McqMate
These multiple-choice questions (MCQs) are designed to enhance your knowledge and understanding in the following areas: Electrical Engineering .
| 1. |
Evaluate the following function in terms of t: {integral from 0 to t}{Integral from -inf to inf}d(t) |
| A. | 1⁄t |
| B. | 1⁄t2 |
| C. | t |
| D. | t2 |
| Answer» C. t | |
| Explanation: the first integral is 1, and the overall integral evaluates to t. | |
| 2. |
The fundamental period of exp(jwt) is |
| A. | pi/w |
| B. | 2pi/w |
| C. | 3pi/w |
| D. | 4pi/w |
| Answer» B. 2pi/w | |
| Explanation: the function assumes the same value after t+2pi/w, hence the period would be 2pi/w. | |
| 3. |
Find the magnitude of exp(jwt). Find the boundness of sin(t) and cos(t). |
| A. | 1, [-1,2], [-1,2] |
| B. | 0.5, [-1,1], [-1,1] |
| C. | 1, [-1,1], [-1,2] |
| D. | 1, [-1,1], [-1,1] |
| Answer» D. 1, [-1,1], [-1,1] | |
| Explanation: the sin(t)and cos(t) can be found using euler’s rule. | |
| 4. |
Find the value of {sum from -inf to inf} exp(jwn)*d[n]. |
| A. | 0 |
| B. | 1 |
| C. | 2 |
| D. | 3 |
| Answer» B. 1 | |
| Explanation: the sum will exist only for n = 0, for which the product will be 1. | |
| 5. |
Compute d[n]d[n-1] + d[n-1]d[n-2] for n = 0, 1, 2. |
| A. | 0, 1, 2 |
| B. | 0, 0, 1 |
| C. | 1, 0, 0 |
| D. | 0, 0, 0 |
| Answer» D. 0, 0, 0 | |
| Explanation: only one of the values can be one at a time, others will be forced to zero, due to the delta function. | |
| 6. |
Defining u(t), r(t) and s(t) in their standard ways, are their derivatives defined at t = 0? |
| A. | yes, yes, no |
| B. | no, yes, no |
| C. | no, no, yes |
| D. | no, no, no |
| Answer» D. no, no, no | |
| Explanation: none of the derivatives are defined at t=0. | |
| 7. |
Which is the correct Euler expression? |
| A. | exp(2jt) = cos(2t) + jsin(t) |
| B. | exp(2jt) = cos(2t) + jsin(2t) |
| C. | exp(2jt) = cos(2t) + sin(t) |
| D. | exp(2jt) = jcos(2t) + jsin(t) |
| Answer» B. exp(2jt) = cos(2t) + jsin(2t) | |
| Explanation: euler rule: exp(jt) = cos(t) + jsin(t). | |
| 8. |
The range for unit step function for u(t – a), is |
| A. | t < a |
| B. | t ≤ a |
| C. | t = a |
| D. | t ≥ a |
| Answer» D. t ≥ a | |
| Explanation: a unit step signal u(t) = 1 when t ≥ 0 and 0 when t < 0 | |
| 9. |
Which one of the following is not a ramp function? |
| A. | r(t) = t when t ≥ 0 |
| B. | r(t) = 0 when t < 0 |
| C. | r(t) = ∫u(t)dt when t < 0 |
| D. | r(t) = du(t)⁄dt |
| Answer» D. r(t) = du(t)⁄dt | |
| Explanation: ramp function r(t) = t when t ≥ 0 and r(t) = 0 when t < 0 | |
| 10. |
Unit Impulse function is obtained by using the limiting process on which among the following functions? |
| A. | triangular function |
| B. | rectangular function |
| C. | signum function |
| D. | sinc function |
| Answer» B. rectangular function | |
| Explanation: unit impulse function can be obtained by using a limiting process on the rectangular pulse function. area under the rectangular pulse is equal to unity. | |
| 11. |
When is a complex exponential signal pure DC? |
| A. | σ = 0 and Ω < 0 |
| B. | σ < 0 and Ω = 0 |
| C. | σ = 0 and Ω = 0 |
| D. | σ < 0 and Ω < 0 |
| Answer» C. σ = 0 and Ω = 0 | |
| Explanation: a complex exponential signal is represented as x(t)= est | |
| 12. |
What is exp(ja) equal to, where j is the square root of unity? |
| A. | cos ja + jsin a |
| B. | sin a + jcos a |
| C. | cos j + a sin j |
| D. | cos a + jsin a |
| Answer» D. cos a + jsin a | |
| Explanation: this is the corollary of demoivre/euler’s theorem. | |
| 13. |
What is the magnitude of exp(2+3j)? |
| A. | exp(2.3) |
| B. | exp(3) |
| C. | exp(2) |
| D. | exp(3/2) |
| Answer» C. exp(2) | |
| Explanation: exp(a+b) =exp(a) * exp(b), and | |
| 14. |
What is the fundamental frequency of exp(2pi*w*j)? |
| A. | 1pi*w |
| B. | 2pi*w |
| C. | w |
| D. | 2w |
| Answer» C. w | |
| Explanation: fundamental period = 2pi/w, hence fundamental frequency will be w. | |
| 15. |
Total energy possessed by a signal exp(jwt) is? |
| A. | 2pi/w |
| B. | pi/w |
| C. | pi/2w |
| D. | 2pi/3w |
| Answer» A. 2pi/w | |
| Explanation: energy possessed by a periodic signal is the integral of the square of the magnitude of the signal over a time period. | |
| 16. |
Sinusoidal signals multiplied by decaying exponentials are referred to as |
| A. | amplified sinusoids |
| B. | neutralized sinusoids |
| C. | buffered sinusoids |
| D. | damped sinusoids |
| Answer» D. damped sinusoids | |
| Explanation: the decaying exponentials | |
| 17. |
What is the period of exp(2+pi*j/4)t? |
| A. | 4 |
| B. | 8 |
| C. | 16 |
| D. | 20 |
| Answer» B. 8 | |
| Explanation: the fundamental period = 2pi/(pi/4) = 8. | |
| 18. |
exp(jwt) is periodic |
| A. | for any w |
| B. | for any t |
| C. | for no w |
| D. | for no t |
| Answer» A. for any w | |
| Explanation: any two instants, t and t + 2pi will be equal, hence the signal will be periodic with period 2pi. | |
| 19. |
Define the fundamental period of the following signal x[n] = exp(2pi*j*n/3) + exp(3*pi*j*n/4)? |
| A. | 8 |
| B. | 12 |
| C. | 18 |
| D. | 24 |
| Answer» D. 24 | |
| Explanation: the first signal, will repeat itself after 3 cycles. the second will repeat itself after 8 cycles. thus, both of them | |
| 20. |
exp[jwn] is periodic |
| A. | for any w |
| B. | for any t |
| C. | for w=2pi*m/n |
| D. | for t = 1/w |
| Answer» C. for w=2pi*m/n | |
| Explanation: discrete exponentials are periodic only for a particular choice of the fundamental frequency. | |
| 21. |
The most general form of complex exponential function is: |
| A. | eσt |
| B. | eΩt |
| C. | est |
| D. | eat |
| Answer» C. est | |
| Explanation: the general form of complex exponential function is: x(t) = est where s = σ | |
| 22. |
A complex exponential signal is a decaying exponential signal when |
| A. | Ω = 0 and σ > 0 |
| B. | Ω = 0 and σ = 0 |
| C. | Ω ≠ 0 and σ < 0 |
| D. | Ω = 0 and σ < 0 |
| Answer» D. Ω = 0 and σ < 0 | |
| Explanation: let x(t) be the complex exponential signal | |
| 23. |
When is a complex exponential signal sinusoidal? |
| A. | σ =0 and Ω = 0 |
| B. | σ < 0 and Ω = 0 |
| C. | σ = 0 and Ω ≠ 0 |
| D. | σ ≠ 0 and Ω ≠ 0 |
| Answer» C. σ = 0 and Ω ≠ 0 | |
| Explanation: a signal is sinusoidal when σ = 0 and Ω ≠ 0 | |
| 24. |
An exponentially growing sinusoidal signal is: |
| A. | σ = 0 and Ω = 0 |
| B. | σ > 0 and Ω ≠ 0 |
| C. | σ < 0 and Ω ≠ 0 |
| D. | σ = 0 and Ω ≠ 0 |
| Answer» B. σ > 0 and Ω ≠ 0 | |
| Explanation: a complex exponential signal is sinusoidal when Ω has a definite value i.e., Ω ≠ 0. it can either be growing exponential or decaying exponential based on the value of σ. | |
| 25. |
Determine the nature of the signal: x(t) = e-0.2t [cosΩt + jsinΩt]. |
| A. | exponentially decaying sinusoidal signal |
| B. | exponentially growing sinusoidal signal |
| C. | sinusoidal signal |
| D. | exponential signal |
| Answer» A. exponentially decaying sinusoidal signal | |
| Explanation: clearly the signal has negative exponential ⇒ decaying exponential signal. the signal also has sinusoidal component. | |
| 26. |
A signal is a physical quantity which does not vary with |
| A. | time |
| B. | space |
| C. | independent variables |
| D. | dependent variables |
| Answer» D. dependent variables | |
| Explanation: a signal is a physical quantity which varies with time, space or any other independent variables. therefore, it does not vary with dependent variables. | |
| 27. |
Most of the signals found in nature are |
| A. | continuous-time and discrete-time |
| B. | continuous-time and digital |
| C. | digital and analog |
| D. | analog and continuous-time |
| Answer» D. analog and continuous-time | |
| Explanation: signals naturally are continuous-time signals. these are also known as analog signals. continuous-time or analog signals are defined for all values of time t. | |
| 28. |
Which one of the following is not a characteristic of a deterministic signal? |
| A. | exhibits no uncertainty |
| B. | instantaneous value can be accurately predicted |
| C. | exhibits uncertainty |
| D. | can be represented by a mathematical equation |
| Answer» C. exhibits uncertainty | |
| Explanation: deterministic signal is one which exhibits no uncertainty and its instantaneous value can be accurately predicted from its mathematical equation. therefore, a deterministic signal doesn’t exhibit uncertainty. however, a random is always uncertain. | |
| 29. |
Sum of two periodic signals is a periodic signal when the ratio of their time periods is |
| A. | a rational number |
| B. | an irrational number |
| C. | a complex number |
| D. | an integer |
| Answer» A. a rational number | |
| Explanation: sum of two periodic signals is a periodic signal only when the ratio of their time periods is a rational number or it is the ratio of two integers. for e.g., t1/t2 = 5/7 → periodic; t1/t2 = 5 → aperiodic. | |
| 30. |
Determine the Time period of: x(t)=3 cos(20t+5)+sin(8t-3). |
| A. | 1/10 sec |
| B. | 1/20 sec |
| C. | 2/5 sec d 2/4 sec |
| Answer» C. 2/5 sec d 2/4 sec | |
| 31. |
Determine the odd component of the signal: x(t)=cost+sint. |
| A. | sint |
| B. | 2sint |
| C. | cost |
| D. | 2cost |
| Answer» C. cost | |
| Explanation: here is the explanation. | |
| 32. |
Is the signal sin(t) anti-symmetric? |
| A. | yes |
| B. | no |
| Answer» A. yes | |
| Explanation: a signal is said to be anti- symmetric or odd signal when it satisfies the following condition: | |
| 33. |
For an energy signal |
| A. | e=0 |
| B. | p= ∞ |
| C. | e= ∞ |
| D. | p=0 |
| Answer» D. p=0 | |
| Explanation: a signal is called an energy signal if the energy satisfies 0<e< ∞ and power p=0. | |
| 34. |
Determine the power of the signal: x(t) = cos(t). |
| A. | 1/2 |
| B. | 1 |
| C. | 3/2 |
| D. | 2 |
| Answer» A. 1/2 | |
|
Explanation: To determine the power of the given signal x(t) = cos(t), we need to calculate the average power over time. The power of a continuous-time signal x(t) can be calculated using the formula: P = (1/T) * ∫[T] |x(t)|^2 dt Where T is the period of the signal. In this case, the signal x(t) = cos(t) is a periodic signal with a period of 2π. So we need to evaluate the integral over one period, from 0 to 2π. P = (1/(2π)) * ∫[0 to 2π] |cos(t)|^2 dt Using the trigonometric identity cos^2(t) = (1 + cos(2t))/2, we can simplify the integral: P = (1/(2π)) * ∫[0 to 2π] (1 + cos(2t))/2 dt P = (1/(2π)) * [t/2 + (sin(2t))/4] evaluated from 0 to 2π P = (1/(2π)) * [(2π/2 + (sin(4π))/4) - (0/2 + (sin(0))/4)] P = (1/(2π)) * (π + 0 - 0) = 1/2 Therefore, the power of the signal x(t) = cos(t) is 1/2. The correct answer is A. 1/2. |
|
| 35. |
Is the following signal an energy signal? x(t) = u(t) – u(t – 1) |
| A. | yes |
| B. | no |
| Answer» A. yes | |
| Explanation: here is the explanation. | |
| 36. |
A signal is anti-causal if |
| A. | x(t) = 0 for t = 0 |
| B. | x(t) = 1 for t < 0 |
| C. | x(t) = 1 for t > 0 |
| D. | x(t) = 0 for t > 0 |
| Answer» D. x(t) = 0 for t > 0 | |
| Explanation: a signal is said to be anti- causal when x(t) = 0 for t > 0. | |
| 37. |
Is the signal x(t)= eat u(t) causal? |
| A. | yes |
| B. | no |
| Answer» A. yes | |
| Explanation: a signal is said to be causal if it is 0 for t < 0. | |
| 38. |
Is the signal x(n) = u(n + 4) – u(n – 4) causal? |
| A. | yes |
| B. | no |
| Answer» B. no | |
| Explanation: a signal is said to be causal if it is 0 for t < 0. | |
| 39. |
The type of systems which are characterized by input and the output capable of taking any value in a particular set of values are called as |
| A. | analog |
| B. | discrete |
| C. | digital |
| D. | continuous |
| Answer» D. continuous | |
| Explanation: continuous systems have a restriction on the basis of the upper bound and lower bound, but within this set, the input and output can assume any value. thus, there are infinite values attainable in this system | |
| 40. |
An example of a discrete set of information/system is |
| A. | the trajectory of the sun |
| B. | data on a cd |
| C. | universe time scale |
| D. | movement of water through a pipe |
| Answer» B. data on a cd | |
| Explanation: the rest of the parameters are continuous in nature. data is stored in the form of discretized bits on cds. | |
| 41. |
A system which is linear is said to obey the rules of |
| A. | scaling |
| B. | additivity |
| C. | both scaling and additivity |
| D. | homogeneity |
| Answer» C. both scaling and additivity | |
| Explanation: a system is said to be additive and scalable in order to be classified as a linear system. | |
| 42. |
A time invariant system is a system whose output |
| A. | increases with a delay in input |
| B. | decreases with a delay in input |
| C. | remains same with a delay in input |
| D. | vanishes with a delay in input |
| Answer» C. remains same with a delay in input | |
| Explanation: a time invariant system’s output should be directly related to the time of the output. there should be no scaling, i.e. y(t) = f(x(t)). | |
| 43. |
Should real time instruments like oscilloscopes be time invariant? |
| A. | yes |
| B. | sometimes |
| C. | never |
| D. | they have no relation with time variance |
| Answer» A. yes | |
| Explanation: oscilloscopes should be time invariant, i.e they should work the same way everyday, and the output should not change with the time at which it is operated. | |
| 44. |
All real time systems concerned with the concept of causality are |
| A. | non causal |
| B. | causal |
| C. | neither causal nor non causal |
| D. | memoryless |
| Answer» B. causal | |
| Explanation: all real time systems are causal, since they cannot have perception of the future, and only depend on their memory. | |
| 45. |
A system is said to be defined as non causal, when |
| A. | the output at the present depends on the input at an earlier time |
| B. | the output at the present does not depend on the factor of time at all |
| C. | the output at the present depends on the input at the current time |
| D. | the output at the present depends on the input at a time instant in the future |
| Answer» D. the output at the present depends on the input at a time instant in the future | |
| Explanation: a non causal system’s output is said to depend on the input at a time in the future. | |
| 46. |
When we take up design of systems, ideally how do we define the stability of a system? |
| A. | a system is stable, if a bounded input gives a bounded output, for some values of the input |
| B. | a system is unstable, if a bounded input gives a bounded output, for all values of the input |
| C. | a system is stable, if a bounded input gives a bounded output, for all values of the input |
| D. | a system is unstable, if a bounded input gives a bounded output, for some values of the input |
| Answer» C. a system is stable, if a bounded input gives a bounded output, for all values of the input | |
| Explanation: for designing a system, it should be kept in mind that the system does not blow out for a finite input. thus, every finite input should give a finite output. | |
| 47. |
All causal systems must have the component of |
| A. | memory |
| B. | time invariance |
| C. | stability |
| D. | linearity |
| Answer» A. memory | |
| Explanation: causal systems depend on the functional value at an earlier time, compelling the system to possess memory. | |
| 48. |
What are fourier coefficients? |
| A. | the terms that are present in a fourier series |
| B. | the terms that are obtained through fourier series |
| C. | the terms which consist of the fourier series along with their sine or cosine values |
| D. | the terms which are of resemblance to fourier transform in a fourier series are called fourier series coefficients |
| Answer» C. the terms which consist of the fourier series along with their sine or cosine values | |
| Explanation: the terms which consist of the fourier series along with their sine or cosine values are called fourier coefficients. fourier coefficients are present in both exponential and trigonometric fourier series. | |
| 49. |
Which are the fourier coefficients in the following? |
| A. | a0, an and bn |
| B. | an |
| C. | bn |
| D. | an and bn |
| Answer» A. a0, an and bn | |
| Explanation: these are the fourier coefficients in a trigonometric fourier series. a0 = 1/t∫x(t)dt | |
| 50. |
Do exponential fourier series also have fourier coefficients to be evaluated. |
| A. | true |
| B. | false |
| Answer» A. true | |
| Explanation: the fourier coefficient is : xn = 1/t∫x(t)e-njwtdt. | |
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