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GATE 2017 questions and answers

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  1. A bar of Gallium Arsenide(GaAs) is doped with silicon in such a way that silicon atoms occupy Gallium and Arsenic sites in GaAs crystal. Which of the following statements is true?

a) Silicon acts as p-type dopants in Arsenic sites and n-type dopants in Gallium sites

b) Silicon acts as n-type dopants in Arsenic sites and p-type dopants in Gallium sites

c) Silicon acts as p-type dopants in both Arsenic and Gallium sites

d) Silicon acts as n-type dopants in both Arsenic and Gallium sites

Correct Ans : a

Background: amphoteric dopant -> element which can act either as a donor or an acceptor in a given semiconductor; e.g. Si is an amphoteric dopant of GaAs where it acts as a donor on a Ga site or as an acceptor on an As site.

 

2)

GATE 2017 opamp

Correct Answer : B

Hint : Apply Kirchoff’s law for the branch involving 10k, 5k and 3v source with vin =15v and for vin=-15v

 

3) A good transconductance amplifier should have

a) High input resistance and low output resistance

b) Low input resistance and high output resistance

c) High input and output resistance

d) Low input and output resistance

Correct Ans : c

 

4) Which one of the following is the general solution of this first order differential equation

\frac {dy}{dx}=  (x+y-1)^2 where x and y are real.

a) y=1+x + tan^-1 (x+c)

b) y=1+x+tan(x+c)

c) y=1-x+tan^-1 (x+c)

d) y=1-x+tan(x+c)

where c is a constant

 

Correct Answer : d

 

5)

Correct Ans : 43.3 to 45.3

6) Assuming that transistors M1 and M2 are identical  and have a threshold voltage of 1V, the state of transistors M1 and M2  are respectively

Screen Shot 2017-08-12 at 1.05.20 PM

a) saturation, saturation

b) Linear, linear

c) saturation,linear

d) Linear, saturation

 

For MOSFET , the condition of saturation is

V_{DS} >= V_{GS} - V_T

Here V_{D2}= 3V, V_{G2}=2.5V,  V_{GS1}=2V(Since source is 0 for M1) V_T=1V

so V_{DS} >= V_{GS} - V_T

V_{DS2} >= V_{GS2} - V_T =2.5-1 = 1.5V

Since V_{DS2} = 3V > 1.5V, M2 is in saturation.

Assuming M1 is also in saturation, then same drain current flows in both M1 and M2. Since the both MOSFET’s are identical , we can write

I_{D1} =I_{D2}

V_{GS1} - V_T = V_{GS2}- V_T

V_{GS1} - V_T = V_{G2}- V_{S2} -   V_T

2-1= 2.5 – V_{S2} -1

1=1.5 –V_{S2}( which is nothing but drain of M1)

V_{S2} =0.5V, which is less than V_{GS1} - V_T , which is equal to 1V

0.5V < 1V, so the M1 transistor is not in saturation, but in Linear region. Hence the correct answer  is “d”

 

7) Standard air filled rectangular waveguides of dimensions a=2.29cm and b=1.02cm are designed for radar applications. It is desired that these waveguides operate only in the dominant TE_{10} mode with the operating frequency at least 25% above the cut-off frequency of the TE_{10} mode, but not higher than the 95% of the next higher cut- off frequency. The range of the allowable frequency is

Note (<= refers to lesser than or equal to)

a) 8.19 GHz<= f <=13.1 GHZ

b) 8.19 GHz <= f <=12.45 GHZ

c) 6.155 GHz<= f <=13.1 GHZ

d) 1.64 GHz<= f <=10.24 GHZ

 

8) Screen Shot 2017-08-19 at 3.32.35 PM

Solution : Since \alpha of the transistor is unity, it means , we can assume I_E= I_c

Voltage at the base of the transistor V_B= \frac {18*16}{60} = 4.8V

V_{BE}=0.8V

so, V_B - V_E = V_{BE}

4.8-V_E=0.8 == > V_E=4V

So, I_E=4/2k = 2 mA , which means I_c=2 mA.

Applying Kirchoff’s law to the transistor on collector and emitter side

V_{CE} + (2k +4k) *2m = 18V

V_{CE}=18 -12=6V

 

9) Consider a characteristic equation given by

s^4 + 3s^3 + 5s^2 +6s +k+10 = 0    , the condition for stability is

a) k > 5

b) -10 < k

c) k > -4

d) -10 < k < -4

 

10)  For a  unit step input, a system with a closed loop transfer function of

G(s) = \frac {20}{s^2+2s+5} has a steady state output of

a) 10

b) 5

c) 2

d) 4

 

11) For the system \frac {2}{s+1} , the approximate time taken for a step response to reach 98% of its final value is

a) 1 s

b) 2 s

c) 4 s

d) 8 s

 

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