MCQOPTIONS
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MCQOPTIONS
This section includes 62 Mcqs, each offering curated multiple-choice questions to sharpen your Matlab knowledge and support exam preparation. Choose a topic below to get started.
| 1. |
A student aims to use Cramer’s rule to find a solution for a homogeneous system. But while finding the solution, he observes that he is getting infinity as a solution. The code is X is the matrix created by replacing a column with constant co-efficients in the equation.C is the co-efficient matrixP is one of the variables in the systemIs this a proper justification? |
| A. | Yes |
| B. | No |
| C. | Maybe |
| D. | It is not possible to find solutions in MATLABView Answer |
| Answer» C. Maybe | |
| 2. |
A second order system with no initial condition is always linear. |
| A. | True |
| B. | False |
| Answer» B. False | |
| 3. |
To apply Cramer’s rule, the condition is _________ |
| A. | Non-homogeneous system of equations |
| B. | Homogeneous system of equations |
| C. | Determinant of co-efficient matrix is not equal to 0 |
| D. | No condition |
| Answer» D. No condition | |
| 4. |
For a homogeneous system, Cramer’s rule will always yield a trivial solution in MATLAB. |
| A. | True |
| B. | False |
| Answer» B. False | |
| 5. |
How can we find the solution of a nonhomogeneous system of equations without dealing with the rank of matrices? |
| A. | Rouche’s theorem |
| B. | Cramer’s rule |
| C. | Gauss’s law |
| D. | Cannot be done |
| Answer» C. Gauss’s law | |
| 6. |
How can we check in MATLAB if an electrical circuit is linear or not? |
| A. | Check consistency |
| B. | Superposition |
| C. | Superposition via Simulink |
| D. | Check homogeneity |
| Answer» D. Check homogeneity | |
| 7. |
The command to find the eigen vector of a matrix in matrix form is _____________a) eig(a,matrix)b) eig(a,’matrix’)c) eigen(a,matr)d) eig( |
| A. | eig(a,matrix) |
| B. | eig(a,’matrix’) |
| C. | eigen(a,matr) |
| D. | eig(a) |
| Answer» C. eigen(a,matr) | |
| 8. |
A student has to find a solution for a system of equations having three variables. He has defined the coefficient matrix as C while the variable matrix as d. He observes that the system is homogeneous. So, to find the solution, he must first check |
| A. | Consistency |
| B. | Homogeneity |
| C. | Heterogeneity |
| D. | Linearity |
| Answer» B. Homogeneity | |
| 9. |
What is the output if the following code? |
| A. | True |
| B. | No output |
| C. | False |
| D. | ErrorView Answer |
| Answer» E. | |
| 10. |
An inductor is described by input-output relation as\(y\left( t \right) = \frac{1}{L}\mathop \smallint \limits_{ - \infty }^t x\left( \tau \right)d\tau \;\)The operation representing the inverse system x(t) will be |
| A. | \(L\frac{d}{{dt}}y\left( t \right)\) |
| B. | L |
| C. | \(\frac{d}{{dt}}y\left( t \right)\) |
| D. | Ly(t) |
| Answer» B. L | |
| 11. |
An ideal low pass filter as a discrete-time system is |
| A. | Causal, realizable |
| B. | Non-causal, physically/computationally unrealizable |
| C. | Non-causal, physically realizable |
| D. | None of the above |
| Answer» C. Non-causal, physically realizable | |
| 12. |
A discrete-time system has input x[̇*] and output y[*] satisfying \(y\left[ m \right] = \mathop \sum \nolimits_{j = - \infty }^m x\left[ j \right]\). The system is |
| A. | linear and unstable |
| B. | linear and stable |
| C. | non-linear and stable |
| D. | non-linear and unstable |
| Answer» B. linear and stable | |
| 13. |
Consider signal x(t) = (1 + sin 100πt) cos(200πt). The fundamental frequency component in x(t) is ________ Hz. |
| A. | 200 |
| B. | 150 |
| C. | 50 |
| D. | 100 |
| Answer» D. 100 | |
| 14. |
A system is characterized by the input-output relation y(t) = x (2t) + x (3t) for all t, where y(t) is the output and x(t) is the input. It is |
| A. | linear and causal |
| B. | linear and non-causal |
| C. | non-linear and causal |
| D. | non-linear non-causal |
| Answer» C. non-linear and causal | |
| 15. |
For a discrete LTI system, the impulse response is u[n]. What is its step response? |
| A. | nu[n - 1] |
| B. | n2 u[n] |
| C. | nu[n] |
| D. | u[n] |
| Answer» D. u[n] | |
| 16. |
A system has impulse response h[n] = cos (n) u[n]. The system is: |
| A. | Causal and stable |
| B. | Non-causal and stable |
| C. | Non-causal and not stable |
| D. | Causal and not stable |
| Answer» E. | |
| 17. |
Consider an LTI system with transfer function\(H\left( s \right) = \frac{1}{{s\left( {s + 4} \right)}}\)If the input to the system is cos(3t) and the steady output is Asin (3t + α), then the value of A is |
| A. | 1/30 |
| B. | 1/15 |
| C. | 3/4 |
| D. | 4/3 |
| Answer» C. 3/4 | |
| 18. |
Consider a system, which computes the ‘MEDIAN’ of signal values in a window of size ‘N’. ‘Such a discrete-time system is: |
| A. | Linear |
| B. | Non-linear |
| C. | Sometimes linear |
| D. | Sometimes non-linear |
| Answer» C. Sometimes linear | |
| 19. |
Consider a discrete-time accumulator system \(y\left[ n \right] = \mathop \sum \nolimits_{k = - \infty }^n x\left[ k \right]\) and the backward difference system y[n] = x[n] – x[n – 1] where x[⋅] represents the input and y[⋅] represents the output of the individual systems.When these two systems are cascaded as in the figure, the impulse response of the combined system with output z[n] is |
| A. | Unit impulse sequence |
| B. | Unit step sequence |
| C. | Unit ramp sequence |
| D. | None of the above |
| Answer» B. Unit step sequence | |
| 20. |
A cascade system having the impulse response \({{\rm{h}}_1}\left( {\rm{n}} \right) = \left\{ {\begin{array}{*{20}{l}}{1, - 1}\\\uparrow\end{array}} \right\}\) and \({{\rm{h}}_2}\left( {\rm{n}} \right) = \left\{ {\begin{array}{*{20}{l}}{1,{\rm{\;}}1}\\\uparrow\end{array}} \right\}\) is shown in the figure below, where symbol ↑ denotes the time origin.The input sequence x(n) for which the cascade system produces an output sequence \({\rm{y}}\left( {\rm{n}} \right) = \left\{ {\begin{array}{*{20}{l}}{1,{\rm{\;}}2,{\rm{\;}}1,{\rm{\;}} - 1,{\rm{\;}} - 2,{\rm{\;}} - 1}\\\uparrow\end{array}} \right\}\) is |
| A. | \({\rm{x}}\left( {\rm{n}} \right) = \left\{ {\begin{array}{*{20}{l}}{1,{\rm{\;}}2,{\rm{\;}}1,{\rm{\;}}1}\\\uparrow\end{array}} \right\}\) |
| B. | \({\rm{x}}\left( {\rm{n}} \right) = \left\{ {\begin{array}{*{20}{l}}{1,{\rm{\;}}1,{\rm{\;}}2,{\rm{\;}}2}\\\uparrow\end{array}} \right\}\) |
| C. | \({\rm{x}}\left( {\rm{n}} \right) = \left\{ {\begin{array}{*{20}{l}}{1,{\rm{\;}}1,{\rm{\;}}1,{\rm{\;}}1}\\\uparrow\end{array}} \right\}\) |
| D. | \({\rm{x}}\left( {\rm{n}} \right) = \left\{ {\begin{array}{*{20}{l}}{1,{\rm{\;}}2,{\rm{\;}}2,{\rm{\;}}1}\\\uparrow\end{array}} \right\}\) |
| Answer» E. | |
| 21. |
In the following, pick out the linear systems(i) d2y(t)/dt2 + 9a1dy(t)/dt + a2y(t) = u(t)(ii) y(t)dy(t)/dt + a1y(t) = a2 u(t)(iii) 2d2y(t)/dt2 + dy(t)/dt + t2y(t) = 5 |
| A. | (i) and (ii) |
| B. | (i) only |
| C. | (i) and (iii) |
| D. | (ii) and (iii) |
| Answer» D. (ii) and (iii) | |
| 22. |
A continuous-time input signal x(t) is an eigenfunction of an LTI system, if the output is |
| A. | k x(t), where k is an eigenvalue |
| B. | Keiωt x(t), where k is an eigenvalue and eiωt is a complex exponential signal |
| C. | x(t) eiωt, where eiωt is a complex exponential signal |
| D. | k H(ω), where k is an eigenvalue and H(ω) is a frequency response of the system |
| Answer» B. Keiωt x(t), where k is an eigenvalue and eiωt is a complex exponential signal | |
| 23. |
A stable LTI system has a transfer function \(H\left( s \right) = \frac{1}{{{s^2} + s - 6}}\). To make this system causal and stable it needs to be cascaded with another LTI system having transfer function H1(s). The correct choice for H1(s) is |
| A. | s + 3 |
| B. | s - 2 |
| C. | s - 6 |
| D. | s + 1 |
| Answer» C. s - 6 | |
| 24. |
If f(t) is the step-response of a linear time invariant system, then its impulse response h(t) is given by:(where ‘t’ indicates continuous time domain) |
| A. | \(h\left( t \right) = \smallint f\left( t \right)\) |
| B. | \(h\left( t \right) = \frac{d}{{dt}}f\left( t \right)\) |
| C. | \(h\left( t \right) = {\left[ {f\left( t \right)} \right]^2}\) |
| D. | h(t) = f(t) |
| Answer» C. \(h\left( t \right) = {\left[ {f\left( t \right)} \right]^2}\) | |
| 25. |
Linear time-invariant systems that are designed to pass some frequencies essentially undistorted and significantly attenuate or eliminate others are |
| A. | Frequency-shaping filters |
| B. | Frequency-selective filters |
| C. | Time-shaping filters |
| D. | Time-selective filters |
| Answer» C. Time-shaping filters | |
| 26. |
If f1(t) = f2(t) = u(t), find out f1(t)*f2(t): where (*) denotes convolution of f1(t) and f2(t). |
| A. | u(t) |
| B. | f2 u(t) |
| C. | tu(t) |
| D. | tδ(t) |
| Answer» D. tδ(t) | |
| 27. |
If x[n] * h[n] = h[n] * x[n], then the property is known as: |
| A. | non-linearity |
| B. | distributive |
| C. | associative |
| D. | commutative |
| Answer» E. | |
| 28. |
If x(t) = e-t u(t) and y(t) = e-3tu(t), then y(t) * x(t) will be |
| A. | (e-t – e-3t) u(t) |
| B. | \(\frac{e^{-3t}-e^{-t}}{2}u(t)\) |
| C. | \(\frac{e^{-t}-e^{-3t}}{2}u(t)\) |
| D. | \(\frac{e^{-t}+e^{-3t}}{2}u(t)\) |
| Answer» D. \(\frac{e^{-t}+e^{-3t}}{2}u(t)\) | |
| 29. |
A linear time-invariant system initially at rest, when subjected to a unit-step input, gives a response y(t) = te-t, t > 0. The transfer function of the system is: |
| A. | \(\frac{1}{{{{\left( {s + 1} \right)}^2}}}\) |
| B. | \(\frac{1}{{{{s\left( {s + 1} \right)}^2}}}\) |
| C. | \(\frac{s}{{{{\left( {s + 1} \right)}^2}}}\) |
| D. | \(\frac{1}{{s + 1}}\) |
| Answer» D. \(\frac{1}{{s + 1}}\) | |
| 30. |
A continuous-time LTI system with system function H(ω) has the following pole-zero plot. For this system, which of the alternatives is TRUE? |
| A. | |H(0 | > | ω |;| ω |>0 |
| B. | H(ω)| has multiple maxima, at ω1 and ω2 |
| C. | | H(0) | < |H(ω)| ; | ω | > 0 |
| D. | | H(ω) | = constant; -∞ < ω < ∞ |
| Answer» E. | |
| 31. |
Let the input be u and the output is y of a system, and the other parameters are real constants. Identify which among the following systems is not a linear system: |
| A. | \(\frac{d^3y}{dt^3}+a_1\frac{d^2y}{dt^2}+a_2\frac{dy}{dt}+a_3y = b_3u + b_2\frac{du}{dt}+ b_1\frac{d^2u}{dt^2} \) (with initial rest conditions) |
| B. | \(y\left( t \right) = \mathop \smallint \limits_0^t {e^{\alpha \left( {t - \tau } \right)}}\beta u\left( \tau \right)d\tau \) |
| C. | y = au + b, b ≠ 0 |
| D. | y = au |
| Answer» D. y = au | |
| 32. |
Directions: The below item consists of two statements, one labelled as the 'Statement (I)' and the other as 'Statement (II)'. Examine these two statements carefully and select the answers to these items using the codes given below:Statement (I): Sinusoidal signals are used as a basic function in electrical systems.Statement (II): The response of a linear system to a sinusoidal input function remains sinusoidal.Codes: |
| A. | Both Statement (I) and Statement (II) are individually true and Statement (II) is the correct explanation of Statement (I) |
| B. | Both Statement (I) and Statement (II) are individually true but Statement (II) is NOT the correct explanation of Statement (I) |
| C. | Statement (I) is true but Statement (II) is false |
| D. | Statement (I) is false but Statement (II) is true |
| Answer» B. Both Statement (I) and Statement (II) are individually true but Statement (II) is NOT the correct explanation of Statement (I) | |
| 33. |
Input \({\rm{x}}\left( {\rm{t}} \right)\) and output \({\rm{y}}\left( {\rm{t}} \right)\) of an LTI system are related by the differential equation \({\rm{y}"}\left( {\rm{t}} \right) - {\rm{y}'}\left( {\rm{t}} \right) - 6{\rm{y}}\left( {\rm{t}} \right){\rm{\;}} = {\rm{\;x}}\left( {\rm{t}} \right)\). If the system is neither causal nor stable, the impulse response h(t) of the system is |
| A. | \(\frac{1}{5}{{\rm{e}}^{3{\rm{t}}}}{\rm{u}}\left( { - {\rm{t}}} \right) + \frac{1}{5}{{\rm{e}}^{ - 2{\rm{t}}}}{\rm{u}}\left( { - {\rm{t}}} \right)\) |
| B. | \(- \frac{1}{5}{{\rm{e}}^{3{\rm{t}}}}{\rm{u}}\left( { - {\rm{t}}} \right) + \frac{1}{5}{{\rm{e}}^{ - 2{\rm{t}}}}{\rm{u}}\left( { - {\rm{t}}} \right)\) |
| C. | \({\rm{\;}}\frac{1}{5}{{\rm{e}}^{3{\rm{t}}}}{\rm{u}}\left( { - {\rm{t}}} \right) - \frac{1}{5}{{\rm{e}}^{ - 2{\rm{t}}}}{\rm{u}}\left( {\rm{t}} \right)\) |
| D. | \(- \frac{1}{5}{{\rm{e}}^{3{\rm{t}}}}{\rm{u}}\left( { - {\rm{t}}} \right) - \frac{1}{5}{{\rm{e}}^{ - 2{\rm{t}}}}{\rm{u}}\left( {\rm{t}} \right)\) |
| Answer» C. \({\rm{\;}}\frac{1}{5}{{\rm{e}}^{3{\rm{t}}}}{\rm{u}}\left( { - {\rm{t}}} \right) - \frac{1}{5}{{\rm{e}}^{ - 2{\rm{t}}}}{\rm{u}}\left( {\rm{t}} \right)\) | |
| 34. |
Consider a continuous-time system A, modelled by the equation y(t) = t x(t) + 4 and a discrete-time system B modelled by the equation y[n] = x2[n]. These systems are |
| A. | A-time invariant and B-time invariant |
| B. | A-time varying and B-time invariant |
| C. | A-time invariant and B-time varying |
| D. | A-time varying and B-time varying |
| Answer» C. A-time invariant and B-time varying | |
| 35. |
Determine the fundamental period of a signal \(x\left( t \right) = \cos \frac{\pi }{3}t + \sin \frac{\pi }{4}t\) |
| A. | 8 |
| B. | 48 |
| C. | 6 |
| D. | 24 |
| Answer» E. | |
| 36. |
Consider the following statements for continuous-time linear time invariant (LTI) systems.I. There is no bounded input bounded output (BIBO) stable system with a pole in the right half of the complex plane.II. There is no causal and BIBO stable system with a pole in the right half of the complex plane.Which one among the following is correct? |
| A. | Both I and II are true |
| B. | Both I and II are not true |
| C. | Only I is true |
| D. | Only II is true |
| Answer» E. | |
| 37. |
A discrete time signal, which is both linear and time invariant has an impulse response is u[n]. What is the response of the system for an input δ[n - 4]? |
| A. | u[n - 2] |
| B. | u[n - 4] |
| C. | u[n + 2] |
| D. | u[n + 4] |
| Answer» C. u[n + 2] | |
| 38. |
Linear time-invariant systems must satisfy |
| A. | additivity and time dependent constants only |
| B. | symmetry and time dependent constants Only |
| C. | additivity, homogeneity (symmetry) and time dependent-constants |
| D. | additivity only |
| Answer» D. additivity only | |
| 39. |
Any system that does not obey the superposition principle is said to be a ________ system. |
| A. | non-linear |
| B. | linear |
| C. | non-classical |
| D. | classical |
| Answer» B. linear | |
| 40. |
Given two continuous time signals x(t) = e-t and y(t) = e-2t which exist for t > 0. The convolution z(t) = x(t) * y(t) is: |
| A. | e-t – e-2t |
| B. | e-t – e2 |
| C. | e-t + e2t |
| D. | e-t + e-2t |
| Answer» B. e-t – e2 | |
| 41. |
Consider a single input single output discrete-time system with x[n] as input and y[n] as output. Where the two are related as\(y\left[ n \right] = \left\{ {\begin{array}{*{20}{c}} {\;n\left| {x\left[ n \right]} \right|,\;}\\ {x\left[ n \right] - x\left[ {n - 1} \right],} \end{array}} \right.\begin{array}{*{20}{c}} {\;for\;0 \le n \le 10}\\ {otherwise.} \end{array}\)Which one of the following statements is true about the system? |
| A. | It is casual and stable |
| B. | It is causal but not stable |
| C. | It is not causal but stable |
| D. | It is neither causal nor stable |
| Answer» B. It is causal but not stable | |
| 42. |
An LTI system is causal if and only if |
| A. | h(t) = 0 for t < 0 |
| B. | h(t) is finite for 0 < t < ∞ |
| C. | h(t) is finite for t < 0 |
| D. | h(t) is non-zero for all t |
| Answer» B. h(t) is finite for 0 < t < ∞ | |
| 43. |
Consider a continuous-time system with input x(t) and output y(t) given byy(t) = x(t)cos(t) This system is |
| A. | linear and time-invariant |
| B. | non-linear and time-invariant |
| C. | linear and time-varying |
| D. | non – linear and time-varying |
| Answer» D. non – linear and time-varying | |
| 44. |
Identify the linear system (s) from the following list:1. y(t) = x(t2)2. y(t) = x2(t)3. y(t) = A x(t) + B4. y(t) = \({e^{x\left( t \right)}}\) |
| A. | 2 and 3 |
| B. | 3 and 4 |
| C. | 1 only |
| D. | 1 and 3 |
| Answer» D. 1 and 3 | |
| 45. |
A input function in any transmission is said to be transmitted without distortion if the output signal r(t) is defined as: |
| A. | r(t) = 1 / f(t - d) |
| B. | r(t) = f(t + d) |
| C. | r(t) = f(t - d) |
| D. | r(t) = K f(t - d) |
| Answer» E. | |
| 46. |
A LTI system described by the following differential equation, where x(t) is the input to system and y(t) is output of systemy'(t) + 3y(t) = x(t)When y (0) = 2, the output y (t) for an unit step input is |
| A. | \(\left( {\frac{1}{3}{e^{ - t}} + \frac{5}{3}{e^{ - 3t}}} \right)u\left( t \right)\) |
| B. | \(\left( {\frac{1}{4}{e^{ - t}} + \frac{3}{4}{e^{ - 2t}}} \right)u\left( t \right)\) |
| C. | \(\left( {\frac{1}{3} + \frac{5}{3}{e^{ - 3t}}} \right)u\left( t \right)\) |
| D. | \(\left( {\frac{1}{4} + \frac{3}{4}{e^{ - 2t}}} \right)u\left( t \right)\) |
| Answer» D. \(\left( {\frac{1}{4} + \frac{3}{4}{e^{ - 2t}}} \right)u\left( t \right)\) | |
| 47. |
Determine the response of LTI system \(h\left[ n \right] = \left\{ {1,\;\begin{array}{*{20}{c}} 2\\ \uparrow \end{array},\;1,\; - 1} \right\}\) if input signal is \(x\left( n \right) = \left\{ {\begin{array}{*{20}{c}} 1\\ \uparrow \end{array},\;2,\;3,\;1} \right\}\) |
| A. | \(y\left[ n \right] = \left\{ {\begin{array}{*{20}{c}} 1\\ \uparrow \end{array},\;4,\;8,\;8,\;3,\; - 2,\; - 1} \right\}\) |
| B. | \(y\left[ n \right] = \left\{ {1,\;\begin{array}{*{20}{c}} 4\\ \uparrow \end{array},\;8,\;8,\;3,\; - 2,\; - 1} \right\}\) |
| C. | \(y\left[ n \right] = \left\{ {1,\;4,\;\begin{array}{*{20}{c}} 8\\ \uparrow \end{array},\;8,\;8,\;3,\; - 2,\; - 1} \right\}\) |
| D. | \(y\left[ n \right] = \left\{ {1,\;4,\;8,\;\begin{array}{*{20}{c}} 8\\ \uparrow \end{array},\;3,\; - 2,\; - 1} \right\}\) |
| Answer» C. \(y\left[ n \right] = \left\{ {1,\;4,\;\begin{array}{*{20}{c}} 8\\ \uparrow \end{array},\;8,\;8,\;3,\; - 2,\; - 1} \right\}\) | |
| 48. |
For the linear time invariant systems that are Bounded Input Bounded stable, which one of the following statement is TRUE? |
| A. | The impulse response will be integral, but may not be absolutely integrable |
| B. | The unit impulse response will have finite support |
| C. | The unit step response will be absolutely integrable |
| D. | The unit step response will be bounded |
| Answer» E. | |
| 49. |
Consider a system.The system is characterized as: |
| A. | Causal, Memoryless and BIBO stable |
| B. | Memoryless, and BIBO unstable |
| C. | Linear and time-invariant system |
| D. | Memoryless, time-invariant system |
| Answer» B. Memoryless, and BIBO unstable | |
| 50. |
Consider the discrete-time signal\(x\left( n \right) = {\left( {\frac{1}{3}} \right)^n}u\left( n \right),where\;u\left( n \right) = \left\{ {\begin{array}{*{20}{c}}{1,}&{n \ge 0}\\{0,}&{n < 0}\end{array}} \right.\) Define the signal y(n) ⇒ as y(n) = x(-n), -∞ < n < ∞Then, \(\mathop \sum \limits_{n = - \infty }^\infty y\left( n \right)\) equals |
| A. | \(- \frac{2}{3}\) |
| B. | \(\frac{2}{3}\) |
| C. | \(\frac{3}{2}\) |
| D. | 3 |
| Answer» D. 3 | |