EEE MCQ — Signals, Systems & Control | ৫০টি প্রশ্ন ও উত্তর
Signals & Systems এবং Control Systems BCS EEE পরীক্ষার পাশাপাশি BUET, RUET-এর MS admission এবং EEE চাকরির পরীক্ষায় গুরুত্বপূর্ণ। নিচে ৫০টি নির্বাচিত MCQ দেওয়া হলো।
📶 Signals & Systems
1. A continuous-time signal is defined as one that:
a) Takes discrete values only b) Is defined for all values of time t
c) Exists only at integer values of t d) Has finite duration only
✅ Answer: b
2. A discrete-time signal is defined at:
a) All values of t b) Only integer values of n (sampling instants)
c) Negative time only d) Irrational time instants
✅ Answer: b
3. The unit step function u(t) is:
a) 1 for t < 0 and 0 for t ≥ 0 b) 1 for t ≥ 0 and 0 for t < 0
c) Defined only at t = 0 d) Equal to the ramp function
✅ Answer: b
4. The unit impulse (Dirac delta) function δ(t) has the property:
a) ∫δ(t)dt = 0 b) ∫δ(t)dt = 1 (over all time)
c) δ(t) = 0 for all t d) δ(t) = 1 for all t ≠ 0
✅ Answer: b
5. A system is said to be linear if it satisfies:
a) Time-invariance only b) Superposition (additivity and homogeneity)
c) Causality d) BIBO stability
✅ Answer: b
6. A causal system is one in which:
a) Output depends on future inputs b) Output depends only on present and past inputs
c) Output is always zero d) The system has infinite memory
✅ Answer: b
7. A BIBO stable system means:
a) Bounded output for unbounded input b) Bounded output for bounded input
c) Unbounded output always d) Output is always zero
✅ Answer: b
8. Convolution in time domain corresponds to what operation in frequency domain?
a) Convolution b) Multiplication c) Addition d) Division
✅ Answer: b
9. The Fourier series represents a periodic signal as a:
a) Single sinusoid b) Sum of sinusoids at harmonically related frequencies
c) Product of exponentials d) Differential equation
✅ Answer: b
10. The Fourier Transform of a time-domain signal converts it to:
a) Time domain with different amplitude b) Frequency domain (spectrum)
c) Z-domain d) Laplace domain
✅ Answer: b
11. The Laplace Transform converts a differential equation into:
a) Another differential equation b) An algebraic equation in the s-domain
c) A difference equation d) A Fourier series
✅ Answer: b
12. The Z-Transform is used for:
a) Continuous-time signals b) Discrete-time signals and systems
c) Only periodic signals d) Power systems analysis
✅ Answer: b
13. Energy of a signal x(t) is defined as:
a) ∫|x(t)| dt b) ∫|x(t)|² dt c) [∫x(t) dt]² d) ∫x(t) dt
✅ Answer: b
14. A periodic signal has:
a) Finite energy b) Infinite energy but finite average power
c) Zero power d) Zero energy and zero power
✅ Answer: b
15. The convolution of two rectangular pulses produces:
a) Another rectangular pulse b) A triangular pulse
c) A sinusoidal signal d) An impulse
✅ Answer: b
🎛️ Control Systems — Fundamentals
16. A closed-loop (feedback) control system has:
a) No feedback path b) A feedback path comparing output to reference
c) Only a forward path d) Infinite gain
✅ Answer: b
17. The transfer function of a system is defined as:
a) Ratio of output to input in time domain b) Laplace transform of output divided by Laplace transform of input (zero initial conditions)
c) Product of input and output d) Differential of the output
✅ Answer: b
18. A first-order system has a transfer function of the form:
a) K/(s² + 2ζωₙs + ωₙ²) b) K/(τs + 1) c) Ks d) K/s²
✅ Answer: b
19. The time constant τ of a first-order system is the time for the step response to reach:
a) 50% of final value b) 63.2% of final value c) 90% of final value d) 100% of final value
✅ Answer: b
20. A second-order system is underdamped when:
a) ζ > 1 b) ζ = 1 c) 0 < ζ < 1 d) ζ = 0
✅ Answer: c
21. For a critically damped second-order system, the damping ratio ζ equals:
a) 0 b) Between 0 and 1 c) 1 d) Greater than 1
✅ Answer: c
22. Natural frequency (ωₙ) of a second-order system determines:
a) Damping only b) The speed of response (oscillation frequency for undamped case)
c) Steady-state error d) Phase margin
✅ Answer: b
23. Steady-state error for a type-1 system with a step input is:
a) Infinity b) Constant finite value c) Zero d) One
✅ Answer: c
24. The number of integrators in the open-loop transfer function determines the:
a) Gain margin b) System type number c) Bandwidth d) Damping ratio
✅ Answer: b
📊 Stability Analysis
25. The Routh-Hurwitz criterion is used to determine:
a) Frequency response b) Stability of a system without finding roots
c) Step response d) Bode plot
✅ Answer: b
26. A system is stable if all poles of the transfer function are:
a) On the right half of the s-plane b) In the left half of the s-plane (negative real parts)
c) On the imaginary axis d) At the origin
✅ Answer: b
27. The Nyquist stability criterion is used to determine stability from:
a) Root locus b) Frequency response (open-loop)
c) Step response d) Impulse response
✅ Answer: b
28. Gain margin is defined as:
a) The gain at phase crossover frequency b) How much gain can be increased before instability (in dB)
c) The phase at gain crossover frequency d) Bandwidth of the system
✅ Answer: b
29. Phase margin is the additional phase lag at:
a) Phase crossover frequency b) Gain crossover frequency (where |G(jω)| = 1)
c) Natural frequency d) Cutoff frequency
✅ Answer: b
30. For a stable system, the gain margin should be:
a) Negative b) Zero c) Positive (more than 0 dB) d) Equal to phase margin
✅ Answer: c
📈 Root Locus & Bode Plot
31. Root locus shows how the poles of a closed-loop system move as:
a) Frequency changes b) Gain (K) varies from 0 to ∞
c) Time changes d) Damping ratio changes
✅ Answer: b
32. A Bode plot consists of:
a) Nyquist plot and root locus b) Magnitude (dB) and phase (degrees) vs log frequency
c) Time response vs frequency d) Pole-zero map
✅ Answer: b
33. The slope of a Bode magnitude plot for a single pole is:
a) +20 dB/decade b) −20 dB/decade c) −40 dB/decade d) +40 dB/decade
✅ Answer: b
34. A proportional (P) controller:
a) Eliminates steady-state error completely b) Reduces error but may not eliminate it
c) Increases settling time d) Has no effect on response
✅ Answer: b
35. An integral (I) controller:
a) Increases steady-state error b) Eliminates steady-state error but may reduce stability
c) Has no effect on steady state d) Improves transient response only
✅ Answer: b
36. A PID controller combines:
a) Phase lead and lag compensation b) Proportional, Integral, and Derivative actions
c) Feedback and feedforward only d) Gain and bandwidth adjustment
✅ Answer: b
🤖 Modern Control
37. State space representation of a system uses:
a) Transfer function only b) State variables — a set of first-order differential equations
c) Bode plot d) Root locus
✅ Answer: b
38. The state equation is written as:
a) y = Cx + Du b) ẋ = Ax + Bu c) u = Bx + Ay d) x = Ay + Bu
✅ Answer: b
39. A system is controllable if:
a) All states can be observed b) All states can be driven to any desired state using control input
c) The system is stable d) The system has zero steady-state error
✅ Answer: b
40. A system is observable if:
a) All states can be controlled b) All states can be determined from the output measurements
c) The system is BIBO stable d) The transfer function has no poles
✅ Answer: b
📡 DSP & Discrete Systems
41. The Discrete Fourier Transform (DFT) is computed efficiently using:
a) Z-Transform b) Fast Fourier Transform (FFT) algorithm
c) Laplace Transform d) Wavelet Transform
✅ Answer: b
42. An FIR (Finite Impulse Response) filter:
a) Has feedback (recursive) b) Has no feedback — impulse response has finite duration
c) Is always unstable d) Requires a differential equation
✅ Answer: b
43. An IIR (Infinite Impulse Response) filter:
a) Has no feedback b) Has feedback — impulse response continues indefinitely
c) Is always FIR d) Cannot be implemented digitally
✅ Answer: b
44. Aliasing in a sampled signal occurs when:
a) Sampling rate is too high b) Sampling rate is less than twice the signal bandwidth
c) Signal frequency is zero d) Filter bandwidth is too wide
✅ Answer: b
45. Anti-aliasing filter is placed:
a) After the ADC b) Before the ADC to remove frequencies above fs/2
c) After the DAC d) In the feedback path
✅ Answer: b
🧮 Mathematical Tools
46. The inverse Laplace transform of 1/s is:
a) δ(t) (impulse) b) u(t) (unit step) c) t·u(t) (ramp) d) e⁻ᵗ
✅ Answer: b
47. The inverse Laplace transform of 1/s² is:
a) u(t) b) δ(t) c) t·u(t) (ramp) d) e⁻ᵗ
✅ Answer: c
48. The final value theorem states: lim(t→∞) f(t) = lim(s→0) s·F(s), valid when:
a) All poles of s·F(s) are in the right half plane b) All poles of s·F(s) are in the left half plane (stable)
c) F(s) has no poles d) The system is non-linear
✅ Answer: b
49. The initial value theorem states: f(0⁺) = lim(s→∞) s·F(s), which gives:
a) The final value of f(t) b) The value of f(t) at t=0⁺
c) The integral of f(t) d) The derivative of f(t)
✅ Answer: b
50. Parseval's theorem relates:
a) Time domain convolution to frequency multiplication b) Total energy in time domain to total energy in frequency domain
c) Phase to amplitude d) Sampling theorem to aliasing
✅ Answer: b
গুরুত্বপূর্ণ সূত্র সংক্ষেপ
| বিষয় | সূত্র |
|---|---|
| First-order time constant | τ (63.2% of final value) |
| Second-order ζ | Underdamped: 0 < ζ < 1 |
| Pole location for stability | Left half s-plane (Re < 0) |
| Bode single pole slope | −20 dB/decade |
| Gain margin | Phase crossover: |
| Nyquist sampling | fs ≥ 2 × fmax |
সিরিজ সম্পূর্ণ!
এই ৫ পর্বের MCQ সিরিজে মোট ২৫০টি প্রশ্ন কভার করা হয়েছে:
| পোস্ট | বিষয় | প্রশ্ন |
|---|---|---|
| পর্ব ১ | Circuit Theory & Network Analysis | ৫০টি |
| পর্ব ২ | Electrical Machines | ৫০টি |
| পর্ব ৩ | Power Systems | ৫০টি |
| পর্ব ৪ | Electronics & Semiconductor | ৫০টি |
| পর্ব ৫ | Signals, Systems & Control | ৫০টি |
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