EC GATE 2015 PAPER 01 (Test 2)



Tag: ec gate 2015 paper 01
Q.1
A 3-input majority gate is defined by the logic function M(a,b,c) = ab + bc + ca. Which one of the following gates is represented by the function 
A. 3-input NAND gate
B. 3-input XOR gate
C. 3-input NOR gate
D. 3-input XNOR gate
Answer : Option B
Explaination / Solution:

3 input majority gate is given as
M(a,b,c) = ab + bc + ca
We have to obtain 


We obtain truth table for the function as

So, the function is odd number of 1’s detector. This function represent the 3-input XOR gate.

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Q.2
The Boolean expression  converted into the canonical product of sum (POS) form is
A.
B.
C.
D.
Answer : Option A
Explaination / Solution:

We have the SOP Boolean form,


Hence, in POS form, we have


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Q.3
The circuit shown in the figure has an ideal opamp. The oscillation frequency and the condition to sustain the oscillations, respectively, are

A. (1/CR) and R1 = R2
B. (1/CR) and R1 = 4R2
C. (1/2CR) and R1 = R2
D. (1/2CR) and R1 = 4R2
Answer : Option D
Explaination / Solution:

By virtual ground property, we write


We equate imaginary part to zero, i.e.

The condition to sustain the oscillation is


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Q.4
A region of negative differential resistance is observed in the current voltage characteristics of a silicon PN junction if
A. Both the P-region and N-region are heavily doped
B. The N-region is heavily doped compared to the P-region
C. The P-region is heavily doped compared to the N-region
D. An intrinsic silicon region is inserted between the P-region and the N-region
Answer : Option A
Explaination / Solution:

In case of Tunnel diode formed by PN junction, tunnel diode gives negative resistance and works in forward bias, and in tunnel diode both N and P regions are heavily doped.

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Q.5
For the NMOSFET in the circuit shown, the threshold voltage is Vth, where Vth > 0. The source voltage VSS is varied from 0 to VDD. Neglecting the channel length modulation, the drain current ID as a function VSS is represented by

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

We have the following conditions

Since it is in saturation, current ID is given by

Thus, ID - VSS graph shows Parabolic relation for Vss < VDD - Vth and zero for Vss > VDD - Vth. Only graph shown in option (A) satisfies this result.


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Q.6
Consider the signal  where  denotes the Hilbert transform of m(t) and the bandwidth of m(t) is very small compared to fcThe signal s(t) is a
A. high-pass signal
B. low-pass signal
C. band-pass signal
D. double side-band suppressed carrier signal
Answer : Option C
Explaination / Solution:

We have the signal,

Here, s(t) represents SSB - Lower side band, and thus a band pass signal.

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Q.7
A sinusoidal signal of 2 kHz frequency is applied to a delta modulator. The sampling rate and step-size Δ of the delta modulator are 20,000 samples per second and 0.1 V, respectively. To prevent slope overload, the maximum amplitude of the sinusoidal signal (in Volts) is
A. 1/2𝜋
B. 1/𝜋
C. 2/𝜋
D. 𝜋
Answer : Option A
Explaination / Solution:

For preventing slope overload, we should have
(slope of m(t) ≤ (slope of sampling)
For sinusoidal signal, if


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Q.8
The longitudinal component of the magnetic field inside an air-filled rectangular waveguide made of a perfect electric conductor is given by the following expression  The cross-sectional dimensions of the waveguide are given as a = 0.08 m and b = 0.033 m. The mode of propagation inside the waveguide is
A.

TM12

B.

TM21

C.

TE21

D.

TE12

Answer : Option C
Explaination / Solution:

We have the expression,

and the cross sectional dimension is
a = 0.08 m, b = 0.033m
Now, we compare the equation for TEm,n mode whose Hz is given as


Hence, given mode is TE21 mode

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Q.9
The polar plot of the transfer function  will be in the
A. first quadrant
B. second quadrant
C. third quadrant
D. fourth quadrant
Answer : Option A
Explaination / Solution:




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Q.10
Negative feedback in a closed-loop control system DOES NOT
A. reduce the overall gain
B. reduce bandwidth
C. improve disturbance rejection
D. reduce sensitivity to parameter variation
Answer : Option B
Explaination / Solution:

Negative feedback in closed-loop control system does not reduce bandwidth.

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