# EC GATE 2013 (Test 1)

Tag: ec gate 2013
Q.1
They were requested not to quarrel with others. Which one of the following options is the closest in meaning to the word quarrel?
A. make out
B. call out
C. dig out
D. fall out
Answer : Option D
Explaination / Solution:

They were requested not to quarrel with others. Quarrel has a similar meaning to ‘fall out’

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Topic: Arithmetic Tag: EC GATE 2013
Q.2
In the summer of 2012, in New Delhi, the mean temperature of Monday to Wednesday was 41°C and of Tuesday to Thursday was 43 °C. If the temperature on Thursday was 15% higher than that of Monday, then the temperature in °C on Thursday was
A. 40
B. 43
C. 46
D. 49
Answer : Option C
Explaination / Solution:
No Explaination.

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Q.3
A bulb in a staircase has two switches, one switch being at the ground floor and the other one at the first floor. The bulb can be turned ON and also can be turned OFF by any one of the switches irrespective of the state of the other switch. The logic of switching of the bulb resembles
A. and AND gate
B. an OR gate
C. an XOR gate
D. a NAND gate
Answer : Option C
Explaination / Solution:

Let A denotes the position of switch at ground floor and B denotes the position of switch at upper floor. The switch can be either in up position or down position.Following are the truth table given for different combinations of A and B

When the switches A and B are both up or both down, output will be zero (i.e.Bulb will be OFF). Any of the switch changes its position leads to the ON state of bulb. Hence, from the truth table, we get

i.e., the XOR gate

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Q.4
In the circuit shown below what is the output voltage  (vout)if a silicon transistor Q and an ideal op-amp are used?

A. -15 V
B. -0.7 V
C. +0.7 V
D. +15 V
Answer : Option B
Explaination / Solution:

For the given ideal op-amp, negative terminal will be also ground (at zero voltage) and so, the collector terminal of the BJT will be at zero voltage.
i.e., VC = 0 volt
The current in 1 k resistor is given by
This current will flow completely through the BJT since, no current will flow into the ideal op-amp (I/P resistance of ideal op-amp is infinity). So, for BJT we have

i.e.,the base collector junction is reverse biased (zero voltage) therefore, the collector current (IC ) can have a value only if base-emitter is forward biased.
Hence,

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Q.5
In the circuit shown below, the knee current of the ideal Zener dioide is 10 mA . To maintain 5 V across RL, the minimum value of RL in Ω and the minimum power rating of the Zener diode in mW, respectively, are

A. 125 and 125
B. 125 and 250
C. 250 and 125
D. 250 and 250
Answer : Option B
Explaination / Solution:
No Explaination.

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Q.6
A band-limited signal with a maximum frequency of 5 kHz is to be sampled. According to the sampling theorem, the sampling frequency which is not valid
A.

5kHZ

B.

12kHZ

C.

15kHZ

D.

20kHZ

E.

Answer : Option A
Explaination / Solution:

Given, the maximum frequency of the band-limited signal
fm = 5 kHz
According to the Nyquist sampling theorem, the sampling frequency must be greater than the Nyquist frequency which is given as

So, the sampling frequency fs must satisfy

only the option (A) does’nt satisfy the condition therefore, 5K HZ is not a valid sampling frequency.

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Q.7
Which one of the following statements is NOT TRUE for a continuous time causal and stable LTI system?
A. All the poles of the system must lie on the left side of the
B. Zeros of the system can lie anywhere in the s-plane
C. All the poles must lie within ƖsƖ  = 1
D.
All the roots of the characteristic equation must be located on the left side of the  axis.
Answer : Option C
Explaination / Solution:

For a system to be casual, the R.O.C of system transfer function H(s) h which is rational should be in the right half plane and to the right of the right most pole.
For the stability of LTI system. All poles of the system should lie in the left half of S -plane and no repeated pole should be on imaginary axis. Hence,
options (A), (B), (D) satisfies an LTI system stability and causality both.
But, Option (C) is not true for the stable system as,  ƖsƖ =1 have one pole in right hand plane also.

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Q.8
The impulse response of a continuous time system is given by   The value of the step response at t = 2 is
A. 0
B. 1
C. 2
D. 3
Answer : Option B
Explaination / Solution:

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Q.9
In the circuit shown below, if the source voltage  then the Thevenin’s equivalent voltage in Volts as seen by the load resistance RL is

A. 100∟900
B. 800∟00
C. 800∟900
D. 100∟600
Answer : Option C
Explaination / Solution:
No Explaination.

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Q.10
A polynomial  with all coefficients positive has
A. no real roots
B. no negative real root
C. odd number of real roots
D. at least one positive and one negative real root
Answer : Option D
Explaination / Solution:

Given, the polynomial
Since, all the coefficients are positive so, the roots of equation is given by
f(x) = 0
It will have at least one pole in right hand plane as there will be least one sign change from (a1) to (a0in the Routh matrix 1st column. Also, there will be a corresponding pole in left hand plane
i.e.; at least one positive root (in R.H.P)
and at least one negative root (in L.H.P)
Rest of the roots will be either on imaginary axis or in L.H.P

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