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GATE EC 2015 Set 1

All 65 solved GATE EC 2015 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 39Hard 3

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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.
    The principal presented the chief guest with a ________, as token of appreciation.
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    Question

    Choose the appropriate word/phrase, out of the four options given below, to complete the following sentence:
    Frogs ________
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    Question

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

    Operators □\square, ⋄\diamond and →\rightarrow are defined by: a□b=a−ba+ba \square b = \frac{a-b}{a+b}; a⋄b=a+ba−ba \diamond b = \frac{a+b}{a-b}; a→b=aba \rightarrow b = ab.
    Find the value of (66□6)→(66⋄6)(66 \square 6) \rightarrow (66 \diamond 6).
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    Question

    If log⁡x(5/7)=−1/3\log_x (5/7) = -1/3, then the value of xx is
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    Question

    The following question presents a sentence, part of which is underlined. Beneath the sentence you find four ways of phrasing the underlined part. Following the requirements of the standard written English, select the answer that produces the most effective sentence.
    Tuberculosis, together with its effects, ranks one of the leading causes of death in India.
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    Question

    Read the following paragraph and choose the correct statement.
    Climate change has reduced human security and threatened human well-being. An ignored reality of human progress is that human security largely depends upon environmental security. But on the contrary, human progress seems contradictory to environmental security. To keep up both at the required level is a challenge to be addressed by one and all. One of the ways to curb the climate change may be suitable scientific innovations, while the other may be the Gandhian perspective on small scale progress with focus on sustainability.
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    Question

    Fill in the missing value
    A diagram showing a hexagonal grid of circles containing numbers. The rows have 3, 5, 7, 5, and 3 circles respectively. The middle circle of the bottom row is empty.
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    Question

    A cube of side 3 units is formed using a set of smaller cubes of side 1 unit. Find the proportion of the number of faces of the smaller cubes visible to those which are NOT visible.
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    Question

    Humpty Dumpty sits on a wall every day while having lunch. The wall sometimes breaks. A person sitting on the wall falls if the wall breaks.
    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

    Consider a system of linear equations:x−2y+3z=−1,x−3y+4z=1, and−2x+4y−6z=k.\begin{aligned} x - 2y + 3z &= -1, \\ x - 3y + 4z &= 1, \text{ and} \\ -2x + 4y - 6z &= k. \end{aligned}The value of kk for which the system has infinitely many solutions is _______.
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    Question

    A function f(x)=1−x2+x3f(x) = 1 - x^2 + x^3 is defined in the closed interval [−1,1][-1, 1]. The value of xx, in the open interval (−1,1)(-1, 1) for which the mean value theorem is satisfied, is
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    Question

    Suppose AA and BB are two independent events with probabilities P(A)≠0P(A) \neq 0 and P(B)≠0P(B) \neq 0. Let A‾\overline{A} and B‾\overline{B} be their complements. Which one of the following statements is FALSE?
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    Question

    Let z=x+iyz = x + iy be a complex variable. Consider that contour integration is performed along the unit circle in anticlockwise direction. Which one of the following statements is NOT TRUE?
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    Question

    The value of pp such that the vector [123]\begin{bmatrix} 1 \\ 2 \\ 3 \end{bmatrix} is an eigenvector of the matrix [412p2114−410]\begin{bmatrix} 4 & 1 & 2 \\ p & 2 & 1 \\ 14 & -4 & 10 \end{bmatrix} is ________.
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    Question

    In the circuit shown, at resonance, the amplitude of the sinusoidal voltage (in Volts) across the capacitor is ________.
    RLC series circuit with a sinusoidal voltage source
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    Question

    In the network shown in the figure, all resistors are identical with R=300 ΩR = 300\ \Omega. The resistance RabR_{ab} (in Ω\Omega) of the network is ________.
    Symmetric resistor bridge network
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    Question

    In the given circuit, the values of V1V_1 and V2V_2 respectively are
    Circuit with independent current source and dependent current source
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    Question

    A region of negative differential resistance is observed in the current voltage characteristics of a silicon PN junction if
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    Question

    A silicon sample is uniformly doped with donor type impurities with a concentration of 1016 /cm310^{16} \text{ /cm}^3. The electron and hole mobilities in the sample are 1200 cm2/V-s1200 \text{ cm}^2/\text{V-s} and 400 cm2/V-s400 \text{ cm}^2/\text{V-s} respectively. Assume complete ionization of impurities. The charge of an electron is 1.6×10−19 C1.6 \times 10^{-19} \text{ C}. The resistivity of the sample (in Ω-cm\Omega\text{-cm}) is ______.
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    Question

    For the circuit with ideal diodes shown in the figure, the shape of the output (voutv_{out}) for the given sine wave input (vinv_{in}) will be
    circuit diagram with two diodes and a resistor
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    Question

    In the circuit shown below, the Zener diode is ideal and the Zener voltage is 6 V6\text{ V}. The output voltage VoV_o (in volts) is ______.
    Circuit diagram with a 10V DC source, a 1kΩ series resistor, a Zener diode in parallel with a 1kΩ load resistor.
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    Question

    In the circuit shown, the switch SW is thrown from position AA to position BB at time t=0t = 0. The energy (in μJ\mu\text{J}) taken from the 3 V3\text{ V} source to charge the 0.1 μF0.1\text{ }\mu\text{F} capacitor from 0 V0\text{ V} to 3 V3\text{ V} is
    Circuit diagram showing a 3V DC source, a 120Ω resistor, a switch SW with positions A and B, and a 0.1μF capacitor connected to ground.
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    Question

    In an 8085 microprocessor, the shift registers which store the result of an addition and the overflow bit are, respectively
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    Question

    A 16 Kb (=16,384 bit)16\text{ Kb } (=16,384\text{ bit}) memory array is designed as a square with an aspect ratio of one (number of rows is equal to the number of columns). The minimum number of address lines needed for the row decoder is _______.
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    Question

    Consider a four bit D to A converter. The analog value corresponding to digital signals of values 00000000 and 00010001 are 0 V0\text{ V} and 0.0625 V0.0625\text{ V} respectively. The analog value (in Volts) corresponding to the digital signal 11111111 is _______.
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    Question

    The result of the convolution x(−t)∗δ(−t−t0)x(-t) * \delta(-t - t_0) is
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    Question

    The waveform of a periodic signal x(t)x(t) is shown in the figure.
    Waveform of a periodic signal x(t)
    A signal g(t)g(t) is defined by g(t)=x(t−12)g(t) = x\left(\frac{t-1}{2}\right). The average power of g(t)g(t) is _______.
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    Question

    Negative feedback in a closed-loop control system DOES NOT
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    Question

    A unity negative feedback system has the open-loop transfer function G(s)=Ks(s+1)(s+3)G(s) = \frac{K}{s(s+1)(s+3)}. The value of the gain K(>0)K (>0) at which the root locus crosses the imaginary axis is _______.
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    Question

    The polar plot of the transfer function G(s)=10(s+1)s+10G(s) = \frac{10(s+1)}{s+10} for 0≤ω<∞0 \leq \omega < \infty will be in the
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    Question

    A sinusoidal signal of 2 kHz2\text{ kHz} frequency is applied to a delta modulator. The sampling rate and step-size Δ\Delta of the delta modulator are 20,000 samples per second20,000\text{ samples per second} and 0.1 V0.1\text{ V}, respectively. To prevent slope overload, the maximum amplitude of the sinusoidal signal (in Volts) is
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    Question

    Consider the signal s(t)=m(t)cos⁡(2πfct)+m^(t)sin⁡(2πfct)s(t) = m(t) \cos(2\pi f_c t) + \hat{m}(t) \sin(2\pi f_c t) where m^(t)\hat{m}(t) denotes the Hilbert transform of m(t)m(t) and the bandwidth of m(t)m(t) is very small compared to fcf_c. The signal s(t)s(t) is a
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    Question

    Consider a straight, infinitely long, current carrying conductor lying on the zz-axis. Which one of the following plots (in linear scale) qualitatively represents the dependence of HϕH_\phi on rr, where HϕH_\phi is the magnitude of the azimuthal component of magnetic field outside the conductor and rr is the radial distance from the conductor?
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    Question

    The electric field component of a plane wave traveling in a lossless dielectric medium is given by E⃗(z,t)=a^y2cos⁡(108t−z2) V/m\vec{E}(z, t) = \hat{a}_y 2 \cos \left( 10^8 t - \frac{z}{\sqrt{2}} \right) \text{ V/m}. The wavelength (in m) for the wave is ________.
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    Question

    The solution of the differential equation d2ydt2+2dydt+y=0\frac{d^2y}{dt^2} + 2 \frac{dy}{dt} + y = 0 with y(0)=y′(0)=1y(0) = y'(0) = 1 is
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    Question

    A vector P⃗\vec{P} is given by P⃗=x3ya^x−x2y2a^y−x2yza^z\vec{P} = x^3 y \hat{a}_x - x^2 y^2 \hat{a}_y - x^2 yz \hat{a}_z. Which one of the following statements is TRUE?
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    Question

    Which one of the following graphs describes the function f(x)=e−x(x2+x+1)f(x) = e^{-x}(x^2 + x + 1)?
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    Question

    The maximum area (in square units) of a rectangle whose vertices lie on the ellipse x2+4y2=1x^2 + 4y^2 = 1 is ___________.
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    Question

    The damping ratio of a series RLCRLC circuit can be expressed as
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    Question

    In the circuit shown, switch SW is closed at t=0t = 0. Assuming zero initial conditions, the value of vc(t)v_c(t) (in Volts) at t=1t = 1 sec is ________.
    Circuit diagram with a 10V source, a switch, a 3 ohm resistor, a 2 ohm resistor, and a 5/6 F capacitor
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    Question

    In the given circuit, the maximum power (in Watts) that can be transferred to the load RLR_L is ________.
    Circuit diagram with an AC source $4 \angle 0 V_{rms}$, a $2 \Omega$ resistor, a $j2 \Omega$ inductor, and a load $R_L$
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    Question

    The built-in potential of an abrupt p-n junction is 0.75 V. If its junction capacitance (CJC_J) at a reverse bias (VRV_R) of 1.25 V is 5 pF, the value of CJC_J (in pF) when VRV_R = 7.25 V is _____.
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    Question

    A MOSFET in saturation has a drain current of 1 mA for VDSV_{DS} = 0.5 V. If the channel length modulation coefficient is 0.05 V−1V^{-1}, the output resistance (in kΩ\Omega) of the MOSFET is _____.
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    Question

    For a silicon diode with long P and N regions, the accepter and donor impurity concentrations are 1×10171 \times 10^{17} cm−3cm^{-3} and 1×10151 \times 10^{15} cm−3cm^{-3}, respectively. The lifetimes of electrons in P region and holes in N region are both 100 μs\mu s. The electron and hole diffusion coefficients are 49 cm2/scm^2/s and 36 cm2/scm^2/s, respectively. Assume kT/qkT/q = 26 mV, the intrinsic carrier concentration is 1×10101 \times 10^{10} cm−3cm^{-3}, and q=1.6×10−19q = 1.6 \times 10^{-19} C. When a forward voltage of 208 mV is applied across the diode, the hole current density (in nA/cm2nA/cm^2) injected from P region to N region is _____.
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    Question

    The Boolean expression F(X,Y,Z)=XˉYˉZ+XˉYZˉ+XYZˉ+XYZF(X, Y, Z) = \bar{X} \bar{Y} Z + \bar{X} Y \bar{Z} + X Y \bar{Z} + X Y Z converted into the canonical product of sum (POS) form is
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    Question

    All the logic gates shown in the figure have a propagation delay of 20 ns. Let A=C=0A = C = 0 and B=1B = 1 until time t=0t = 0. At t=0t = 0, all the inputs flip (i.e., A=C=1A = C = 1 and B=0B = 0) and remain in that state. For t>0t > 0, output Z=1Z = 1 for a duration (in ns) of ________.
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    A 3-input majority gate is defined by the logic function M(a,b,c)=ab+bc+caM(a, b, c) = ab + bc + ca. Which one of the following gates is represented by the function M(M(a,b,c),M(a,b,cˉ),c)M(M(a, b, c), M(a, b, \bar{c}), c)?
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    Question

    For the NMOSFET in the circuit shown, the threshold voltage is VthV_{th}, where Vth>0V_{th} > 0. The source voltage VSSV_{SS} is varied from 00 to VDDV_{DD}. Neglecting the channel length modulation, the drain current IDI_D as a function of VSSV_{SS} is represented by
    NMOSFET circuit diagram
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    Question

    In the circuit shown, assume that the opamp is ideal. The bridge output voltage V0V_0 (in mV) for δ=0.05\delta = 0.05 is ______.
    Bridge circuit connected to an ideal op-amp with a 1V source
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    Question

    The circuit shown in the figure has an ideal opamp. The oscillation frequency and the condition to sustain the oscillations, respectively, are
    Oscillator circuit with series and parallel RC networks
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    Question

    In the circuit shown, I1=80I_1 = 80 mA and I2=4I_2 = 4 mA. Transistors T1T_1 and T2T_2 are identical. Assume that the thermal voltage VTV_T is 26 mV at 27 °C. At 50 °C, the value of the voltage V12=V1−V2V_{12} = V_1 - V_2 (in mV) is
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    Question

    Two sequences [a,b,c][a, b, c] and [A,B,C][A, B, C] are related as,(ABC)=(1111W3−1W3−21W3−2W3−4)(abc) where W3=ej2π3.\begin{pmatrix} A \\ B \\ C \end{pmatrix} = \begin{pmatrix} 1 & 1 & 1 \\ 1 & W_3^{-1} & W_3^{-2} \\ 1 & W_3^{-2} & W_3^{-4} \end{pmatrix} \begin{pmatrix} a \\ b \\ c \end{pmatrix} \text{ where } W_3 = e^{j\frac{2\pi}{3}}.If another sequence [p,q,r][p, q, r] is derived as,(pqr)=(1111W32W341W34W32)(A/3B/3C/3)\begin{pmatrix} p \\ q \\ r \end{pmatrix} = \begin{pmatrix} 1 & 1 & 1 \\ 1 & W_3^2 & W_3^4 \\ 1 & W_3^4 & W_3^2 \end{pmatrix} \begin{pmatrix} A/3 \\ B/3 \\ C/3 \end{pmatrix}then the relationship between the sequences [p,q,r][p,q,r] and [a,b,c][a, b, c] is
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    Question

    A 3-input majority gate is defined by the logic function M(a,b,c)=ab+bc+caM(a, b, c) = ab+bc+ca. Which one of the following gates is represented by the function M(M(a,b,c),M(a,b,c),c)M(M(a,b,c), M(a,b,c), c) ?
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    Question

    The pole-zero diagram of a causal and stable discrete-time system is shown in the figure. The zero at the origin has multiplicity 4. The impulse response of the system is h[n]h[n]. If h[0]=1h[0] = 1, we can conclude
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    Question

    The open-loop transfer function of a plant in a unity feedback configuration is given as G(s)=K(s+4)(s+8)(s2−9)G(s) = \frac{K(s+4)}{(s+8)(s^2-9)}. The value of the gain K(>0)K(>0) for which −1+j2-1 + j2 lies on the root locus is _________.
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    Question

    A lead compensator network includes a parallel combination of RR and CC in the feed-forward path. If the transfer function of the compensator is Gc(s)=s+2s+4G_c(s) = \frac{s+2}{s+4}, the value of RCRC is _________.
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    A plant transfer function is given as G(s)=(Kp+KIs)1s(s+2)G(s) = \left( K_p + \frac{K_I}{s} \right) \frac{1}{s(s+2)}. When the plant operates in a unity feedback configuration, the condition for the stability of the closed loop system is
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    The input XX to the Binary Symmetric Channel (BSC) shown in the figure is '1' with probability 0.8. The cross-over probability is 1/7. If the received bit Y=0Y = 0, the conditional probability that '1' was transmitted is ________.
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    The transmitted signal in a GSM system is of 200 kHz bandwidth and 8 users share a common bandwidth using TDMA. If at a given time 12 users are talking in a cell, the total bandwidth of the signal received by the base station of the cell will be at least (in kHz) ________.
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    In the system shown in Figure (a), m(t)m(t) is a low-pass signal with bandwidth WW Hz. The frequency response of the band-pass filter H(f)H(f) is shown in Figure (b). If it is desired that the output signal z(t)=10x(t)z(t) = 10x(t), the maximum value of WW (in Hz) should be strictly less than ________.
    System block diagram (a) and filter frequency response (b)
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    A source emits bit 0 with probability 13\frac{1}{3} and bit 1 with probability 23\frac{2}{3}. The emitted bits are communicated to the receiver. The receiver decides for either 0 or 1 based on the received value RR. It is given that the conditional density functions of RR are asfR∣0(r)={14,−3≤r≤1,0,otherwise,andfR∣1(r)={16,−1≤r≤5,0,otherwise.f_{R|0}(r) = \begin{cases} \frac{1}{4}, & -3 \leq r \leq 1, \\ 0, & \text{otherwise}, \end{cases} \quad \text{and} \quad f_{R|1}(r) = \begin{cases} \frac{1}{6}, & -1 \leq r \leq 5, \\ 0, & \text{otherwise}. \end{cases}The minimum decision error probability is
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    The longitudinal component of the magnetic field inside an air-filled rectangular waveguide made of a perfect electric conductor is given by the following expressionHz(x,y,z,t)=0.1cos⁡(25πx)cos⁡(30.3πy)cos⁡(12π×109t−βz) (A/m)H_z(x, y, z, t) = 0.1 \cos(25\pi x) \cos(30.3 \pi y) \cos(12\pi \times 10^9 t - \beta z) \text{ (A/m)}The cross-sectional dimensions of the waveguide are given as a=0.08 ma = 0.08 \text{ m} and b=0.033 mb = 0.033 \text{ m}. The mode of propagation inside the waveguide is
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    The electric field intensity of a plane wave traveling in free space is given by the following expressionE(x,t)=ay 24 πcos⁡(ωt−k0x) (V/m)\mathbf{E}(x, t) = \mathbf{a}_y \, 24 \, \pi \cos(\omega t - k_0 x) \, (\text{V/m})In this field, consider a square area 10 cm×10 cm10 \text{ cm} \times 10 \text{ cm} on a plane x+y=1x + y = 1. The total time-averaged power (in mW) passing through the square area is _________.
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    Consider a uniform plane wave with amplitude (E0E_0) of 10 V/m10 \text{ V/m} and 1.1 GHz1.1 \text{ GHz} frequency travelling in air, and incident normally on a dielectric medium with complex relative permittivity (εr\varepsilon_r) and permeability (μr\mu_r) as shown in the figure.
    A uniform plane wave incident normally from air onto a dielectric medium with complex properties
    The magnitude of the transmitted electric field component (in V/m) after it has travelled a distance of 10 cm10 \text{ cm} inside the dielectric region is _________.
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