MCQOPTIONS
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MCQOPTIONS
This section includes 150 Mcqs, each offering curated multiple-choice questions to sharpen your Control Systems knowledge and support exam preparation. Choose a topic below to get started.
| 1. |
For a right hand sequence, the ROC is entire z-plane. |
| A. | True |
| B. | False |
| Answer» C. | |
| 2. |
Find the Z-transform of u(-n). |
| A. | \(\frac{1}{1-z}\) |
| B. | \(\frac{1}{1+z}\) |
| C. | \(\frac{z}{1-z}\) |
| D. | \(\frac{z}{1+z}\) |
| Answer» B. \(\frac{1}{1+z}\) | |
| 3. |
Find the Z-transform of x(n) = a|n|; |a|<1.a) \(\frac{z}{z-a} – \frac{z}{z-(1/a)}\) b) \(\frac{z}{z-(1/a)} – \frac{z}{z-a}\) c) \(\frac{z}{z-a} + \frac{z}{z-(1/a)}\) d) \(\frac{1}{z-a} – \frac{1}{z-(1/ |
| A. | \(\frac{z}{z-a} – \frac{z}{z-(1/a)}\) |
| B. | \(\frac{z}{z-(1/a)} – \frac{z}{z-a}\) |
| C. | \(\frac{z}{z-a} + \frac{z}{z-(1/a)}\) |
| D. | \(\frac{1}{z-a} – \frac{1}{z-(1/a)}\) |
| Answer» B. \(\frac{z}{z-(1/a)} – \frac{z}{z-a}\) | |
| 4. |
Find the Z-transform of y(n) = x(n+2)u(n). |
| A. | z2 X(Z) – z2 x(0) – zx(1) |
| B. | z2 X(Z) + z2 x(0) – zx(1) |
| C. | z2 X(Z) – z2 x(0) + zx(1) |
| D. | z2 X(Z) + z2 x(0) + zx(1) |
| Answer» B. z2 X(Z) + z2 x(0) – zx(1) | |
| 5. |
x(n) = an u(n) and x(n) = -an u(-n-1) have the same X(Z) and ROC. |
| A. | True |
| B. | False |
| Answer» C. | |
| 6. |
For causal sequences, the ROC is the exterior of a circle of radius r. |
| A. | True |
| B. | False |
| Answer» B. False | |
| 7. |
Find the Z-transform of cosωn u(n). |
| A. | \(\frac{z(z+cosω)}{z^2-2z cosω+1}\) |
| B. | \(\frac{z(z-cosω)}{z^2-2z cosω+1}\) |
| C. | \(\frac{z(z-cosω)}{z^2+2z cosω+1}\) |
| D. | \(\frac{z(z+cosω)}{z^2+2z cosω+1}\) |
| Answer» C. \(\frac{z(z-cosω)}{z^2+2z cosω+1}\) | |
| 8. |
Find the Z-transform of an u(n);a>0. |
| A. | \(\frac{z}{z-a}\) |
| B. | \(\frac{z}{z+a}\) |
| C. | \(\frac{1}{1-az}\) |
| D. | \(\frac{1}{1+az}\) |
| Answer» B. \(\frac{z}{z+a}\) | |
| 9. |
Find the Z-transform of δ(n+3). |
| A. | z |
| B. | z2 |
| C. | 1 |
| D. | z3 |
| Answer» E. | |
| 10. |
When do DTFT and ZT are equal? |
| A. | When σ = 0 |
| B. | When r = 1 |
| C. | When σ = 1 |
| D. | When r = 0 |
| Answer» C. When σ = 1 | |
| 11. |
H (z) is discrete rational transfer function. To ensure that both H(z) and its inverse are stable: |
| A. | Poles must be inside the unit circle and zeros must be outside the unit circle |
| B. | Poles and zeroes must be inside the unit circle |
| C. | Poles and zeroes must be outside the unit circle |
| D. | Poles must be outside the unit circle and zeros must be inside the unit circle |
| Answer» C. Poles and zeroes must be outside the unit circle | |
| 12. |
A sequence x (n) with the z-transform X (z) = Z4 + Z2 – 2z + 2 – 3Z-4 is applied to an input to a linear time invariant system with the impulse response h (n) = 2δ (n-3). The output at n = 4 will be: |
| A. | -6 |
| B. | Zero |
| C. | 2 |
| D. | -4 |
| Answer» C. 2 | |
| 13. |
Which one of the following is the correct statement? The region of convergence of z-transform of x[n] consists of the values of z for which x[n] is: |
| A. | Absolutely integrable |
| B. | Absolutely summable |
| C. | Unity |
| D. | <1 |
| Answer» C. Unity | |
| 14. |
The ROC of z-transform of the discrete time sequence x(n) = is: |
| A. | 1/3>|z|<1/2 |
| B. | |z|>1/2 |
| C. | |z|<1/3 |
| D. | 2>|z|<3 |
| Answer» B. |z|>1/2 | |
| 15. |
Two sequences x1 (n) and x2 (n) are related by x2 (n) = x1 (- n). In the z- domain, their ROC’s are |
| A. | The same |
| B. | Reciprocal of each other |
| C. | Negative of each other |
| D. | Complements of each other |
| Answer» C. Negative of each other | |
| 16. |
The frequency of a continuous time signal x (t) changes on transformation from x (t) to x (α t), α > 0 by a factor |
| A. | α |
| B. | 1/α |
| C. | α2 |
| D. | α |
| Answer» B. 1/α | |
| 17. |
The discrete-time signal x (n) = (-1)n is periodic with fundamental period |
| A. | 6 |
| B. | 4 |
| C. | 2 |
| D. | 0 |
| Answer» D. 0 | |
| 18. |
What is the ROC of a causal infinite length sequence? |
| A. | |z|<r1 |
| B. | |z|>r1 |
| C. | r2<|z|<r1 |
| D. | None of the mentioned |
| Answer» C. r2<|z|<r1 | |
| 19. |
Is the discrete time LTI system with impulse response h(n)=an(n) (|a| < 1) BIBO stable? |
| A. | True |
| B. | False |
| Answer» B. False | |
| 20. |
The ROC of z-transform of any signal cannot contain poles. |
| A. | True |
| B. | False |
| Answer» B. False | |
| 21. |
The z-transform of a sequence x(n) which is given as X(z)=\(\sum_{n=-\infty}^{\infty}x(n)z^{-n}\) is known as _____________ |
| A. | Uni-lateral Z-transform |
| B. | Bi-lateral Z-transform |
| C. | Tri-lateral Z-transform |
| D. | None of the mentioned |
| Answer» C. Tri-lateral Z-transform | |
| 22. |
What is the ROC of z-transform of an two sided infinite sequence? |
| A. | |z|>r1 |
| B. | |z|<r1 |
| C. | r2<|z|<r1 |
| D. | None of the mentioned |
| Answer» D. None of the mentioned | |
| 23. |
What is the ROC of z-transform of finite duration anti-causal sequence? |
| A. | z=0 |
| B. | z=∞ |
| C. | Entire z-plane, except at z=0 |
| D. | Entire z-plane, except at z=∞ |
| Answer» E. | |
| 24. |
What is the ROC of the z-transform of the signal x(n)= anu(n)+bnu(-n-1)? |
| A. | |a|<|z|<|b| |
| B. | |a|>|z|>|b| |
| C. | |a|>|z|<|b| |
| D. | |a|<|z|>|b| |
| Answer» B. |a|>|z|>|b| | |
| 25. |
What is the z-transform of the signal x(n) = -αnu(-n-1)? |
| A. | \(\frac{1}{1-\alpha z^{-1}}\);ROC |z|<|α| |
| B. | \(-\frac{1}{1+\alpha z^{-1}}\);ROC |z|<|α| |
| C. | \(-\frac{1}{1-\alpha z^{-1}}\);ROC |z|>|α| |
| D. | \(-\frac{1}{1-\alpha z^{-1}}\);ROC |z|<|α| |
| Answer» E. | |
| 26. |
Which of the following series has an ROC as mentioned below? |
| A. | α-nu(n) |
| B. | αnu(n) |
| C. | α-nu(-n) |
| D. | αnu(n) |
| Answer» C. α-nu(-n) | |
| 27. |
What is the z-transform of the signal x(n)=(0.5)nu(n)? |
| A. | \(\frac{1}{1-0.5z^{-1}};ROC |z|>0.5\) |
| B. | \(\frac{1}{1-0.5z^{-1}};ROC |z|<0.5\) |
| C. | \(\frac{1}{1+0.5z^{-1}};ROC |z|>0.5\) |
| D. | \(\frac{1}{1+0.5z^{-1}};ROC |z|<0.5\) |
| Answer» B. \(\frac{1}{1-0.5z^{-1}};ROC |z|<0.5\) | |
| 28. |
What is the ROC of the signal x(n)=δ(n-k), k>0? |
| A. | z=0 |
| B. | z=∞ |
| C. | Entire z-plane, except at z=0 |
| D. | Entire z-plane, except at z=∞ |
| Answer» D. Entire z-plane, except at z=∞ | |
| 29. |
What is the z-transform of the following finite duration signal? |
| A. | 2 + 4z + 5z2 + 7z3 + z4 |
| B. | 2 + 4z + 5z2 + 7z3 + z5 |
| C. | 2 + 4z-1 + 5z-2 + 7z-3 + z-5 |
| D. | 2z2 + 4z + 5 +7z-1 + z-3 |
| Answer» E. | |
| 30. |
The Z-Transform X(z) of a discrete time signal x(n) is defined as ____________ |
| A. | \(\sum_{n=-\infty}^{\infty}x(n)z^n\) |
| B. | \(\sum_{n=-\infty}^{\infty}x(n)z^{-n}\) |
| C. | \(\sum_{n=0}^{\infty}x(n)z^n\) |
| D. | None of the mentioned |
| Answer» C. \(\sum_{n=0}^{\infty}x(n)z^n\) | |
| 31. |
Let Laplace transform of f(t) is f̅ (s), then |
| A. | L[f(ta) u(t - a)] = e-as f̅ (s) |
| B. | L[f(t + a) u(t + a)] = e-as f̅ (s) |
| C. | L[f(t - a) u(t - a)] = e-as f̅ (s) where\(u(t-a)= \begin{cases} 0 ,~~~ta\\ \end{cases}\) |
| D. | L[f(t - a) / u(t - a)] = e-as f̅ (s) where\(u(t-a)= \begin{cases} 0 ,~~~ta\\ \end{cases}\) |
| Answer» D. L[f(t - a) / u(t - a)] = e-as f̅ (s) where\(u(t-a)= \begin{cases} 0 ,~~~ta\\ \end{cases}\) | |
| 32. |
Find the final value of the signal y(t) whose unilateral Laplace transform is:\(Y\left( s \right) = \frac{{7s + 9}}{{s\left( {s + 5} \right)}}\) |
| A. | \(\frac{7}{9}\) |
| B. | \(\frac{7}{3}\) |
| C. | \(\frac{9}{5}\) |
| D. | \(\frac{9}{7}\) |
| Answer» D. \(\frac{9}{7}\) | |
| 33. |
An impulse function consists of |
| A. | entire frequency range with same relative phase |
| B. | infinite bandwidth with linear phase variation |
| C. | pure DC |
| D. | large DC with weak harmonics |
| Answer» B. infinite bandwidth with linear phase variation | |
| 34. |
A signal has \(FT\;x\left( t \right)\mathop \leftrightarrow \limits^{FT} X\left( {j\omega } \right) = {e^{ - j\omega }}\left| \omega \right|{e^{ - 2\left| \omega \right|}}\) Without determining x(t), use the scaling property to find the FT representation of y(t) = x( - 2t). |
| A. | \(Y\left( {j\omega } \right) = \left( {\frac{1}{2}} \right){e^{\frac{{j\omega }}{2}}}\left| {\frac{\omega }{2}} \right|{e^{\left| \omega \right|}}\) |
| B. | \(Y\left( {j\omega } \right) = \left( {\frac{1}{2}} \right){e^{\frac{{j\omega }}{2}}}\left| {\frac{\omega }{2}} \right|{e^{2\left| \omega \right|}}\) |
| C. | \(Y\left( {j\omega } \right) = \left( {\frac{1}{2}} \right){e^{\frac{{j\omega }}{2}}}\left| {\frac{\omega }{2}} \right|{e^{ - 2\left| \omega \right|}}\) |
| D. | \(Y\left( {j\omega } \right) = \left( {\frac{1}{2}} \right){e^{\frac{{j\omega }}{2}}}\left| {\frac{\omega }{2}} \right|{e^{ - \left| \omega \right|}}\) |
| Answer» E. | |
| 35. |
Consider the following statements:1. The Laplace transform of the unit impulse function is s × Laplace transform of the unit ramp function.2. The impulse function is a time derivative of the ramp function.3. The Laplace transform of the unit impulse function is s × Laplace transform of the unit step function4. The impulse function is a time derivative of the unit step function.Which of the above statements are correct ? |
| A. | 1 and 2 only |
| B. | 3 and 4 only |
| C. | 2 and 3 only |
| D. | 1, 2, 3 and 4 |
| Answer» C. 2 and 3 only | |
| 36. |
If X(ω) = δ(ω - ω0) then x(t) is |
| A. | \({e^{ - j{\omega _0}t}}\) |
| B. | \(\delta (t)\) |
| C. | \(\frac{1}{{2\pi }}{e^{j{\omega _0}t}}\) |
| D. | 1 |
| Answer» D. 1 | |
| 37. |
Laplace transform of t cos (at) is |
| A. | \(\frac{{{s^2} + {a^2}}}{{{{\left( {{a^2} - {a^2}} \right)}^2}}}\) |
| B. | \(\frac{s}{{{{\left( {{s^2} - {a^2}} \right)}^2}}}\) |
| C. | \(\frac{{{s^2} - {a^2}}}{{{{\left( {{s^2} + {a^2}} \right)}^2}}}\) |
| D. | \(\frac{s}{{{{\left( {{s^2} + {a^2}} \right)}^2}}}\) |
| Answer» D. \(\frac{s}{{{{\left( {{s^2} + {a^2}} \right)}^2}}}\) | |
| 38. |
Let F(ω) be the Fourier Transform of a function f(t). The F(0) is |
| A. | \(\int\limits_{ - \infty }^\infty {f\left( t \right)} dt\) |
| B. | \(\int\limits_{ - \infty }^\infty {{{\left| {f\left( t \right)} \right|}^2}dt}\) |
| C. | \(\int\limits_{ - \infty }^\infty {{{\left| {t \cdot f\left( t \right)} \right|}^2}dt}\) |
| D. | \(\int\limits_{ - \infty }^\infty {t \cdot f\left( t \right)dt}\) |
| Answer» B. \(\int\limits_{ - \infty }^\infty {{{\left| {f\left( t \right)} \right|}^2}dt}\) | |
| 39. |
Laplace transform of e-at u(t), is ______, where u(t) is unit step. |
| A. | \(\frac{1}{{s + a}}\) |
| B. | \(\frac{1}{s}\) |
| C. | \(\frac{1}{{s\left( {s + a} \right)}}\) |
| D. | \(\frac{s}{{s + a\;}}\) |
| Answer» B. \(\frac{1}{s}\) | |
| 40. |
Laplace Transform is used in |
| A. | Fourier Series |
| B. | Probability Distribution |
| C. | Complex Numbers |
| D. | None of these |
| Answer» C. Complex Numbers | |
| 41. |
Laplace transform of \(\cos \left( {{\rm{\omega t}}} \right){\rm{is}}\frac{{\rm{s}}}{{{{\rm{s}}^2} + {{\rm{\omega }}^2}}}\). The laplace transform of e-2t cos(4t) is |
| A. | \(\frac{{{\rm{s}} - 2}}{{{{\left( {{\rm{s}} - 2} \right)}^2} + 16}}\) |
| B. | \(\frac{{{\rm{s}} + 2}}{{{{\left( {{\rm{s}} - 2} \right)}^2} + 16}}\) |
| C. | \(\frac{{{\rm{s}} - 2}}{{{{\left( {{\rm{s}} + 2} \right)}^2} + 16}}\) |
| D. | \(\frac{{{\rm{s}} + 2}}{{{{\left( {{\rm{s}} + 2} \right)}^2} + 16}}\) |
| Answer» E. | |
| 42. |
If the waveform, shown in the following figure, corresponds to the second derivative of a given function f(t), then the Fourier transform of f(t) is |
| A. | 1 + sin ω |
| B. | 1 + cos ω |
| C. | \(\frac{{2\left( {1 - \cos \omega } \right)}}{{{\omega ^2}}}\) |
| D. | \(\frac{{2\left( {1 + \cos \omega } \right)}}{{{\omega ^2}}}\) |
| Answer» D. \(\frac{{2\left( {1 + \cos \omega } \right)}}{{{\omega ^2}}}\) | |
| 43. |
Fourier transform of the unit impulse δ(t) is |
| A. | π |
| B. | 1 |
| C. | 0 |
| D. | δ(ω) |
| Answer» C. 0 | |
| 44. |
A system with zero initial conditions has the closed loop transfer function T(s) = (s2 + 4)/[(s + 1)(s + 4)]. At which frequency, will the system output be zero? |
| A. | 0.5 rad/sec |
| B. | 1 rad/sec |
| C. | 2 rad/sec |
| D. | 4 rad/sec |
| Answer» D. 4 rad/sec | |
| 45. |
Match the following Lists:List - I List – IIa) i) b) ii) c) iii) d) iv) Correct codes are:Code: |
| A. | a-iii, b-iv, c-ii, d-i |
| B. | a-ii, b-i, c-iii, d-iv |
| C. | a-ii, b-i, c-iv, d-iii |
| D. | a-iv, b-iii, c-ii, d-i |
| Answer» D. a-iv, b-iii, c-ii, d-i | |
| 46. |
Laplace transform of 3t4 is |
| A. | \(\frac{{18}}{{{s^4}}}\) |
| B. | \(\frac{{24}}{{{s^4}}}\) |
| C. | \(\frac{{72}}{{{s^5}}}\) |
| D. | \(\frac{{12}}{{{s^5}}}\) |
| Answer» D. \(\frac{{12}}{{{s^5}}}\) | |
| 47. |
If Laplace transform \(Lf\left( t \right) = \log \left( {\frac{{s + a}}{{s + b}}} \right)\), then f(t) equals |
| A. | \(\frac{1}{t}\left( {{e^{ - bt}} - {e^{ - at}}} \right)\) |
| B. | \(\frac{1}{t}\left( {{e^{bt}} - {e^{at}}} \right)\) |
| C. | \({e^{ - bt}} - {e^{ - at}}\) |
| D. | \({e^{bt}} - {e^{at}}\) |
| Answer» B. \(\frac{1}{t}\left( {{e^{bt}} - {e^{at}}} \right)\) | |
| 48. |
If u (t), r (t) denote the unit step and unit ramp functions respectively and u (t) * r (t) their convolution, then the function u (t + 1) * r (t -2) is given by |
| A. | ½ (t -1) u (t -1) |
| B. | ½ (t -1) u (t -2) |
| C. | ½ (t -1)2 u (t-1) |
| D. | None of above |
| Answer» D. None of above | |
| 49. |
Laplace transform of the function v(t) shown in the figure is: |
| A. | \({s}^{2}{[1 - e^{s}]}\) |
| B. | \({s}^{2}{[1 - e^{- s}]}\) |
| C. | \(\frac{1}{{s}^{2}} {[1 - e^{s}]}\) |
| D. | \(\frac{1}{{s}^{2}} {[1 - e^{ - s}]}\) |
| Answer» E. | |
| 50. |
Match the two lists and choose the correct answer from the code given belowList I(Function)List II(Laplace transform)(a) tx(t)(i)∞(b)\(\frac{x(t)}{t}\)(ii)\(\mathop {\lim }\limits_{s \to \infty} \left[ {sX\left( s \right)} \right]\)(c) x(0-)(iii)\(\mathop {\lim }\limits_{s \to 0} \left[ {sX\left( s \right)} \right]\)(d) x(∞)(iv)\(-\frac{dx(s)}{ds}\) |
| A. | (a) – (i), (b) – (ii), (c) – (iii), (d) – (iv) |
| B. | (a) – (iv), (b) – (i), (c) – (ii), (d) – (iii) |
| C. | (a) – (iv), (b) – (i), (c) – (iii), (d) – (ii) |
| D. | (a) – (i), (b) – (iv), (c) – (ii), (d) – (iii) |
| Answer» C. (a) – (iv), (b) – (i), (c) – (iii), (d) – (ii) | |