# EC GATE 2013 (Test 5)

Tag: ec gate 2013
Q.1
Statement: There were different streams of freedom movements in colonial India carried out by the moderates, liberals, radicals, socialists, and so on. Which one of the following is the best inference from the above statement?
A. The emergence of nationalism in colonial India led to our Independence
B. Nationalism in India emerged in the context of colonialism
C. Nationalism in India is homogeneous
D. Nationalism in India is heterogeneous
Explaination / Solution:
No Explaination.

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Topic: Arithmetic Tag: EC GATE 2013
Q.2
What is the chance that a leap year, selected at random, will contain 53 Sundays?
A. 2/7
B. 3/7
C. 1/7
D. 5/7
Explaination / Solution:

In a leap year, there are 366 days So, 52 weeks will have 52 saturdays and for remaining two days (366 - 52 × 7 = 2) We can have the following combinations
Saturday, Sunday
Sunday, Monday
Monday, Tuesday
Tuesday, Wednesday
Wednesday, Thursday
Thursday, Friday
Friday, Saturday
Out of these seven possibilities, only two consist a saturday. Therefore, the probability of saturday is given as
P = 2/7

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Q.3
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 respectively are mappped to addresses

A. 0C00H-0FFFH, 1C00H-1FFFH, 2C00H-2FFFH, 3C00H-3FFFH
B. 1800H-1FFFH, 2800H-2FFFH, 3800H-3FFFH, 4800H-4FFFH
C. 0500H-08FFH, 1500H-18FFH, 3500H-38FFH, 5500H-58FFH
D. 0800H-0BFFH, 1800H-1BFFH, 2800H-2BFFH, 3800H-3BFFH
Explaination / Solution:
No Explaination.

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Q.4
In a MOSFET operating in the saturation region, the channel length modulation effect causes
A. an increase in the gate-source capacitance
B. a decrease in the transconductance
C. a decrease in the unity-gain cutoff frequency
D. a decrease in the output resistance
Explaination / Solution:

In a MOSFET operating in the saturation region, the channel length modulation effect causes a decrease in output resistance.

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Q.5
The bit rate of a digital communication system is R kbits/s. The modulation used is 32-QAM. The minimum bandwidth required for ISI free transmission is
A. R/10 Hz
B. R/10 Hz
C. R/10 Hz
D. R/5 kHz
Explaination / Solution:

In ideal Nyquist Channel, bandwidth required for ISI (Inter Symbol reference) free transmission is

Here, the used modulation is 32 - QAM (Quantum Amplitude modulation

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Q.6
In a voltage-voltage feedback as shown below, which one of the following statements is TRUE if the gain k is increased?

A. The input impedance increases and output impedance decreases
B. The input impedance increases and output impedance also increases
C. The input impedance decreases and output impedance also decreases
D. The input impedance decreases and output impedance increases
Explaination / Solution:

The i/p voltage of the system is given as
Therefore, if k is increased then input voltage is also increased so, the input impedance increases. Now, we have

Since, Vin is independent of k when seen from output mode, the output voltage decreases with increase in k that leads to the decrease of output impedance. Thus, input impedance increases and output impedance decreases.

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Q.7
For a periodic signal  the fundamental frequency in rad/s
A. 100
B. 300
C. 500
D. 1500
Explaination / Solution:

Given, the signal

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Q.8
A source has an internal impedance of If a purely resistive load connected to this source has to extract the maximum power out of the source, its value inΩ should be
A. 3
B. 4
C. 5
D. 7
Explaination / Solution:

For the purely resistive load, maximum average power is transferred when

where
is the equivalent thevinin (input) impedance of the circuit. Hence,
we obtain

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Q.9
The minimum eigen value of the following matrix is

A. 0
B. 1
C. 2
D. 3
Explaination / Solution:

For, a given matrix [A] the eigen value is calculated as where  gives the eigen values of matrix. Here, the minimum eigen value among the given options is We check the characteristic equation of matrix for this eigen value
= 3(60 - 49h- 5(25 - 14)+ 2)35 - 24h
= 33 - 55 + 22
= 0
Hence, it satisfied the characteristic equation and so, the minimum eigen value is

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Q.10
A system described by the differential equation   Let x(t) be a rectangular pulse given by

Assuming that y(0) = 0 and dy/dt = 0 at t = 0, the Laplace transform of y(t) is
A.
B.
C.
D.