GATE ECE purpose:exam-prep PYQs & Answers — Page 55

Questions 541–550 of 715. Imported answers require independent review unless marked reviewed.

Let M be a real

matrix. Consider the following statements:

S1: M has 4 linearly independent eigenvectors.

S2: M has 4 distinct eigenvalues.

S3: M is non-singular (invertible).

Which one among the following is TRUE?

Your answerChoose one option.

S1 implies S2

S1 implies S3

S2 implies S1

S3 implies S2

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Let

, where a and b are constants. If

and

, then the relation between a and b is

Your answerChoose one option.

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A discrete-time all-pass system has two of its poles at

and

. Which one of the following statements about the system is TRUE?

Your answerChoose one option.

It has two more poles at

and

It is stable only when the impulse response is two-sided.

It has constant phase response over all frequencies.

It has constant phase response over the entire z-plane.

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Let

be a periodic function with period

. The Fourier series coefficients for this series are denoted by

, that is

The same function

can also be considered as a periodic function with period

. Let

be the Fourier series coefficients when period is taken as

. If

, then

is equal to

Your answerChoose one option.

256

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Consider the following amplitude modulated signal:

The ratio (accurate to three decimal places) of the power of the message signal to the power of the carrier signal is __________.

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Consider a binary channel code in which each codeword has a fixed length of 5 bits. The Hamming distance between any pair of distinct codewords in this code is at least 2. The maximum number of codewords such a code can contain is __________.

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A binary source generates symbols

which are transmitted over a noisy channel. The probability of transmitting

is 0.5. Input to the threshold detector is

. The probability density function

of the noise

is shown below.

Diagram for Electronics and Communication Engineering question 17

If the detection threshold is zero, then the probability of error (correct to two decimal places) is __________.

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A p-n step junction diode with a contact potential of 0.65 V has a depletion width of 1 μm at equilibrium. The forward voltage (in volts, correct to two decimal places) at which this width reduces to 0.6 μm is ______.

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A traffic signal cycles from GREEN to YELLOW, YELLOW to RED and RED to GREEN. In each cycle, GREEN is turned on for 70 seconds, YELLOW is turned on for 5 seconds and the RED is turned on for 75 seconds. This traffic light has to be implemented using a finite state machine (FSM). The only input to this FSM is a clock of 5 second period. The minimum number of flip-flops required to implement this FSM is ______.

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There are two photolithography systems: one with light source of wavelength

nm (System 1) and another with light source of wavelength

nm (System 2). Both photolithography systems are otherwise identical. If the minimum feature sizes that can be realized using System 1 and System 2 are

and

respectively, the ratio

(correct to two decimal places) is__________.

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GATE ECE purpose:exam-prep PYQs

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