A plane wave of wavelength λ is traveling in a direction making an angle 30^{0} with positive x − axis and 90^{0} with positive y − axis. The field of the plane
wave can be represented as (E is constant)

**A. **

**B. **

**C. **

**D. **

**Answer : ****Option A**

**Explaination / Solution: **

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The field in a rectangular waveguide of inner dimension a × b is given by **A. ** TE_{20}

**B. ** TM_{11}

**C. ** TM_{20}

**D. ** TE_{10}

**Answer : ****Option A**

**Explaination / Solution: **

Where H_{0} is a constant, and a and b are the dimensions along the x − axis and
the y − axis respectively. The mode of propagation in the waveguide is

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The circuit shown in the figure is used to charge the capacitor C alternately
from two current sources as indicated. The switches S1 and S2 are mechanically
coupled and connected as follows:

**A. **

**B. **

**C. **

**D. **

**Answer : ****Option C**

**Explaination / Solution: **

Assume that the capacitor has zero initial charge. Given that u(t) is a unit step function , the voltage v_{c}(t) across the capacitor is given by

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Consider the frequency modulated signal with carrier frequency of 10^{5} Hz. The modulation index is

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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

**Answer : ****Option D**

**Explaination / Solution: **

For distortion less transmission line characteristics impedance

For distortion less transmission line characteristics impedance

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In binary frequency shift keying (FSK), the given signal waveform are

**A. ** 0.25 ms

**B. ** 0.5 ms

**C. ** 0.75 ms

**D. ** 1.0 ms

**Answer : ****Option B**

**Explaination / Solution: **

u0 (t) = 5cos (20000 πt); 0 ≤ t ≤ T, and

u1 (t) = 5cos (22000 πt); 0 ≤ t ≤ T,

Where T is the bit-duration interval and t is in seconds. Both u0 (t) and u1 (t) are zero outside the interval 0 ≤ t ≤ T. With a matched filter (correlator) based receiver, the smallest positive value of T (in milliseconds) required to have u0 (t) and u1 (t) uncorrelated is

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A transmission line terminates in two branches, each of length as shown. The branches are terminated by 50W loads. The lines are lossless and have the characteristic impedances shown. Determine the impedance Zi as seen by the source.

_{}

_{}

_{}

_{}

The transmission line are as shown below. Length of all line is

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x(t) is a stationary random process with auto-correlation function. This process is passed through the system shown below. The
power spectral density of the output process y(t) is

**A. ** (4π^{2}f^{2} + 1) exp (-πf^{2})

**B. ** (4π^{2}f^{2} - 1) exp (-πf^{2})

**C. ** (4π^{2}f^{2} + 1) exp (-πf)

**D. ** (4π^{2}f^{2} - 1) exp (-πf)

**Answer : ****Option A**

**Explaination / Solution: **

The given circuit can be simplified as

Power spectral density of output is

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Two magnetically uncoupled inductive coils have Q factors q_{1} and q_{2} at the
chosen operating frequency. Their respective resistances are R_{1} and R_{2}. When
connected in series, their effective Q factor at the same operating frequency is

**A. ** q1 + q2
**B. ** (1/q1) + (1/q2)
**C. ** (q1R1 + q2R2) / (R1 + R2)
**D. ** (q1R2 + q2R1) / (R1 + R2)

**Answer : ****Option C**

**Explaination / Solution: **

The quality factor of the inductances are given by

The quality factor of the inductances are given by

So, in series circuit, the effective quality factor is given by

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The state variable description of an LTI system is given by**A. **

**B. **

**C. **

**D. **

**Answer : ****Option D**

**Explaination / Solution: **

where y is the output and u is the input. The system is controllable for

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**Preparation Study Material**- Physics Vol A1 (Study/Preparation)
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