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Affaan 19/11/2016 in  GATE Coaching classes,

Define Laplace transform?

Vikas replied | 02/12/2016

The Laplace transform is an integral transform named after its discoverer Pierre-Simon Laplace.
It takes a function of a positive real variable t (often time) to a function of a complex variable s (frequency).
While the Fourier transform of a function is a complex function of a real variable (frequency), the Laplace transform of a function is a complex function of a complex...  more»
The Laplace transform is an integral transform named after its discoverer Pierre-Simon Laplace.
It takes a function of a positive real variable t (often time) to a function of a complex variable s (frequency).
While the Fourier transform of a function is a complex function of a real variable (frequency), the Laplace transform of a function is a complex function of a complex variable. Laplace transforms are usually restricted to functions of t with t > 0. A consequence of this restriction is that the Laplace transform of a function is a holomorphic function of the variable s. Unlike the Fourier transform, the Laplace transform of a distribution is generally a well-behaved function. Also techniques of complex variables can be used directly to study Laplace transforms. As a holomorphic function, the Laplace transform has a power series representation. This power series expresses a function as a linear superposition of moments of the function. This perspective has applications in probability theory. «less

Vikas replied | 02/12/2016

The Laplace transform is an integral transform named after its discoverer Pierre-Simon Laplace.
It takes a function of a positive real variable t (often time) to a function of a complex variable s (frequency).
While the Fourier transform of a function is a complex function of a real variable (frequency), the Laplace transform of a function is a complex function of a complex...  more»
The Laplace transform is an integral transform named after its discoverer Pierre-Simon Laplace.
It takes a function of a positive real variable t (often time) to a function of a complex variable s (frequency).
While the Fourier transform of a function is a complex function of a real variable (frequency), the Laplace transform of a function is a complex function of a complex variable. Laplace transforms are usually restricted to functions of t with t > 0. A consequence of this restriction is that the Laplace transform of a function is a holomorphic function of the variable s. Unlike the Fourier transform, the Laplace transform of a distribution is generally a well-behaved function. Also techniques of complex variables can be used directly to study Laplace transforms. As a holomorphic function, the Laplace transform has a power series representation. This power series expresses a function as a linear superposition of moments of the function. This perspective has applications in probability theory.
The Laplace transform is invertible on a large class of functions. The inverse Laplace transform takes a function of a complex variable s (often frequency) and yields a function of a real variable t (time). Given a simple mathematical or functional description of an input or output to a system, the Laplace transform provides an alternative functional description that often simplifies the process of analyzing the behavior of the system, or in synthesizing a new system based on a set of specifications. So, for example, Laplace transformation from the time domain to the frequency domain transforms differential equations into algebraic equations and convolution into multiplication.
The Laplace transform is particularly useful in solving linear ordinary differential equations such as those arising in the analysis of electronic circuits. «less

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Priyanka 19/11/2016 in  GATE Coaching classes,

What is the chance that a leap year, selected at random, will contain 53 Saturdays?

Vikas replied | 02/12/2016

A leap year has 366 days = 52 weeks ( 52x7 days) + 2 days = 364 + 2 = 366 Days
So, we are looking for either of these extra 2 days being Saturday.
We have 7 week days , we have 2 extra days in leap year over 52 weeks.
Thus probability that any day of the week is Saturday is 1/7
Here we have 2 Extra days ==> Total Probability = 1/7 + 1/7 = 2/7
Hence the chance...  more»
A leap year has 366 days = 52 weeks ( 52x7 days) + 2 days = 364 + 2 = 366 Days
So, we are looking for either of these extra 2 days being Saturday.
We have 7 week days , we have 2 extra days in leap year over 52 weeks.
Thus probability that any day of the week is Saturday is 1/7
Here we have 2 Extra days ==> Total Probability = 1/7 + 1/7 = 2/7
Hence the chance that a leap year selected at random will contain 53 Saturdays is 2/7. «less

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A

Aishwarya 19/11/2016 in  GATE Coaching classes,

Complete the sentence: Dare _____ mistakes.

Vikas replied | 09/12/2016

Options are:- 1) to learn from, 2) not to do , 3) to commit.
Any proper verb in the context is good for completing the sentence.

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P

Pranav 19/11/2016 in  GATE Coaching classes,

What is the synonym of quarrel?

Sunil replied | 14/12/2016

Alteration.

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K

Kanak 19/11/2016 in  GATE Coaching classes,

In the summer of 2012, in New Delhi, the mean temperature of Monday to Wednesday was 41 degree celsius of Tuesday to Thursday was 43 degree celsius. If the temperature on Thursday was 15% higher than that of Monday, then the temperature in degree celsius on Thursday was______ ?

Shantanu replied | 24/11/2016

Let the temperatures on Monday,Tuesday,Wednesday and Thursday is M,T,W and Th respectively.
The mean temperature of Monday to Wednesday was 41 deg C => (M+T+W)/3 = 41
=> M+T+W = 123 ---(a).
The mean temperature of Tuesday to Thursday was 43 deg C=> (T+W+Th)/3 = 43
=> T+W+Th = 129 ---(b).
(b)-(a) => Th-M = 6 ---(c).
temperature on Thursday...  more»
Let the temperatures on Monday,Tuesday,Wednesday and Thursday is M,T,W and Th respectively.
The mean temperature of Monday to Wednesday was 41 deg C => (M+T+W)/3 = 41
=> M+T+W = 123 ---(a).
The mean temperature of Tuesday to Thursday was 43 deg C=> (T+W+Th)/3 = 43
=> T+W+Th = 129 ---(b).
(b)-(a) => Th-M = 6 ---(c).
temperature on Thursday was 15% higher than that of Monday => Th = 1.15*M ---(d).
From (c) and (d), 0.15 M = 6 => M = 6/0.15 => Th = 1.15*6/0.15 = 46 «less

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R

Ritu 19/11/2016 in  GATE Coaching classes,

What is the difference between Laplace transform and Fourier series?

Santosh replied | 13/12/2016

Fourier series is applicable only to periodic functions only and Laplace transform is also applicable for a periodic functions with some convergence factor.

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R

Ritu 19/11/2016 in  GATE Coaching classes,

How many roots does the given polynomial have: f(x) = a4 (x power 4) + a3 (x power 3) + a2 (x power 2) + a1 (x) - an with all positive coefficients?

Sanjeev replied | 30/11/2016

4 since its degree is 4

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P

Perl 19/11/2016 in  GATE Coaching classes,

Complete the sentence with suitable grammar: Mount Everest is ____ ?

Siva Naga Raju replied | 22/11/2016

Options please. It is an incomplete sentence and can end in different ways without needing much of grammar like "Mount Everest is a mountain"

Vikas replied | 23/11/2016

Tallest mountain on the earth.

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D

Devinder 19/11/2016 in  GATE Coaching classes,

Fill up: The policeman asked the victim of a theft, “ What did you_____?

Vikas replied | 23/11/2016

Lost.

Vikas replied | 23/11/2016

Lose.

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B

Baiju 19/11/2016 in  GATE Coaching classes,

A person moving through a T.B prone zone has a 50% probability of becoming infected. However, only 30% of infected people develop the disease. What percentage of people moving through a T.B prone zone remains infected but does not show symptoms of disease?

Vikas replied | 30/11/2016

Two events : Getting Infected & Developing Disease:-
Non-Infected Persons percentages.
Person moving in TB prone zone.
50% of persons remains non-infected.

Infected Persons Percentages:-
TB prone zone = 50% Infected persons
Out of Infected Persons 30% develop the disease. (@ 0.5 x30% = 15% of persons moving through TB Zone
get infected & develop...  more»
Two events : Getting Infected & Developing Disease:-
Non-Infected Persons percentages.
Person moving in TB prone zone.
50% of persons remains non-infected.

Infected Persons Percentages:-
TB prone zone = 50% Infected persons
Out of Infected Persons 30% develop the disease. (@ 0.5 x30% = 15% of persons moving through TB Zone
get infected & develop disease).

==> Out if Infected Persons 70% do not develop the disease (@0.5 x 70% = 35% of persons moving through TB Zone get infected but does not develop disease)

So, the answer is 35% of people moving through a T.B. prone zone remains infected but does not show symptoms of disease. «less

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A

Ashish 19/11/2016 in  GATE Coaching classes,

Michael lives 10 km away from where i live. Ahmed lives 5 km away and Susan lives 7 km away from where I live. Arun is farther away than Ahmed but closer than Susan from where I live. From the information provided here, What is one possible distance (in km) at which I live from Arun’s place?

Vikas replied | 09/12/2016

Assume you are at the center of circle, and possible location of other individual is on the perimeter of circle.
So we have 3 circles around you i.e., 5 km circle on which Ahmed lives, 7 km circle on which Susan lives,
10 km circle on which Michael Leaves.
Arun's location is somewhere between 5 km to 7 km , as he is away from...  more»
Assume you are at the center of circle, and possible location of other individual is on the perimeter of circle.
So we have 3 circles around you i.e., 5 km circle on which Ahmed lives, 7 km circle on which Susan lives,
10 km circle on which Michael Leaves.
Arun's location is somewhere between 5 km to 7 km , as he is away from Ahmed (5 km Circle) , but closer than
Susan (7 km Circle). Hence Arun's location is given by range in between 5 km to 7 km i.e., 5 km «less

Santosh replied | 13/12/2016

6 km.

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S

Sarvepalli 19/11/2016 in  GATE Coaching classes,

What is the mean of the random variable, if the second moment of a Poisson distributed random variable is 2?

Vikas replied | 23/11/2016

Random variable means value is not known at the start.
Poisson distributed random variable means value of unknown discrete variable follows Poisson's distribution (Type of frequency distribution).

K

Key replied | 24/11/2016

For Poisson R.V
Mean = Variance.
So, Second Moment = Variance + (Mean)*(Mean) = Mean + Mean2 = 2.
On Solving, Mean = 2.

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S

Sangeeta 19/11/2016 in  GATE Coaching classes,

A continuous time function x(t) is periodic with period T. The function is sampled uniformly with a sampling Ts, in which one of the following cases is the sampled signal periodic?

Shantanu replied | 29/11/2016

T=1.2Ts

Shantanu replied | 29/11/2016

Consider x(t) = cos w(0) t
if x(t) s sampled with a sampling period Ts, x[n] =cos (ohm)(0) n is obtained.
(ohm)(0) n/Ts = w(0)
2*pi*m/NoTs = 2*pi/To
To/Tm=N0/m, must be a rational number
T/Ts=12/10=6/5 lives a periodic signal after sampling

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S

Santosh 19/11/2016 in  GATE Coaching classes,

What is the difference between AND gate and NAND gate?

Sukhwinder replied | 27/11/2016

Digital logic only uses 2 voltage levels, at or near supply voltage(high logic state) & ground or zero(low logic state).
These states = "yes" or "no" or "on" or "off".
On a AND gate, if there's 1 low input , it has a low output.
This doesn't change until there's 2 high inputs, at which time the output is high.
AND gate
A + B = output
L+ L =L
L+H=...  more»
Digital logic only uses 2 voltage levels, at or near supply voltage(high logic state) & ground or zero(low logic state).
These states = "yes" or "no" or "on" or "off".
On a AND gate, if there's 1 low input , it has a low output.
This doesn't change until there's 2 high inputs, at which time the output is high.
AND gate
A + B = output
L+ L =L
L+H= L
H+L= L
H+H=H .......A NAND gate is the opposite.
NAND gate
A+B= output
L+L=H
L+H=H
H+L=H
H+H=L «less

M replied | 28/11/2016

AND gate is basic logic gate and NAND gate is universal gate. Negation of AND gate is NAND gate.

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N

Nagasanthoshi 19/11/2016 in  GATE Coaching classes,

What is the integral value of the function: s(x) = 5 cos(160 t) + 20 cos(180 t) + 5 cos(200 t)?

M replied | 28/11/2016

(5 cos(160 t) + 20 cos(180 t) + 5 cos(200 t))*x+constant

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N

Nayan 19/11/2016 in  GATE Coaching classes,

What do you mean by communication with respect to telecommunication?

Vikas replied | 23/11/2016

Telecommunication is the transmission of signs, signals, messages, writings, images and sounds or intelligence of any nature by wire, radio, optical or other electromagnetic systems. Telecommunication occurs when the exchange of information between communication participants includes the use of technology. It is transmitted either electrically over physical media, such as cables,...  more»
Telecommunication is the transmission of signs, signals, messages, writings, images and sounds or intelligence of any nature by wire, radio, optical or other electromagnetic systems. Telecommunication occurs when the exchange of information between communication participants includes the use of technology. It is transmitted either electrically over physical media, such as cables, or via electromagnetic radiation. Such transmission paths are often divided into communication channels which afford the advantages of multiplexing. The term is often used in its plural form, telecommunications, because it involves many different technologies. «less

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M

Madhu 19/11/2016 in  GATE Coaching classes,

What do you mean by Oscilloscope?

Sunil replied | 14/12/2016

It allows observation of constantly varying signal voltages, usually as a two-dimensional plot of one or more signals as a function of time.

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B

Baiju 19/11/2016 in  GATE Coaching classes,

What is the purpose of using Oscilloscope?

Amit replied | 07/12/2016

Oscilloscopes are used to observe the change of an electrical signal over time, such that voltage and time describe a shape which is continuously graphed against a calibrated scale. The observed waveform can be analyzed for such properties as amplitude, frequency, rise time, time interval, distortion and others.

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S

Satish 19/11/2016 in  GATE Coaching classes,

What do you mean by L,C,R circuit?

Vikas replied | 01/12/2016

An inductor (L), and a capacitor (C), a resistor (R), connected in series or in parallel make electrical circuit.
The name of the circuit is derived from the letters that are used to denote the constituent components of this circuit.

M Balal replied | 15/12/2016

L is for Inductor. C is Capacitor and R is Resistance. So any Circuit having these three elements is called LCR circuit.

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P

Piyush 19/11/2016 in  GATE Coaching classes,

What is the property of impedance?

Siva Naga Raju replied | 22/11/2016

Property of impedance can be observed from the word 'Impede' which means create hindrance (stop or reduce speed of some thing). In electrical terminology, an impedance provides an obstruction in the path of current and its properties differ based on both the nature of impedance (resistive, inductive or capacitive and current(AC or DC). Pure ideal resistive load offers same resistance...  more»
Property of impedance can be observed from the word 'Impede' which means create hindrance (stop or reduce speed of some thing). In electrical terminology, an impedance provides an obstruction in the path of current and its properties differ based on both the nature of impedance (resistive, inductive or capacitive and current(AC or DC). Pure ideal resistive load offers same resistance for both AC and DC. The impedance offered by inductance is directly proportional to the frequency of the current (i.e. 0 for DC and increases as the frequency of AC increases) while the impedance offered by the capacitance is inversely proportional to frequency (infinite for DC and decreases with increase in frequency) «less

Sukhwinder replied | 27/11/2016

Electrical impedance is the measure of the opposition that a circuit presents to a current when a voltage is applied.
In quantitative terms, it is the complex ratio of the voltage to the current in an alternating current (AC) circuit. Impedance extends the concept of resistance to AC circuits, and possesses both magnitude and phase, unlike resistance, which has only magnitude....  more»
Electrical impedance is the measure of the opposition that a circuit presents to a current when a voltage is applied.
In quantitative terms, it is the complex ratio of the voltage to the current in an alternating current (AC) circuit. Impedance extends the concept of resistance to AC circuits, and possesses both magnitude and phase, unlike resistance, which has only magnitude. When a circuit is driven with direct current (DC), there is no distinction between impedance and resistance; the latter can be thought of as impedance with zero phase angle. «less

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S

Shaun 19/11/2016 in  GATE Coaching classes,

What do you mean by discrete - time function?

Prateek replied | 01/12/2016

Discontinuous time. For example a doctor measure temperature of a patient after an interval of 5 hours. So doctor will have patient's temperature at interval of 5 hours. So temperature is a discrete time function.

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V

Vishal 19/11/2016 in  GATE Coaching classes,

What is the difference between ramp signal and triangular signal?

Sushil replied | 25/11/2016

Ramp signal is monotonically increasing/decreasing signal with positive or negative slope while triangular signal has discontinuities after which slop sign gets reversed.

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K

Keerthiga 19/11/2016 in  GATE Coaching classes,

What is Amplification?

Shantanu replied | 22/11/2016

The operation of an amplifier, a natural or artificial device intended to make a signal stronger.
The amount of increase that an amplifier provides on the output side of the circuit is amplification.
In other way we can say that Amplification is an increase in signal power or voltage produced by an amplifier in transmitting a signal from one point to another. The amount...  more»
The operation of an amplifier, a natural or artificial device intended to make a signal stronger.
The amount of increase that an amplifier provides on the output side of the circuit is amplification.
In other way we can say that Amplification is an increase in signal power or voltage produced by an amplifier in transmitting a signal from one point to another. The amount of gain is usually expressed in decibels above a reference level.
Antenna gain is a measure of the effectiveness of a directional antenna as compared to a nondirectional antenna.
Generally, an amplifier is any device that uses a small amount of energy to control a larger amount of energy. In popular use, the term today usually refers to an electronic amplifier, often as applied to audio applications. The relationship of the input to the output of an amplifier — usually expressed as a function of the input frequency — is called the transfer function of the amplifier, and the magnitude of the transfer function is termed the gain «less

Sukhwinder replied | 27/11/2016

Amplification may refer to: The operation of an amplifier, a natural or artificial device intended to make a signal stronger. Amplify (distributor), a NY-based all-rights film distributor. Amplification (rhetoric), a figure of speech that adds importance to increase its rhetorical effect.

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A

Abinaya 19/11/2016 in  GATE Coaching classes,

What is signal to noise ratio?

Fast replied | 01/12/2016

Signal-to-noise ratio (abbreviated SNR or S/N) is a measure used in science and engineering that compares the level of a desired signal to the level of background noise. It is defined as the ratio of signal power to the noise power, often expressed in decibels.

Shyama replied | 02/12/2016

Signal to noise ratio is defined as the ratio of power of signal to the power of noise. The signal is the needed information and the noise is an unwanted signal.
This is a parameter used by Shannon to give a relationship between signal power and noise power.
SNR=Signal Power/ Noise Power.
SNR in decibels(db) gives how much the intended signal exceeds noise signal.
SNRdb=...  more»
Signal to noise ratio is defined as the ratio of power of signal to the power of noise. The signal is the needed information and the noise is an unwanted signal.
This is a parameter used by Shannon to give a relationship between signal power and noise power.
SNR=Signal Power/ Noise Power.
SNR in decibels(db) gives how much the intended signal exceeds noise signal.
SNRdb= 10log to the base 10 SNR «less

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N

Non 19/11/2016 in  GATE Coaching classes,

Complete the following sentence: Despite the new medicine’s ______________ in treating diabetes, it is not ______________widely.

Vikas replied | 30/11/2016

ability, available.
Despite the new medicine's ability in treating diabetes, it is not available widely.

Sanjeev replied | 30/11/2016

capability, accepted.

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