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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.
| 51. |
Fourier transform of a function f(at) is given by |
| A. | a F(ω) |
| B. | \(\frac{2}{a} F(\omega)\) |
| C. | \(\frac{1}{|a|} ~F(\frac{\omega}{a})\) |
| D. | None of these |
| Answer» D. None of these | |
| 52. |
If G(t) is Hilbert transform of g(t), then G(t) is: |
| A. | \( - \frac{1}{\pi }\mathop \smallint \limits_{ - \infty }^\infty \frac{{ - g\left( \tau \right)}}{{t - \tau }}d\tau \) |
| B. | \( - \frac{1}{\pi }\mathop \smallint \limits_{ - \infty }^\infty \frac{{g\left( \tau \right)}}{{t - \tau }}d\tau \) |
| C. | \( - \frac{1}{\pi }\mathop \smallint \limits_{ - \infty }^0 \frac{{ - g\left( \tau \right)}}{{t - \tau }}d\tau \) |
| D. | \(\frac{1}{\pi }\mathop \smallint \limits_0^\infty \frac{{g\left( \tau \right)}}{{t - \tau }}d\tau \) |
| Answer» B. \( - \frac{1}{\pi }\mathop \smallint \limits_{ - \infty }^\infty \frac{{g\left( \tau \right)}}{{t - \tau }}d\tau \) | |
| 53. |
Inverse Laplace transform of F(s) = (s + 2)/s(s + 3)(s + 4) would be |
| A. | (1/6) + (1/3e-3t) + (1/2e4t) |
| B. | (1/6) – (1/3e-3t) + (1/2e-4t) |
| C. | (1-3e-3t) + (1/2e4t) |
| D. | (1/6) + (1/3e-3t) – (1/2e-4t) |
| Answer» E. | |
| 54. |
Fourier transform of a unit step signal is |
| A. | π δ(ω) |
| B. | \(\frac{1}{j\omega}\) |
| C. | \(\pi ~\delta (\omega)+\frac{1}{j\omega}\) |
| D. | \(\pi ~\delta (\omega)-\frac{1}{j\omega}\) |
| Answer» D. \(\pi ~\delta (\omega)-\frac{1}{j\omega}\) | |
| 55. |
If the Laplace transform of eωt is \(\dfrac{1}{s-\omega}\), the Laplace transform of t cosh t is |
| A. | \(\frac{1+s^2}{\left( s^2-1\right)^2}\) |
| B. | \(\frac{st}{\left( s^2-1\right)}\) |
| C. | \(\frac{1-s^2}{\left( s^2-1\right)^2}\) |
| D. | \(\frac{1+s^2}{1-s^2}\) |
| Answer» B. \(\frac{st}{\left( s^2-1\right)}\) | |
| 56. |
If f(t) is a function defined for all t ≥ 0, its Laplace transform F(s) is defined as |
| A. | \(\mathop \smallint \nolimits_0^\infty {e^{st}}f\left( t \right)dt\) |
| B. | \(\mathop \smallint \nolimits_0^\infty {e^{ - st}}f\left( t \right)dt\) |
| C. | \(\mathop \smallint \nolimits_0^\infty {e^{ist}}f\left( t \right)dt\) |
| D. | \(\mathop \smallint \nolimits_0^\infty {e^{ - ist}}f\left( t \right)dt\) |
| Answer» C. \(\mathop \smallint \nolimits_0^\infty {e^{ist}}f\left( t \right)dt\) | |
| 57. |
Laplace transform of (t sin ωt) is: |
| A. | \(\frac{{\omega \;s}}{{{{\left( {{s^2} + {\omega ^2}} \right)}^2}}}\) |
| B. | \(\frac{{2\omega \;s}}{{\left( {{s^2} + {\omega ^2}} \right)}}\) |
| C. | \(\frac{{2\omega s}}{{{{\left( {{s^2} + {\omega ^2}} \right)}^2}}}\) |
| D. | \(\frac{{\omega s}}{{\left( {{s^2} + {\omega ^2}} \right)}}\) |
| Answer» D. \(\frac{{\omega s}}{{\left( {{s^2} + {\omega ^2}} \right)}}\) | |
| 58. |
Let f(t) = sin2 t, find the Laplace transform of f(t) |
| A. | \(\frac{2}{{{s^2} \;+ \;4}}\) |
| B. | \(\frac{2}{{s\left( {{s^2}\; + \;4} \right)}}\) |
| C. | \(\frac{{2s}}{{{s^2}\; +\; 4}}\) |
| D. | \(\frac{2}{{s\left( {{s^2} \;- \;4} \right)}}\) |
| Answer» C. \(\frac{{2s}}{{{s^2}\; +\; 4}}\) | |
| 59. |
Identify the following series\(f\left( x \right) = f\left( 0 \right) + xf'\left( 0 \right) + \frac{{{x^2}}}{{2!}}f\left( 0 \right) + \frac{{{x^3}}}{{3!}}f'''\left( 0 \right) + \ldots \infty \;\) |
| A. | Fourier’s series |
| B. | Maclurin’s series |
| C. | Taylor’s series |
| D. | Neumann’s Series |
| Answer» C. Taylor’s series | |
| 60. |
An ideal low-pass filter has a cutoff frequency of 100 Hz. If the input to the filter in volts is \(30 \sqrt{2} ~sin (1256 t)\) the magnitude of the output of the filter will be |
| A. | 0 V |
| B. | 20 V |
| C. | 100 V |
| D. | 200 V |
| Answer» B. 20 V | |
| 61. |
If x(t) = tn u(t), then the Laplace transform of x(t) is: |
| A. | \(\frac{{n!}}{{{s^{n + 1}}}}\) |
| B. | \(\frac{{n!}}{{{s^n}}}\) |
| C. | \(\frac{n}{{{s^{n + 1}}}}\) |
| D. | \(\frac{{n!}}{{{s^{n - 1}}}}\) |
| Answer» B. \(\frac{{n!}}{{{s^n}}}\) | |
| 62. |
Fourier transform of a discrete and aperiodic sequence is: |
| A. | Continuous and aperiodic |
| B. | Continuous and periodic |
| C. | Discontinuous and periodic |
| D. | Discontinuous and aperiodic |
| Answer» C. Discontinuous and periodic | |
| 63. |
Inverse Laplace transform of \(\frac{1}{{s + a}}\) is: |
| A. | e-at |
| B. | eat |
| C. | \(e^{\frac{1}{a}t}\) |
| D. | seat |
| Answer» B. eat | |
| 64. |
Given \(f\left( t \right)={L^{ - 1}}\left[ {\frac{{3s + 1}}{{{s^3} + 4{s^2} + s\left( {k - 3} \right)}}} \right]\) if \(\mathop {\lim }\limits_{t \to \infty } f\left( t \right) = 1\), then the value of k is |
| A. | 1 |
| B. | 2 |
| C. | 3 |
| D. | 4 |
| Answer» E. | |
| 65. |
If L-1 [f(s)] = f(t), then L-1 [f(s – a)] is |
| A. | eat L-1 [f(s)] |
| B. | e-at L-1 [f(s)] |
| C. | L-1 [f(s)] |
| D. | L-1 [f’(s)] |
| Answer» B. e-at L-1 [f(s)] | |
| 66. |
Determine transfer function if the impulse response is e-2t. |
| A. | 1 / (s + 2) |
| B. | 1 / (s - 2) |
| C. | 1 / (s + 2)2 |
| D. | 1 / (s - 2)2 |
| Answer» B. 1 / (s - 2) | |
| 67. |
Let \(x\left( n \right)={{\left( \frac{1}{2} \right)}^{n}}u\left( n \right),~y\left( n \right)={{x}^{2}}n\) and Y(ejω) to be the Fourier transform of y(n) then Y(ej0) |
| A. | \(\frac{1}{4}\) |
| B. | 2 |
| C. | 4 |
| D. | \(\frac{4}{3}\) |
| Answer» E. | |
| 68. |
If the Fourier transform of f(t) is F(ω) then Fourier transform of f (at) is: |
| A. | \(\frac{1}{{\left| a \right|}} \times F(\frac{\omega }{a})\) |
| B. | a F(ω) |
| C. | F(a ω) |
| D. | \(F (\frac{\omega }{a})\) |
| Answer» B. a F(ω) | |
| 69. |
Laplace transform of the function f(t) is given by \(F\left( s \right) = L\left\{ {f\left( t \right)} \right\} = \mathop \smallint \limits_0^\infty f\left( t \right){e^{ - st}}dt\). Laplace transform of the function shown below is given by |
| A. | \(\frac{{1 - {e^{ - 2s}}}}{s}\) |
| B. | \(\frac{{1 - {e^{ - s}}}}{{2s}}\) |
| C. | \(\frac{{2 - 2{e^{ - s}}}}{s}\) |
| D. | \(\frac{{1 - 2{e^{ - s}}}}{s}\) |
| Answer» D. \(\frac{{1 - 2{e^{ - s}}}}{s}\) | |
| 70. |
A real-valued signal |
| A. | x(t + 4) |
| B. | x(t - 4) |
| C. | x(t + 2) |
| D. | x(t - 2) |
| Answer» E. | |
| 71. |
Let z(t) = x(t) * y(t), where “ * ” denotes convolution. Let c be a positive real-valued constant. Choose the correct expression for z(ct). |
| A. | c . x(ct) * y(ct) |
| B. | x(ct) * y(ct) |
| C. | c . x(t) * y(ct) |
| D. | c . x(ct) * y(t) |
| Answer» B. x(ct) * y(ct) | |
| 72. |
If F(s) is the Laplace transform of function f(t), then Laplace transform of \(\mathop \smallint \limits_0^t f\left( \tau \right)d\tau\) is |
| A. | \(\frac{1}{s}F\left( s \right)\) |
| B. | \(\frac{1}{s}F\left( s \right) - f\left( 0 \right)\) |
| C. | \(sF\left( s \right)\;-\;f\left( 0 \right)\) |
| D. | \(\smallint F\left( s \right)ds\) |
| Answer» B. \(\frac{1}{s}F\left( s \right) - f\left( 0 \right)\) | |
| 73. |
Laplace transform of e-at f(t) is |
| A. | F(s)eat |
| B. | F(s - a) |
| C. | F(s + a) |
| D. | \(\frac{{F\left( s \right)}}{s} + a\) |
| Answer» D. \(\frac{{F\left( s \right)}}{s} + a\) | |
| 74. |
Lapalce transform is a tool for converting: |
| A. | amplitude domain equations to frequency domain equations |
| B. | phase domain equations to amplitude domain equations |
| C. | Time domain equations to frequency domain equations |
| D. | frequency domain equations to time domain equations |
| Answer» D. frequency domain equations to time domain equations | |
| 75. |
If x(t) is as shown in the figure, its Laplace transform is |
| A. | \(\frac{{2{e^{ + 5s}} + 2{e^{ - 5s}}}}{{{s^2}}}\) |
| B. | \(\frac{{2{e^{ + 5s}} - 4 + 2{e^{ - 5s}}}}{{{s^2}}}\) |
| C. | \(\frac{{2{e^{ + 5s}} - 2 + 2{e^{ - 5s}}}}{{{s^2}}}\) |
| D. | \(\frac{{2{e^{ + 5s}} + 4 - 2{e^{ - 5s}}}}{{{s^2}}}\) |
| Answer» C. \(\frac{{2{e^{ + 5s}} - 2 + 2{e^{ - 5s}}}}{{{s^2}}}\) | |
| 76. |
Let \(x\left( t \right) = rect\left( {t - \frac{1}{2}} \right)\) where rect(t) = 1 for \( - \frac{1}{2} \le t \le \frac{1}{2}\) and zero otherwise, then Fourier Transform of x(t) + x(-t) will be given by |
| A. | \(\sin c\left( {\frac{\omega }{2}} \right)\) |
| B. | \(2\sin c\left( {\frac{\omega }{2}} \right)\) |
| C. | \(2\sin c\left( {\frac{\omega }{2}} \right)\cos \left( {\frac{\omega }{2}} \right)\) |
| D. | \(2\sin c\left( {\frac{\omega }{2}} \right)\sin \left( {\frac{\omega }{2}} \right)\) |
| Answer» D. \(2\sin c\left( {\frac{\omega }{2}} \right)\sin \left( {\frac{\omega }{2}} \right)\) | |
| 77. |
If F(s) and G(s) are the Laplace transforms of f(t) and g(t), then their product F(s) . G(s) = H(s), where H(s) is the Laplace transform of h(t), is defined as |
| A. | (f . g) (t) |
| B. | \(\int\limits_0^t f(\tau)~g(t-\tau) d\tau \) |
| C. | Both (a) and (b) are correct |
| D. | f (t). g(t) |
| Answer» C. Both (a) and (b) are correct | |
| 78. |
Evaluate cos t δ(t – π) |
| A. | 0 |
| B. | -δ(t – π) |
| C. | -δ(t + π) |
| D. | δ(t + π) |
| Answer» C. -δ(t + π) | |
| 79. |
Laplace transform of a unity function is |
| A. | 1/s |
| B. | 1/s2 |
| C. | 1/s3 |
| D. | Zero |
| Answer» B. 1/s2 | |
| 80. |
For the given transfer function:\(G\left( s \right) = \frac{{Y\left( s \right)}}{{R\left( s \right)}} = \frac{1}{{{s^2} + 3s + 2}}\)the response y(t) for a step input r(t) = 5u(t) will be |
| A. | \(\left[ {\frac{5}{2} - 5{e^{ - t}} + \frac{5}{2}{e^{ - 2t}}} \right]u\left( t \right)\) |
| B. | \(\left[ {\frac{5}{2} - 5{e^{ - t}}} \right]u\left( t \right)\) |
| C. | \(\left[ {\frac{5}{2} + \frac{5}{2}{e^{ - 2t}}} \right]u\left( t \right)\) |
| D. | \(\left[ { - 5{e^{ - t}} + \frac{5}{2}{e^{ - 2t}}} \right]u\left( t \right)\) |
| Answer» B. \(\left[ {\frac{5}{2} - 5{e^{ - t}}} \right]u\left( t \right)\) | |
| 81. |
Laplace Transform of eat is given by: |
| A. | s/(s - a) |
| B. | 1/(s - a) |
| C. | s/(s + a |
| D. | 1/(s + a) |
| Answer» C. s/(s + a | |
| 82. |
Laplace transform of the function f(t) shown in the figure is |
| A. | \(\dfrac{2}{s^2}[1-e^{-0.5 s}]^2\) |
| B. | \(\dfrac{2}{s^2}[1+e^{-0.5 s}]^2\) |
| C. | \(\dfrac{2}{s^2}[1-e^{0.5 s}]^2\) |
| D. | \(\dfrac{2}{s^2}[1+e^{0.5 s}]^2\) |
| Answer» B. \(\dfrac{2}{s^2}[1+e^{-0.5 s}]^2\) | |
| 83. |
Consider the following statements regarding a parabolic function:1. A parabolic function is one degree faster than the lamp function.2. A unit parabolic function is defined as\(f\left( t \right) = \left\{ {\begin{array}{*{20}{c}}{\frac{{{t^2}}}{2},\;\;for\;\;t > 0}\\{0,\;\;\;\;\;\;\;\;otherwise}\end{array}} \right.\)3. Laplace transform of a unit parabolic function is \(\frac{1}{{{s^3}}}\)Which of the above statements are correct? |
| A. | 1 and 2 only |
| B. | 1 and 3 only |
| C. | 2 and 3 only |
| D. | 1, 2 and 3 |
| Answer» E. | |
| 84. |
Consider the following transforms:1. Fourier transform2. Laplace transformWhich of the above transforms is/are used in signal processing? |
| A. | 1 only |
| B. | 2 only |
| C. | Both 1 and 2 |
| D. | Neither 1 nor 2 |
| Answer» D. Neither 1 nor 2 | |
| 85. |
Consider a signal defined by\(x\left( t \right) = \left\{ {\begin{array}{*{20}{c}} {{e^{~j10t}}}&{for\left| t \right| \le 1}\\ 0&{for\left| t \right| > 1} \end{array}} \right.\)Its Fourier Transform is |
| A. | \(\frac{{2\sin \left( {\omega - 10} \right)}}{{\omega - 10}}\) |
| B. | \(\frac{{2{e^{j10}}\sin \left( {\omega - 10} \right)}}{{\omega - 10}}\) |
| C. | \(\frac{{2sin\omega }}{{\omega - 10}}\) |
| D. | \(\frac{{{e^{j10\omega }}2sin\omega }}{\omega }\) |
| Answer» B. \(\frac{{2{e^{j10}}\sin \left( {\omega - 10} \right)}}{{\omega - 10}}\) | |
| 86. |
\(\mathop {{\rm{Lt}}}\limits_{x \to 0} \frac{{{{\log }_e}\left( {1 + 4x} \right)}}{{{e^{3x}} - 1}}\) is equal to |
| A. | 0 |
| B. | \(\frac{1}{{12}}\) |
| C. | \(\frac{4}{3}\) |
| D. | 1 |
| Answer» D. 1 | |
| 87. |
A system is described by the following differential equation:\(\frac{{dy\left( t \right)}}{{dt}} + 2y\left( t \right) = \frac{{dx\left( t \right)}}{{dt}} + x\left( t \right),x\left( 0 \right) = y\left( 0 \right) = 0\)Where x(t) and y(t) are the input and output variables respectively. The transfer function of the inverse system is |
| A. | \(\frac{{s + 1}}{{s - 2}}\) |
| B. | \(\frac{{s + 2}}{{s + 1}}\) |
| C. | \(\frac{{s + 1}}{{s + 2}}\) |
| D. | \(\frac{{s - 1}}{{s - 2}}\) |
| Answer» C. \(\frac{{s + 1}}{{s + 2}}\) | |
| 88. |
Find the Laplace transform of e-3t cos 5t. |
| A. | \(\frac{\left( s=3 \right)}{\left( {{s}^{2}}-6s+34 \right)}\) |
| B. | \(\frac{\left( s-5 \right)}{\left( {{s}^{2}}-10s+34 \right)}\) |
| C. | \(\frac{\left( s+3 \right)}{\left( {{s}^{2}}+6s+34 \right)}\) |
| D. | \(\frac{\left( s+5 \right)}{({{S}^{2}}+10s+34}\) |
| Answer» D. \(\frac{\left( s+5 \right)}{({{S}^{2}}+10s+34}\) | |
| 89. |
Let \(X\left( s \right) = \frac{{3s + 5}}{{{s^2} + 10s + 21}}\) be the Laplace Transform of a signal x(t). Then x(0+) is |
| A. | 0 |
| B. | 3 |
| C. | 5 |
| D. | 21 |
| Answer» C. 5 | |
| 90. |
Consider a distortionless system H(ω) with magnitude and phase responses as shown in Fig. If an input signal x(t) = 2 cos 10 πt + sin 26 πt is given to this system, the output will be |
| A. | 4cos(10πt) + sin(26πt) |
| B. | 8cos(10πt) + sin(26πt) |
| C. | \(4 \cos \left(10 \pi t - \dfrac{\pi}{6}\right)+ \sin \left(26 \pi t - \dfrac{13\pi}{30}\right)\) |
| D. | \(8 \cos \left(10 \pi t - \dfrac{\pi}{2}\right)+ \sin \left(26 \pi t - \dfrac{\pi}{2}\right)\) |
| Answer» B. 8cos(10πt) + sin(26πt) | |
| 91. |
Consider the following transfer functions:1. \(\frac{1}{{j\omega + 1}}\)2. \(\frac{1}{{{{\left( {j\omega + 1} \right)}^2}}}\) 3. \(\frac{1}{{\left( {j\omega + 1} \right)\left( {j\omega + 2} \right)}}\) The transfer functions which have a linear phase are: |
| A. | 1 and 2 only |
| B. | 1 and 3 only |
| C. | 2 and 3 only |
| D. | 1, 2 and 3 |
| Answer» E. | |
| 92. |
A function c(t) satisfies the differential equation ċ (t) + c(t) = δ(t). For zero initial condition c(t) can be represented by: |
| A. | e-t |
| B. | et |
| C. | et u(t) |
| D. | e-t u(t) |
| Answer» E. | |
| 93. |
If L{f(t)} = F(s), then the value of L{e-at f(t)} is |
| A. | F(s + a) |
| B. | F(s + 1) |
| C. | F(s) |
| D. | F(eas) |
| Answer» B. F(s + 1) | |
| 94. |
An absolutely integrable signal x(t) is known to have Laplace transform with only one pole at s = 4 the x(t) is |
| A. | Left sided signal |
| B. | Right sided signal |
| C. | Signal of finite duration |
| D. | Double sided signal |
| Answer» B. Right sided signal | |
| 95. |
From the options given below, which of the one is correct Laplace transform of the signalS = x(t) = e-at u(t) –e-bt u(-t)? |
| A. | L(s) = (s + a +b)/(s + a)(s +b) |
| B. | L(s) = (2s + a +b)/(s + a)(s +b) |
| C. | L(s) = (2s + a +b)/(s - a)(s +b) |
| D. | L(s) = (s + a +b)/(s - a)(s -b) |
| Answer» C. L(s) = (2s + a +b)/(s - a)(s +b) | |
| 96. |
Consider a signal v(t) with Fourier transform V(f). If V '(f) represents the Fourier transform of v(2t), what is the relation between V '(f) to V(f) |
| A. | Magnitude scaled by 0.5 and bandwidth compressed |
| B. | Magnitude scaled by 0.5 and bandwidth expanded |
| C. | Magnitude scaled by 2 and bandwidth compressed |
| D. | Magnitude scaled by 2 and bandwidth expanded |
| Answer» C. Magnitude scaled by 2 and bandwidth compressed | |
| 97. |
Find the Laplace transform of y(t) = te-5t |
| A. | \(\frac{s}{{{{\left( {s + 5} \right)}^2}}}\) |
| B. | \(\frac{1}{{2{{\left( {s + 5} \right)}^2}}}\) |
| C. | \(\frac{1}{{{{\left( {s + 5} \right)}^2}}}\) |
| D. | \(\frac{1}{{s{{\left( {s + 5} \right)}^2}}}\) |
| Answer» D. \(\frac{1}{{s{{\left( {s + 5} \right)}^2}}}\) | |
| 98. |
Consider the following statements regarding the use of Laplace transforms and Fourier transforms in circuit analysis1. Both make the solution of circuit problems simple and easy.2. Both are applicable for the study of circuit behavior for t = - ∞ to ∞3. Both convert differential equations to algebraic equations.4. Both can be used for transient and steady-state analysis.Which of the above statements are correct? |
| A. | 1, 2, 3 and 4 |
| B. | 2, 3 and 4 only |
| C. | 1, 2 and 4 only |
| D. | 1, 3 and 4 only |
| Answer» E. | |
| 99. |
If x(t) ↔ X(f) denotes a Fourier transform (FT) pair, \(\Pi \left(\dfrac{t}{T}\right)\) denotes a rectangular pulse of width T and '⋆' denotes the convolution operation, then the FT of the signal \(x(t)=\Pi \left(\dfrac{t}{T}\right) * \Pi \left(\dfrac{t}{T}\right)\) is |
| A. | T2 sinc2 (fT) |
| B. | -j sgn (fT) |
| C. | \(T^2 e^{-(F/T)^2}\) |
| D. | T sinc (2fT) |
| Answer» B. -j sgn (fT) | |
| 100. |
Let h(t) denote the impulse response of causal system with transfer function \(H\left( s \right) = \frac{1}{{s + 1}}\) Consider the following three statements S1: The system is stable S2: \(\frac{{h\left( {t + 1} \right)}}{{h\left( t \right)}}\) is independent of time S3: A non – causal system with same transfer function is stable for the above system |
| A. | Only S1 is true |
| B. | Only S3 is true |
| C. | Only S1 and S2 are true |
| D. | Only S1 and S3 are true |
| Answer» D. Only S1 and S3 are true | |