# EC GATE 2010 (Test 5)

Tag: ec gate 2010
Q.1
Modern warfare has changed from large scale clashes of armies to suppression of civilian populations. Chemical agents that do their work silently appear to be suited to such warfare; and regretfully, there exist people in military establishments who think that chemical agents are useful tools for their cause. Which of the following statements best sums up the meaning of the above passage:
A. Modern warfare has resulted in civil strife.
B. Chemical agents are useful in modern warfare.
C. Use of chemical agents in warfare would be undesirable
D. People in military establishment like to use agents in war
Explaination / Solution:
No Explaination.

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Topic: Arithmetic Tag: EC GATE 2010
Q.2
Hari(H), Gita(G), Irfan(I) and Saira(S) are sibilings (i.e. brothers and sisters). All were born on Ist January. The age difference between any two successive siblings (that is born one after another) is less than 3 years. Given the following facts: (i) Hari’s age + Gita’s age > Irfan’s age + Saira’s age (ii) The age difference between Gita and Saira is 1 year. However, Gita is not the oldest and Saira is not the youngest (iii) There are not twins. In what order were they born (oldest first)
A. HSIG
B. SGHI
C. IGSH
D. IHSG
Explaination / Solution:

Let H , G, S and I be ages of Hari, Gita, Saira and Irfan respectively. Now from statement (1) we have H + G > I + S Form statement (2) we get that G - S = 1 or S - G = 1 As G can’t be oldest and S can’t be youngest thus either GS or SG possible. From statement (3) we get that there are no twins (A) HSIG : There is I between S and G which is not possible (B) SGHI : SG order is also here and S > G > H > I andG + H > S + I which is possible. (C) IGSH : This gives I > G and S > H and adding these both inequalities we have I + S > H + G which is not possible. (D) IHSG : This gives I > H and S > G and adding these both inequalities we have I + S > H + G which is not possible.

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Q.3
The Boolean function realized by the logic circuit shown is

A. F = ∑m(0, 1, 3, 5, 9, 10, 14)
B. F = ∑m(2, 3, 5, 7, 8, 12, 13)
C. F = ∑m(1, 2, 4, 5, 11, 14, 15)
D. F = ∑m(2, 3, 5, 7, 8, 9, 12)
Explaination / Solution:

Output of the MUX can be written as

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Q.4
Thin gate oxide in a CMOS process in preferably grown using
A. wet oxidation
B. dry oxidation
C. epitaxial oxidation
D. ion implantation
Explaination / Solution:

Dry oxidation is used to achieve high quality oxide growth.

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Q.5
Compared to a p-n junction with NA  = ND = 10-14/cm3, which one of the following statements is TRUE for a p-n junction with NA  = ND = 10-20/cm3?
A. Reverse breakdown voltage is lower and depletion capacitance is lower
B. Reverse breakdown voltage is higher and depletion capacitance is lower
C. Reverse breakdown voltage is lower and depletion capacitance is higher
D. Reverse breakdown voltage is higher and depletion capacitance is higher
Explaination / Solution:

Reverse bias breakdown or Zener effect occurs in highly doped PN junction through tunneling mechanism. In a highly doped PN junction, the conduction and valence bands on opposite sides of the junction are sufficiently close during reverse bias that electron may tunnel directly from the valence band on the p-side into the conduction band on n-side.
Breakdown voltage
So, breakdown voltage decreases as concentration increases
Depletion capacitance

Depletion capacitance increases as concentration increases

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Q.6
A transmission line has a characteristic impedance of 50 Ω and a resistance of 0.1Ω/m . If the line is distortion less, the attenuation constant(in Np/m) is
A. 500
B. 5
C. 0.014
D. 0.002
Explaination / Solution:

For distortion less transmission line characteristics impedance

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Q.7
Consider a baseband binary PAM receiver shown below. The additive channel noise n(t) is with power spectral density  The lowpass filter is ideal with unity gain and cut-off frequency 1 MHz. Let Yk represent the random variable y(tk).
Yk = Nk , if transmitted bit bk = 0
Yk = a + Nk if transmitted bit bk = 1
Where Nk represents the noise sample value. The noise sample has a probability density function,  (This has mean zero and variance 2/α2). Assume transmitted bits to be equiprobable and threshold z is set to a/2 = 10-6 V.

The probability of bit error is
A. 0.5 × e-3.5
B. 0.5 × e-5
C. 0.5 × e-7
D. 0.5 × e-10
Explaination / Solution:

Probability of error is given by

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Q.8
The transfer function of a discrete time LTI system is given by

Consider the following statements:
S1: The system is stable and causal for ROC: |z| > 1/2
S2: The system is stable but not causal for ROC: |z| < 1/4
S3: The system is neither stable nor causal for ROC: 1/4 < |z| < 1/2
Which one of the following statements is valid ?
A. Both S1 and S2 are true
B. Both S2 and S3 are true
C. Both S1 and S3 are true
D. S1, S2 and S3 are all true
Explaination / Solution:

By partial fraction H(z) can be written as

For ROC : |z| > 1/2

Thus system is causal. Since ROC of H(z) includes unit circle, so it is stable also. Hence S1 is True
For ROC : |z| < 1/4

System is not causal. ROC of H(z) does not include unity circle, so it is not stable and S3 is True

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Q.9
Consider the pulse shape s(t) as shown. The impulse response h(t) of the filter matched to this pulse is

A.
B.
C.
D.
Explaination / Solution:

Impulse response of the matched filter is given by

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Q.10
The silicon sample with unit cross-sectional area shown below is in thermal equilibrium. The following information is given: T = 300 K electronic charge = 1.6 × 10-19 C, thermal voltage = 26 mV and electron mobility = 1350 cm2 / V-s

The magnitude of the electron of the electron drift current density at x = 0.5 μm is
A. 2. 16 × 104 A/cm2
B. 1.08 × 104 A/cm2
C. 4.32 × 103 A/cm2
D. 6.48 × 102 A/cm2