Chebyshev Polynomials Properties MCQ’s

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This set of Antenna Multiple Choice Questions & Answers (MCQs) focuses on “Chebyshev Polynomials Properties”.

1. How many times the polynomial T5(x) crosses the x-axis between [-1, 1]?
a) 5
b) 4
c) 2
d) 6

2. Which of the following statements is true?
a) The polynomials are unstable at interval [-1, 1]
b) The polynomials are marginally stable at interval [-1, 1]
c) The polynomial doesn’t oscillate at interval [-1, 1]
d) The polynomials crosses the axis m-1 times at [-1, 1]

3. Which of the following statement is true about the Chebyshev function Tm(x)?
a) It is a continuously increasing function after x=1
b) It is a continuously decreasing function after x=1
c) It is a continuously increasing function after x=0
d) It is a continuously decreasing function after x=0

4. What is the possible level from the following for the minor lobe when the main beam level is at 50db and SLL at 10 db according to Chebyshev?
a) 40dB
b) 45dB
c) 50dB
d) 80dB

5. The condition for the existence of the main lobe according to the Chebyshev is _________
a) |x| > 1
b) |x| < 1
c) |x| = 0
d) 2|x| > 1

6. Which of the following properties of Chebyshev polynomial is false?
a) The minor lobes have unequal amplitudes
b) The polynomial Tm(x) is symmetric for m = even
c) The polynomial Tm(x) crosses the x axis m times between -1 and 1
d) Minor lobes exists for |x| < 1

7. The condition for the existence of the main lobe according to the Chebyshev is _________
a) |x| > 1
b) |x| < 1
c) |x| = 0
d) 2|x| > 1

8. Which of the following statements regarding Chebyshev polynomial is true?
a) The polynomial Tm(x) is symmetric for m = even
b) The polynomial Tm(x) is symmetric for m = odd
c) The polynomial Tm(x) is anti-symmetric for m = even
d) The polynomial Tm(x) is symmetric for m = even and odd

9. As the order of the polynomial increases, the slope becomes steeper.
a) True
b) False

10. All the polynomials of the order m pass through the point ____________
a) (1, 1)
b) (0, 0)
c) (0, 1)
d) (-1, 0)

11. All the nulls occur at (-1, 1) in the Chebyshev polynomial.
a) True
b) False

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