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

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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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,

We have the SOP Boolean form,

Hence, in POS form, we have

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

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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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.

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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For the NMOSFET in the circuit shown, the threshold voltage is V_{th}, where V_{th} > 0. The source voltage V_{SS} is varied from 0 to V_{DD}. Neglecting the channel length modulation, the drain current ID as a function V_{SS} is represented by

We have the following conditions

Since it is in saturation, current ID is given by

Thus, I_{D} - V_{SS} graph shows Parabolic relation for V_{ss} < V_{DD}
- V_{th }and zero for V_{ss} > V_{DD}
- V_{th. }Only graph shown in option (A) satisfies this result.

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Consider the signal where denotes the Hilbert transform of m(t) and the bandwidth of m(t) is very small compared to f_{c}. The 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,

We have the signal,

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

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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

For preventing slope overload, we should have

(slope of m(t) ≤ (slope of sampling)

For sinusoidal signal, if

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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

TM_{12}

TM_{21}

TE_{21}

TE_{12}

We have the expression,

and the cross sectional dimension is

a = 0.08 m, b = 0.033m

Now, we compare the equation for TE_{m,n} mode whose H_{z} is given as

Hence, given mode is TE21 mode

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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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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.

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

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