GATE ECE 2013
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## GATE ECE

In the circuit shown below, the silicon npn transistor Q has a very high value of $$\beta$$. The required value of R2 i
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The ac schematic of an NMOS common-source stage is shown in the figure below, where part of the biasing circuits has bee
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In a voltage-voltage feedback as shown below, which one of the following statements is TRUE, if the gain k is increased?
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In the circuit shown below, what is the output voltage (vout ) if a silicon transistor Q and an ideal op-amp are used?
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In the circuit shown below the op-amps are ideal. Then Vout in Volts is
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The bit rate of a digital communication system is R kbits/s. The modulation used is 32-QAM. The minimum bandwidth requir
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Bits 1 and 0 are transmitted with equal probability. At the receiver, the pdf of the respective received signals for bot
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Bits 1 and 0 are transmitted with equal probability. At the receiver, the pdf of the respective received signals for bot
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Let U and V be two independent zero mean Gaussian random variables of variances $${{1 \over 4}}$$ and $${{1 \over 9}}$$
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The signal flow graph for a system is given below. The transfer function $$\frac{Y(s)}{U(s)}$$ for this system is
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Which one of the following statements is NOT TRUE for a continuous time causal and stable LTI system?
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A polynomial $$f\left(x\right)\;=\;a_4x^4\;+\;a_3x^3\;+\;a_2x^2\;+\;a_1x\;-\;a_0$$ with all coefficients positive has
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The open-loop transfer function of a dc motor is given as $$\;\frac{\omega\left(s\right)}{V_a\left(s\right)}=\frac{10}{1 View Question The Bode plot of a transfer function G (s) is shown in the figure below. The gain (20 log$$\left| {G(s)} \right|$$View Question The state diagram of a system is shown below. A system is shown below. A system is described by the state variable equat View Question The state diagram of a system is shown below. A system is shown below. A system is described by the state variable equat View Question In the sum of products function f (x,y,z) =$$\sum {} $$m (2,3,4,5), the prime implicants are View Question A bulb in a staircase has two switches, one switch being at the ground floor and the other one at the first floor. The b View Question In the circuit shown below, Q1 has negligible collector-to-emitter saturation voltage and the diode drops negligible vol View Question The divergence of the vector field$$\overrightarrow A\;=\;x{\widehat a}_x\;+\;y{\widehat a}_y\;+\;z{\widehat a}_z$$is View Question The return loss of a device is found to be 20 dB. The voltage standing wave ratio (VSWR) and magnitude of reflection coe View Question A monochromatic plane wave of wavelength$$\lambda = 600$$is propagating in the direction as shown in the figure below View Question A monochromatic plane wave of wavelength$$\lambda = 600$$is propagating in the direction as shown in the figure below View Question In a forward biased P-N junction diode, the sequence of events that best describes the mechanism of current flow is View Question In the circuit shown below, the knee current of the ideal Zener diode is 10 mA. To maintain 5V across RL, the minimum va View Question In IC technology, dry oxidation (using dry oxygen) as compared to wet oxidation (using steam or water vapor) produces View Question In a MOSFET operating in the saturation region, the channel length modulation effect causes View Question The small-signal resistance (i.e.,$${{d{V_B}} \over {d{I_D}}}$$) in$$k\Omega $$offered by the n-channel MOSFET M sho View Question The minimum eigenvalue of the following matrix is$$\left[ {\matrix{ 3 &amp; 5 &amp; 2 \cr 5 &amp; {12} &amp; 7
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Let $$A$$ be an $$m\,\, \times \,\,n$$ matrix and $$B$$ an $$n\,\, \times \,\,m$$ matrix. It is given that determinant $View Question Consider a vector field $$\overrightarrow A \left( {\overrightarrow r } \right).$$ The closed loop line integral $$\oint View Question The divergence of the vector field$$\,\overrightarrow A = x\widehat a{}_x + y\widehat a{}_y + z\widehat a{}_z\,\,$$View Question Let$$U$$and$$V$$be two independent zero mean Gaussian random variables of variances$${1 \over 4}$$and$${1 \over View Question Consider two identically distributed zero - mean random variables $$U$$ and $$V.$$ Let the cumulative distribution funct View Question There are four chips each of 1024 bytes connected to a 16 bit address bus as shown in the figure below. RAMs 1,2,3 and 4 View Question For 8085 microprocessor, the following program is executed. At the end of program, accumulator contains View Question Consider a delta connection of resistors and its equivalent star connection as shown below. If all elements of the delta View Question Two magnetically uncoupled inductive coils have Q factors q1 and q2 at the chosen operating frequency. Their respective View Question Three capacitors C1 ,C2 and C3 whose values are 10 µF, 5µF and 2µF respectively, have breakdown voltages of 10V, 5V, and View Question Consider the following figure The current IS in Amps in the voltage source, and voltage VS in Volts across the current View Question Consider the following figure The current in the 1Ω resistor in Amps is View Question A source vs(t) = V cos 100 $$\pi$$t has an internal impedance of (4 + j3) $$\Omega$$. If a purely resistive load connect View Question In the circuit shown below, if the source voltage Vs =100$$\angle$$53.130V then the Thevenin’s equivalent voltage in Vol View Question The following arrangement consists of an ideal transformer and an attenuator which attenuates by a factor of 0.8. An ac View Question A system is described by the differential equation $${{{d^2}y} \over {d{t^2}}} + 5{{dy} \over {dt}} + 6y\left( t \right View Question The DFT of a vector [a b c d] is the vector [α β γ δ ]. Consider the product The DFT of the vector [ p q r s] is a sc View Question The impulse response of a system is h(t) = t u(t). For an input u(t - 1), the output is View Question Two system with impulse responses h1(t) and h2(t) are connected in cascade. Then the overall impulse response of the cas View Question The impulse response of a continuous time system is given by$$h(t) = \delta (t - 1) + \delta (t - 3)$$. The value of th View Question A band-limited signal with a maximum frequency of 5 kHz is to be sampled. According to the sampling theorem, the samplin View Question Assuming zero initial condition, the response y (t) of the system given below to a unit step input u(t) is View Question Let g(t) =$${e^{ - \pi {t^2}}}$$, and h(t) is a filter matched to g(t). If g(t) is applied as input to h(t), then the View Question For a periodic signal v(t) = 30 sin 100t + 10cos 300t + 6sin$${\rm{(500t + }}\,\pi /4)$\$, the fundamental frequency in
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## General Aptitude

The set of values of p for which the roots of the equation 3x2 + 2x + p(p - 1) = 0 are of opposite sign is
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Find the sum to n terms of the series 10 + 84 + 734 +.........
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A car travels 8 km in the first quarter of an hour, 6 km in the second quarter and 16 km in the third quarter. The avera
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In the summer of 2012, in New Delhi, the mean temperature of Monday to Wednesday was 41ºC and of Tuesday to Thursday was
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What is the chance that a leap year, selected at random, will contain 53 Sundays?
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