GATE ECE 2013

## 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

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The Bode plot of a transfer function G (s) is shown in the figure below.
The gain (20 log $$\left| {G(s)} \right|$$

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The state diagram of a system is shown below. A system is shown below. A system is described by the state variable equat

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The state diagram of a system is shown below. A system is shown below. A system is described by the state variable equat

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In the sum of products function f (x,y,z) = $$\sum {} $$m (2,3,4,5), the prime implicants are

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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

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In the circuit shown below, Q1 has negligible collector-to-emitter saturation voltage and the diode
drops negligible vol

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The divergence of the vector field $$\overrightarrow A\;=\;x{\widehat a}_x\;+\;y{\widehat a}_y\;+\;z{\widehat a}_z$$ is

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The return loss of a device is found to be 20 dB. The voltage standing wave ratio (VSWR) and magnitude of reflection coe

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A monochromatic plane wave of wavelength $$\lambda = 600$$ is propagating in the direction as shown in the
figure below

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A monochromatic plane wave of wavelength $$\lambda = 600$$ is propagating in the direction as shown in the
figure below

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In a forward biased P-N junction diode, the sequence of events that best describes
the mechanism of current flow is

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In the circuit shown below, the knee current of the ideal Zener diode is 10 mA. To
maintain 5V across RL, the minimum va

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In IC technology, dry oxidation (using dry oxygen) as compared to wet oxidation
(using steam or water vapor) produces

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In a MOSFET operating in the saturation region, the channel length modulation
effect causes

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The small-signal resistance (i.e., $${{d{V_B}} \over {d{I_D}}}$$ ) in $$k\Omega $$ offered by the n-channel MOSFET M sho

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The minimum eigenvalue of the following matrix is $$\left[ {\matrix{
3 & 5 & 2 \cr
5 & {12} & 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 $

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Consider a vector field $$\overrightarrow A \left( {\overrightarrow r } \right).$$ The closed loop line integral $$\oint

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The divergence of the vector field $$\,\overrightarrow A = x\widehat a{}_x + y\widehat a{}_y + z\widehat a{}_z\,\,$$

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Let $$U$$ and $$V$$ be two independent zero mean Gaussian random variables of variances $${1 \over 4}$$ and $${1 \over

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Consider two identically distributed zero - mean random variables $$U$$ and $$V.$$ Let the cumulative distribution funct

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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

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For 8085 microprocessor, the following program is executed.
At the end of program, accumulator contains

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Consider a delta connection of resistors and its equivalent star connection as
shown below. If all elements of the delta

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Two magnetically uncoupled inductive coils have Q factors q1 and q2 at the
chosen operating frequency. Their respective

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Three capacitors C1 ,C2 and C3 whose values are 10 µF, 5µF and 2µF respectively, have breakdown voltages of 10V, 5V, and

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Consider the following figure
The current IS in Amps in the voltage source, and voltage VS in Volts across the
current

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Consider the following figure
The current in the 1Ω resistor in Amps is

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A source vs(t) = V cos 100 $$\pi$$t has an internal impedance of (4 + j3) $$\Omega$$. If a purely resistive load connect

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In the circuit shown below, if the source voltage Vs =100$$\angle$$53.130V then the
Thevenin’s equivalent voltage in Vol

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The following arrangement consists of an ideal transformer and an attenuator
which attenuates by a factor of 0.8. An ac

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A system is described by the differential equation $$${{{d^2}y} \over {d{t^2}}} + 5{{dy} \over {dt}} + 6y\left( t \right

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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

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The impulse response of a system is h(t) = t u(t). For an input u(t - 1), the output is

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Two system with impulse responses h1(t) and h2(t) are connected in cascade. Then the overall impulse response of the cas

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The impulse response of a continuous time system is given by $$h(t) = \delta (t - 1) + \delta (t - 3)$$. The value of th

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A band-limited signal with a maximum frequency of 5 kHz is to be sampled. According to the sampling theorem, the samplin

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Assuming zero initial condition, the response y (t) of the system given below to a unit step input u(t) is

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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

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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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