r' = 2.1, \tan \delta = 0). Which one of the following circuits can represent the lumped element model of a small piece of this cable having length Δz\Delta z?
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    Question

    The Newton-Raphson method is used to solve the equation f(x)=x3−5x2+6x−8=0f(x) = x^3 - 5x^2 + 6x - 8 = 0. Taking the initial guess as x=5x = 5, the solution obtained at the end of the first iteration is ________.
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    Question

    A fair die with faces {1,2,3,4,5,6}\{1, 2, 3, 4, 5, 6\} is thrown repeatedly till '3' is observed for the first time. Let XX denote the number of times the die is thrown. The expected value of XX is ______.
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    Question

    Consider the differential equation d2x(t)dt2+3dx(t)dt+2x(t)=0.\frac{d^2x(t)}{dt^2} + 3\frac{dx(t)}{dt} + 2x(t) = 0. Given x(0)=20x(0) = 20 and x(1)=10/ex(1) = 10/e, where e=2.718e = 2.718, the value of x(2)x(2) is ______.
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    Question

    A vector field D=2ρ2aρ+zaz\mathbf{D} = 2\rho^2 \mathbf{a}_\rho + z \mathbf{a}_z exists inside a cylindrical region enclosed by the surfaces ρ=1,z=0\rho = 1, z = 0 and z=5z = 5. Let SS be the surface bounding this cylindrical region. The surface integral of this field on SS (∮SD⋅ds\oint_S \mathbf{D} \cdot d\mathbf{s}) is ______.
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    Question

    In the circuit shown, the current II flowing through the 50 Ω50\ \Omega resistor will be zero if the value of capacitor CC (in μF\mu\text{F}) is ______.
    A circuit diagram with a sinusoidal source, a resistor, three inductors, and a capacitor
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    Question

    The ABCD parameters of the following 2-port network are
    A T-network with three complex impedances
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    Question

    A network is described by the state model asx˙1=2x1−x2+3u\dot{x}_1 = 2x_1 - x_2 + 3ux˙2=−4x2−u\dot{x}_2 = -4x_2 - uy=3x1−2x2y = 3x_1 - 2x_2The transfer function H(s)(=Y(s)U(s))H(s) (= \frac{Y(s)}{U(s)}) is
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    Question

    The electric field profile in the depletion region of a p-n junction in equilibrium is shown in the figure. Which one of the following statements is NOT TRUE?
    Electric field profile E(V/cm) vs X(μm) for a p-n junction
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    Question

    The current in an enhancement mode NMOS transistor biased in saturation mode was measured to be 1 mA at a drain-source voltage of 5 V. When the drain-source voltage was increased to 6 V while keeping gate-source voltage same, the drain current increased to 1.02 mA. Assume that drain to source saturation voltage is much smaller than the applied drain-source voltage. The channel length modulation parameter λ\lambda (in V−1V^{-1}) is ______.
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    Question

    An npn BJT having reverse saturation current Is=10−15 AI_s = 10^{-15} \text{ A} is biased in the forward active region with VBE=700 mVV_{BE} = 700 \text{ mV}. The thermal voltage (VTV_T) is 25 mV and the current gain (β\beta) may vary from 50 to 150 due to manufacturing variations. The maximum emitter current (in μ\mu A) is ______.
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    Question

    A three bit pseudo random number generator is shown. Initially the value of output Y=Y2Y1Y0Y = Y_2 Y_1 Y_0 is set to 111. The value of output YY after three clock cycles is
    A 3-bit linear feedback shift register (LFSR) circuit using three D flip-flops and an XOR gate. The XOR gate inputs are connected to the outputs of the second and third flip-flops (Y1 and Y0).
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    Question

    A universal logic gate can implement any Boolean function by connecting sufficient number of them appropriately. Three gates are shown.
    Three logic gates: Gate 1 is an OR gate ($F1 = X + Y$), Gate 2 is an AND gate ($F2 = X \cdot Y$), and Gate 3 is a gate with function $F3 = \bar{X} + Y$.
    Which one of the following statements is TRUE?
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    Question

    An SR latch is implemented using TTL gates as shown in the figure. The set and reset pulse inputs are provided using the push-button switches. It is observed that the circuit fails to work as desired. The SR latch can be made functional by changing
    A circuit diagram showing an SR latch made of two cross-coupled NOR gates. The inputs S and R are driven by inverters, which are connected to a 5V supply through push-button switches.
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    Question

    In the circuit shown, assume that the opamp is ideal. If the gain (vo/vinv_o / v_{in}) is −12-12, the value of RR (in kΩk\Omega) is ______.
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    Question

    In the circuit shown, both the enhancement mode NMOS transistors have the following characteristics: kn=μnCox(W/L)=1 mA/V2k_n = \mu_n C_{ox} (W/L) = 1\text{ mA/V}^2; VTN=1 VV_{TN} = 1\text{ V}. Assume that the channel length modulation parameter λ\lambda is zero and body is shorted to source. The minimum supply voltage VDDV_{DD} (in volts) needed to ensure that transistor M1M_1 operates in saturation mode of operation is ______.
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    Question

    In the circuit shown, assume that the diodes D1D_1 and D2D_2 are ideal. The average value of voltage VabV_{ab} (in Volts), across terminals 'a' and 'b' is ______.
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    Question

    Suppose x[n]x[n] is an absolutely summable discrete-time signal. Its z-transform is a rational function with two poles and two zeroes. The poles are at z=±2jz = \pm 2j. Which one of the following statements is TRUE for the signal x[n]x[n]?
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    Question

    A realization of a stable discrete time system is shown in the figure. If the system is excited by a unit step sequence input x[n]x[n], the response y[n]y[n] is
    Block diagram of a discrete-time system realization with feedback coefficients 1 and -2/9, and feedforward coefficients -5/3 and 5/3
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    Question

    Let x~[n]=1+cos⁡(πn8)\tilde{x}[n] = 1 + \cos\left(\frac{\pi n}{8}\right) be a periodic signal with period 16. Its DFS coefficients are defined by ak=116∑n=015x~[n]exp⁡(−jπ8kn)a_k = \frac{1}{16} \sum_{n=0}^{15} \tilde{x}[n] \exp\left(-j \frac{\pi}{8} kn\right) for all kk. The value of the coefficient a31a_{31} is ______.
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    Question

    An npn BJT having reverse saturation current Is=10−15I_s = 10^{-15} A is biased in the forward active region with VBE=700V_{BE} = 700 mV. The thermal voltage (VTV_T) is 25 mV and the current gain (β\beta) may vary from 50 to 150 due to manufacturing variations. The maximum emitter current (in μ\mu A) is _______.
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    Question

    A three bit pseudo random number generator is shown. Initially the value of output Y=Y2Y1Y0Y = Y_2 Y_1 Y_0 is set to 111. The value of output YY after three clock cycles is
    three bit pseudo random number generator circuit diagram
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    Question

    A universal logic gate can implement any Boolean function by connecting sufficient number of them appropriately. Three gates are shown.
    Three logic gates Gate 1, Gate 2, Gate 3
    Which one of the following statements is TRUE?
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    Question

    The characteristic equation of an LTI system is given by F(s)=s5+2s4+3s3+6s2−4s−8=0F(s) = s^5 + 2s^4 + 3s^3 + 6s^2 - 4s - 8 = 0. The number of roots that lie strictly in the left half ss-plane is ______.
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    Question

    Two sequences x1[n]x_1[n] and x2[n]x_2[n] have the same energy. Suppose x1[n]=α 0.5nu[n]x_1[n] = \alpha \ 0.5^n u[n], where α\alpha is a positive real number and u[n]u[n] is the unit step sequence. Assumex2[n]={1.5for n=0,10otherwise.x_2[n] = \begin{cases} \sqrt{1.5} & \text{for } n = 0, 1 \\ 0 & \text{otherwise.} \end{cases}Then the value of α\alpha is ______.
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    Question

    The variance of the random variable XX with probability density function f(x)=12∣x∣e−∣x∣f(x) = \frac{1}{2} |x| e^{-|x|} is ______.
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    The complex envelope of the bandpass signal x(t)=−2(sin⁡(πt/5)πt/5)sin⁡(πt−π4)x(t) = -\sqrt{2} \left( \frac{\sin(\pi t / 5)}{\pi t / 5} \right) \sin(\pi t - \frac{\pi}{4}), centered about f=12f = \frac{1}{2} Hz, is
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    A random binary wave y(t)y(t) is given byy(t)=∑n=−∞∞Xnp(t−nT−ϕ)y(t) = \sum_{n=-\infty}^{\infty} X_n p(t - nT - \phi)where p(t)=u(t)−u(t−T)p(t) = u(t) - u(t - T), u(t)u(t) is the unit step function and ϕ\phi is an independent random variable with uniform distribution in [0,T][0, T]. The sequence {Xn}\{X_n\} consists of independent and identically distributed binary valued random variables with P{Xn=+1}=P{Xn=−1}=0.5P\{X_n = +1\} = P\{X_n = -1\} = 0.5 for each nn. The value of the autocorrelation Ryy(3T4)≜E[y(t)y(t−3T4)]R_{yy} \left( \frac{3T}{4} \right) \triangleq E \left[ y(t) y \left( t - \frac{3T}{4} \right) \right] equals ________.
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    Consider the 3 m long lossless air-filled transmission line shown in the figure. It has a characteristic impedance of 120πΩ120\pi \Omega, is terminated by a short circuit, and is excited with a frequency of 37.5 MHz. What is the nature of the input impedance (ZinZ_{in})?
    Transmission line diagram showing a 3 m line with $Z_L = 0$
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    A 200 m200\text{ m} long transmission line having parameters shown in the figure is terminated into a load RLR_L. The line is connected to a 400 V400\text{ V} source having source resistance RSR_S through a switch, which is closed at t=0t = 0. The transient response of the circuit at the input of the line (z=0z = 0) is also drawn in the figure. The value of RLR_L (in Ω\Omega) is ______.
    Circuit diagram of a transmission line with source and load, and a graph of voltage vs time at z=0
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    A coaxial capacitor of inner radius 1 mm1\text{ mm} and outer radius 5 mm5\text{ mm} has a capacitance per unit length of 172 pF/m172\text{ pF/m}. If the ratio of outer radius to inner radius is doubled, the capacitance per unit length (in pF/m\text{pF/m}) is ______.
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