MCQOPTIONS
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MCQOPTIONS
This section includes 34 Mcqs, each offering curated multiple-choice questions to sharpen your Non-Verbal Reasoning knowledge and support exam preparation. Choose a topic below to get started.
| 1. |
A periodic function of half wave symmetry is necessarily |
| A. | an even function |
| B. | an odd function |
| C. | neither odd nor even |
| D. | either odd or even |
| Answer» E. | |
| 2. |
Consider the trigonometric series, which holds true for all t, given by\(x(t)=\sin ω_0 t + \dfrac{1}{3} \sin 3 ω_0 t + \dfrac{1}{5} \sin 5 ω_0 t + \dfrac{1}{7}\sin 7 ω_0 t + ...\) At \(\omega_0 t = \dfrac{\pi}{2}\), the series converges to |
| A. | 0.5 |
| B. | π/4 |
| C. | π/2 |
| D. | 2 |
| Answer» C. π/2 | |
| 3. |
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): Dirichlet's conditions restrict the periodic signal x(t), to be represented by Fourier series, to have only finite number of maxima and minima.Statement (II): x(t) should possess only a finite number of discontinuities.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» C. Statement (I) is true but Statement (II) is false | |
| 4. |
A signal \(2\cos \left( {\frac{{2{\rm{\pi }}}}{3}{\rm{t}}} \right) - {\rm{cos}}\left( {{\rm{\pi t}}} \right){\rm{\;}}\)is input to an LTI system with the transfer functionH(s) = es + e-sIf ck denotes the kth coefficient in the exponential Fourier series of the output signal, then c3 is equal to |
| A. | 0 |
| B. | 1 |
| C. | 2 |
| D. | 3 |
| Answer» C. 2 | |
| 5. |
If \(f\left( x \right) = \frac{l}{4} - x\), when \(0 < x < \frac{l}{2}\)\( = x - \frac{{3l}}{4}\) ,when \(\frac{l}{2} < x < l\)then the value of a0 in the Fourier series of this function is |
| A. | 0 |
| B. | \(\frac{{\pi l}}{6}\) |
| C. | \(\frac{l}{6}\) |
| D. | \( - \frac{{{l^2}}}{4}\) |
| Answer» B. \(\frac{{\pi l}}{6}\) | |
| 6. |
For a waveform to be expressed in Fourier series, which of the following conditions must be satisfied?I. Maxwell’s conditionsII. Drichlet conditionsIII. Sampling Theorem |
| A. | I only |
| B. | II only |
| C. | II and III only |
| D. | I, II and III |
| Answer» C. II and III only | |
| 7. |
A periodic function satisfies Dirichlet’s conditions. This implies that the function |
| A. | is non-linear |
| B. | is not absolutely integrable |
| C. | guarantees that Fourier series representation of the function exists |
| D. | has an infinite number of maxima and minima within a period |
| Answer» D. has an infinite number of maxima and minima within a period | |
| 8. |
Find the Fourier series of the waveform shown below. |
| A. | f(t) = 2A/jnπ for n = 1, 3, 5, 7 and so onf(t) = 0 for n = 2, 4, 6, 8 and so on |
| B. | f(t) = 2A/jnπ for n = 2, 4, 6, 8 and so onf(t) = 0 for n = 1, 3, 5, 7 and so on |
| C. | f(t) = 4A/jnπ for n = 1, 3, 5, 7 and so onf(t) = 0 for n = 2, 4, 6, 8 and so on |
| D. | f(t) = 4A/jnπ for n = 2, 4, 6, 8 and so onf(t) = 0 for n = 1, 3, 5, 7 and so on |
| Answer» B. f(t) = 2A/jnπ for n = 2, 4, 6, 8 and so onf(t) = 0 for n = 1, 3, 5, 7 and so on | |
| 9. |
Parseval’s relation for a periodic signal relates |
| A. | Total average power in the signal |
| B. | Total harmonic distortion |
| C. | Sum of Fourier coefficients |
| D. | Average of the Fourier coefficients |
| Answer» B. Total harmonic distortion | |
| 10. |
Fourier series of an odd periodic function contains only |
| A. | odd harmonics |
| B. | even harmonics |
| C. | cosine harmonics |
| D. | sine harmonics |
| Answer» E. | |
| 11. |
Let x(t) be a continuous time periodic signal with fundamental period T = 1 seconds. Let {ak} be the complex Fourier series coefficients of x(t), where k is integer valued. Consider the following statements about x(3t):I. The complex Fourier series coefficients of x(3t) are {ak} where k is integer valuedII. The complex Fourier series coefficients of x(3t) are {3ak} where k is integer valuedIII. The fundamental angular frequency of x(3t) is 6π rad/sFor the three statements above, which one of the following is correct? |
| A. | only II and III are true |
| B. | only I and III are true |
| C. | only III is true |
| D. | only I is true |
| Answer» C. only III is true | |
| 12. |
f(x), shown in the figure is represented by \(f\left( x \right) = {a_0} + \mathop \sum \limits_{n = 1}^\infty \left( {{a_n}\cos \left( {nx} \right) + {b_n}\sin \left( {nx} \right)} \right)\)The value of a0 is |
| A. | 0 |
| B. | π/2 |
| C. | π |
| D. | 2π |
| Answer» B. π/2 | |
| 13. |
Consider a rectified sine wave x(t) defined by x(t) = |A sin πt|. Determine its fundamental period and complex exponential Fourier series |
| A. | \({T_0} = 1\;and\;x\left( t \right) = - \frac{{2A}}{\pi }\mathop \sum \limits_{k = - \infty }^\infty \frac{1}{{4{k^2} - 1}}{e^{jk2\pi t}}\) |
| B. | \({T_0} = \frac{1}{2}\;and\;x\left( t \right) = - \frac{{2A}}{\pi }\mathop \sum \limits_{k = - \infty }^\infty \frac{1}{{4{k^2} + 1}}{e^{jk2\pi t}}\) |
| C. | \({T_0} = 1\;and\;x\left( t \right) = - \frac{{2A}}{\pi }\mathop \sum \limits_{k = - \infty }^\infty \frac{1}{{4{k^2} + 1}}{e^{jk2\pi t}}\) |
| D. | \({T_0} = \frac{1}{2}\;and\;x\left( t \right) = - \frac{{2A}}{\pi }\mathop \sum \limits_{k = - \infty }^\infty \frac{1}{{4{k^2} - 1}}{e^{jk2\pi t}}\) |
| Answer» B. \({T_0} = \frac{1}{2}\;and\;x\left( t \right) = - \frac{{2A}}{\pi }\mathop \sum \limits_{k = - \infty }^\infty \frac{1}{{4{k^2} + 1}}{e^{jk2\pi t}}\) | |
| 14. |
Let the signal \(x\left( t \right) = \mathop \sum \limits_{k = - \infty }^{ + \infty } {\left( { - 1} \right)^k}\delta \left( {t - \frac{k}{{2000}}} \right)\) be passed through an LTI system with frequency response H(ω), as given in the figure below.The Fourier series coefficients of the output is given as |
| A. | 4000 + 4000 cos(2000 πt) + 4000 cos(4000 πt) |
| B. | 2000 + 2000 cos(2000 πt) + 2000 cos(4000 πt) |
| C. | 4000 cos(2000 πt) |
| D. | 2000 cos(2000 πt) |
| Answer» D. 2000 cos(2000 πt) | |
| 15. |
An energy signal has S(f) = 19. What will be the energy density spectrum? |
| A. | 19 |
| B. | 81 |
| C. | 38 |
| D. | 361 |
| Answer» E. | |
| 16. |
Consider a continuous time periodic signal x(t) with fundamental period T and Fourier series coefficient X[k]. What is the Fourier series coefficient of the signal y(t) = x(t – t0) + x(t + t0) ? |
| A. | \(2\cos \left( {\frac{{2\pi }}{T}K{t_0}} \right)X\left[ K \right]\) |
| B. | \(2\sin \left( {\frac{{2\pi }}{T}K{t_0}} \right)X\left[ K \right]\) |
| C. | \({e^{ - {t_0}}}X\left[ K \right] + {e^{{t_0}}}X\left[ { - K} \right]\) |
| D. | \({e^{ - {t_0}}}X\left[ { - K} \right] + {e^{{t_0}}}X\left[ K \right]\) |
| Answer» B. \(2\sin \left( {\frac{{2\pi }}{T}K{t_0}} \right)X\left[ K \right]\) | |
| 17. |
Let x(t) be a periodic function with period T = 10. The Fourier series coefficients for this series are denoted by ak, that is:\(x\left( t \right) = \mathop \sum \limits_{k = - \infty }^\infty {a_k}{e^{jk\frac{{2\pi }}{T}t}}\)The same function x(t) can also be considered as a periodic function with period T′ = 40. Let \(b_k\) be the Fourier series coefficients when the period is taken as T’. If \(\mathop \sum \limits_{{\rm{k}} = - \infty }^\infty \left| {{{\rm{a}}_{\rm{k}}}} \right|=16{\rm{\;}}\), then \(\mathop \sum \limits_{{\rm{k}} = - \infty }^\infty \left| {{{\rm{b}}_{\rm{k}}}} \right|{\rm{\;}}\)is equal to |
| A. | 256 |
| B. | 64 |
| C. | 16 |
| D. | 4 |
| Answer» D. 4 | |
| 18. |
For a periodic signal f(t) satisfying Dirchlet conditions, the Fourier Series consists of |
| A. | sine and cosine terms |
| B. | DC, sine and cosine terms |
| C. | DC and cosine terms |
| D. | only sine terms |
| Answer» C. DC and cosine terms | |
| 19. |
A periodic function f(t), with a period of 2π, is represented as its Fourier series,\(f\left( t \right) = {a_0} + {\rm{\Sigma }}_{n = 1}^\infty \;{a_n}\cos nt + {\rm{\Sigma }}_{n = 1}^\infty \;{b_n}\sin nt\)If\(f\left( t \right) = \{ \begin{array}{*{20}{c}}{A\sin t,}&{0 \le t \le \pi }\\{0,}&{\pi < t < 2\pi }\end{array}\) ,the Fourier series coefficients a1 and b1 of f(t) are |
| A. | \({a_1} = \frac{A}{\pi };{b_1} = 0\) |
| B. | \({a_1} = \frac{A}{2};{b_1} = 0\) |
| C. | \({a_1} = 0;{b_1} = A/\pi\) |
| D. | \({a_1} = 0;{b_1} = \frac{A}{2}\) |
| Answer» E. | |
| 20. |
A 4 kHz square wave of duty cycle 50% and p-p (0.2V to +0.2V) is applied as input to 20 kHz narrow bandpass filter which is followed by an amplifier of voltage gain 20. Find out the frequency components present in the output. Given that cut off frequencies of a narrow bandpass filter is 20 kHz and 40 kHz. |
| A. | 12 kHz, 20 kHz, 28 kHz |
| B. | 20 kHz, 28 kHz, 36 kHz |
| C. | 20 kHz, 28 kHz, 32 kHz |
| D. | 20 kHz, 24 kHz, 28 kHz |
| Answer» C. 20 kHz, 28 kHz, 32 kHz | |
| 21. |
A digital board has a unipolar square clock of 250 MHz. If the clock on the board at all places should have all the harmonic components which have more than 10% of DC value, the board has to be designed for at least- |
| A. | 250 MHz |
| B. | 750 MHz |
| C. | 1250 MHz |
| D. | 2500 MHz |
| Answer» D. 2500 MHz | |
| 22. |
A periodic signal x(t) has a trigonometric Fourier series expansion\(x\left( t \right) = {a_0} + \mathop \sum \limits_{n = 1}^\infty ({a_n}\;cos\;n\;{\omega _0}t + {b_n}\sin n\;{\omega _0}t)\)If x(t) = -x (- t) = -x (t - π/ω0), we can conclude that |
| A. | an are zero for all n and bn are zero for n even |
| B. | an are zero for all n and bn are zero for n odd |
| C. | an are zero for n even and bn are zero for n odd |
| D. | an are zero for n odd and bn are zero for n even |
| Answer» B. an are zero for all n and bn are zero for n odd | |
| 23. |
For the periodic signal x(t) shown below with period T = 8s, the power in the 10th harmonic is |
| A. | 0 |
| B. | \(\frac{1}{2}{\left( {\frac{2}{{10\;\pi }}} \right)^2}\) |
| C. | \(\frac{1}{2}{\left( {\frac{4}{{10\pi }}} \right)^2}\) |
| D. | \(\frac{1}{2}{\left( {\frac{4}{{5\pi }}} \right)^2}\) |
| Answer» B. \(\frac{1}{2}{\left( {\frac{2}{{10\;\pi }}} \right)^2}\) | |
| 24. |
For a periodic square wave, which one of the following statements is TRUE? |
| A. | The Fourier series coefficients do not exist. |
| B. | The Fourier series coefficients exist but the reconstruction converges at no point. |
| C. | The Fourier series coefficients exist and the reconstruction converges at most points. |
| D. | The Fourier series coefficients exist and the reconstruction converges at every point. |
| Answer» D. The Fourier series coefficients exist and the reconstruction converges at every point. | |
| 25. |
Let be a real, periodic function satisfying \(f\left( { - x} \right) = - f\left( x \right)\). The general form of its Fourier series representation would be |
| A. | \(f\left( x \right) = {a_0} + \mathop \sum \limits_{k = 1}^\infty {a_k}\cos \left( {kx} \right)\) |
| B. | \(f\left( x \right) = \mathop \sum \limits_{k = 1}^\infty {b_k}\sin \left( {kx} \right)\) |
| C. | \(f\left( x \right) = {a_0} + \mathop \sum \limits_{k = 1}^\infty {a_{2k}}\cos \left( {kx} \right)\) |
| D. | \(f\left( x \right) = \mathop \sum \limits_{k = 0}^\infty {a_{2k}} + \sin \left( {2k + 1} \right)x\) |
| Answer» C. \(f\left( x \right) = {a_0} + \mathop \sum \limits_{k = 1}^\infty {a_{2k}}\cos \left( {kx} \right)\) | |
| 26. |
Consider a periodic signal x(t) as shown below:It has a Fourier series representation\(x\left( t \right) = \mathop \sum \limits_{k = - \infty }^\infty {a_k}{e^{j\left( {\frac{{2\pi }}{T}} \right)kt}}\)Which one of the following statements is TRUE? |
| A. | ak = 0, for k odd integer and T = 2 |
| B. | ak = 0, for k even integer and T = 2 |
| C. | ak = 0, for k even integer and T = 4 |
| D. | ak = 0, for k odd integer and T = 4 |
| Answer» C. ak = 0, for k even integer and T = 4 | |
| 27. |
Select a figure from amongst the Answer Figures which will continue the same series as established by the five Problem Figures. |
| A. | 1 |
| B. | 2 |
| C. | both 3 and 4 |
| D. | 5 |
| Answer» E. | |
| 28. |
Select a figure from amongst the Answer Figures which will continue the same series as established by the five Problem Figures . |
| A. | 1 |
| B. | 2 |
| C. | 3 |
| D. | 4 |
| Answer» C. 3 | |
| 29. |
Select a figure from amongst the Answer Figures which will continue the same series as established by the five Problem Figures. |
| A. | 1 |
| B. | 2 |
| C. | 3 |
| D. | 4 |
| Answer» B. 2 | |
| 30. |
Select a figure from amongst the Answer Figures which will continue the same series as established by the five Problem Figures. |
| A. | 1 |
| B. | 2 |
| C. | 3 |
| D. | 4 |
| Answer» E. | |
| 31. |
Select a figure from amongst the Answer Figures which will continue the same series as established by the five Problem Figures. |
| A. | 1 |
| B. | 2 |
| C. | 3 |
| D. | 4 |
| Answer» D. 4 | |
| 32. |
Select a figure from amongst the Answer Figures which will continue the same series as established by the five Problem Figures. |
| A. | 1 |
| B. | 2 |
| C. | 3 |
| D. | 4 |
| Answer» B. 2 | |
| 33. |
Select a figure from amongst the Answer Figures which will continue the same series as established by the five Problem Figures. |
| A. | 1 |
| B. | 2 |
| C. | 3 |
| D. | 4 |
| Answer» C. 3 | |
| 34. |
Select a figure from the Right side Answer Figures |
| A. | 1 |
| B. | 2 |
| C. | 3 |
| D. | 4 |
| E. | 5 |
| Answer» E. 5 | |