Major Competitive Exams
Q. In a damped harmonic oscillator, if the mass is doubled while keeping the damping coefficient constant, what happens to the damping ratio?
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A.
Doubles
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B.
Halves
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C.
Remains the same
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D.
Increases by a factor of √2
Solution
Damping ratio (ζ) = c / (2√(mk)). If m is doubled, ζ is halved.
Correct Answer: B — Halves
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Q. In a damped harmonic oscillator, what effect does increasing the damping coefficient have on the oscillation?
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A.
Increases amplitude
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B.
Decreases amplitude
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C.
Increases frequency
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D.
Decreases frequency
Solution
Increasing the damping coefficient results in a decrease in amplitude over time, leading to quicker energy loss.
Correct Answer: B — Decreases amplitude
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Q. In a damped harmonic oscillator, what happens to the amplitude of oscillation over time?
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A.
Increases
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B.
Decreases
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C.
Remains constant
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D.
Oscillates
Solution
In a damped harmonic oscillator, the amplitude of oscillation decreases over time due to energy loss.
Correct Answer: B — Decreases
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Q. In a damped harmonic oscillator, which factor primarily determines the rate of energy loss?
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A.
Mass of the oscillator
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B.
Spring constant
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C.
Damping coefficient
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D.
Frequency of oscillation
Solution
The damping coefficient determines how quickly the energy is lost in a damped harmonic oscillator.
Correct Answer: C — Damping coefficient
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Q. In a damped harmonic oscillator, which of the following quantities decreases over time?
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A.
Amplitude
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B.
Frequency
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C.
Angular frequency
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D.
Phase constant
Solution
In a damped harmonic oscillator, the amplitude decreases over time due to the energy lost to damping forces.
Correct Answer: A — Amplitude
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Q. In a damped harmonic oscillator, which of the following statements is true?
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A.
Energy is conserved
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B.
Amplitude decreases over time
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C.
Frequency increases over time
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D.
Phase remains constant
Solution
In a damped harmonic oscillator, the amplitude decreases over time due to the loss of energy.
Correct Answer: B — Amplitude decreases over time
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Q. In a damped harmonic oscillator, which parameter is primarily responsible for energy loss?
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A.
Mass
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B.
Spring constant
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C.
Damping coefficient
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D.
Driving force
Solution
The damping coefficient determines the rate of energy loss in a damped harmonic oscillator.
Correct Answer: C — Damping coefficient
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Q. In a damped harmonic oscillator, which parameter primarily determines the rate of energy loss?
-
A.
Mass of the oscillator
-
B.
Spring constant
-
C.
Damping coefficient
-
D.
Driving force
Solution
The damping coefficient determines how quickly energy is lost in a damped harmonic oscillator.
Correct Answer: C — Damping coefficient
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Q. In a damped oscillator, if the energy decreases to 25% of its initial value in 10 seconds, what is the damping ratio?
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A.
0.1
-
B.
0.2
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C.
0.3
-
D.
0.4
Solution
Using E(t) = E_0 e^(-2ζω_nt), we find ζ = 0.2.
Correct Answer: B — 0.2
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Q. In a Daniell cell, which metal acts as the anode?
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A.
Copper
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B.
Zinc
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C.
Silver
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D.
Lead
Solution
In a Daniell cell, Zinc acts as the anode.
Correct Answer: B — Zinc
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Q. In a Daniell cell, which metal is oxidized?
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A.
Copper
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B.
Zinc
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C.
Lead
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D.
Silver
Solution
In a Daniell cell, zinc is oxidized.
Correct Answer: B — Zinc
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Q. In a data set, if the mean is 30 and the median is 25, what can be inferred about the data?
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A.
Skewed right
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B.
Skewed left
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C.
Symmetrical
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D.
Uniform
Solution
Since the mean is greater than the median, the data is skewed right.
Correct Answer: A — Skewed right
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Q. In a data set, if the mean is 30 and the median is 25, what can be inferred?
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A.
Data is skewed right
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B.
Data is skewed left
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C.
Data is symmetric
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D.
Data is uniform
Solution
Since the mean is greater than the median, the data is skewed to the right.
Correct Answer: A — Data is skewed right
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Q. In a data set, if the mean is 50 and the median is 45, what can be inferred about the data?
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A.
Skewed right
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B.
Skewed left
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C.
Symmetric
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D.
Uniform
Solution
Since the mean is greater than the median, the data is skewed right.
Correct Answer: A — Skewed right
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Q. In a data set, if the mean is 50 and the sum of all values is 500, how many values are there?
Solution
Number of values = Sum / Mean = 500 / 50 = 10.
Correct Answer: C — 10
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Q. In a data set, if the mode is 15 and the mean is 20, what can be said about the data?
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A.
Positively skewed
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B.
Negatively skewed
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C.
Symmetrical
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D.
Uniform
Solution
Since the mean is greater than the mode, the data is positively skewed.
Correct Answer: A — Positively skewed
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Q. In a data set, if the values are 2, 4, 4, 4, 5, 5, 7, what is the mode?
Solution
Mode = 4 (most frequently occurring value).
Correct Answer: A — 4
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Q. In a data set, the mean is 10 and the standard deviation is 2. What is the coefficient of variation?
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A.
20%
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B.
10%
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C.
5%
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D.
15%
Solution
Coefficient of Variation = (Standard Deviation / Mean) * 100 = (2/10) * 100 = 20%.
Correct Answer: A — 20%
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Q. In a data set, the mean is 20 and the median is 18. What can be inferred about the data?
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A.
Skewed right
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B.
Skewed left
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C.
Symmetric
-
D.
Uniform
Solution
Since the mean is greater than the median, the data is skewed right.
Correct Answer: A — Skewed right
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Q. In a data set, the mean is 20 and the median is 18. What can be said about the data?
-
A.
Positively skewed
-
B.
Negatively skewed
-
C.
Symmetrical
-
D.
Uniform
Solution
Since the mean is greater than the median, the data is positively skewed.
Correct Answer: A — Positively skewed
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Q. In a data set, the mean is 20 and the standard deviation is 4. What is the coefficient of variation?
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A.
20%
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B.
15%
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C.
10%
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D.
5%
Solution
Coefficient of Variation = (Standard Deviation / Mean) * 100 = (4/20) * 100 = 20%.
Correct Answer: A — 20%
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Q. In a data set, the mean is 50 and the number of observations is 10. What is the sum of all observations?
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A.
400
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B.
500
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C.
600
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D.
700
Solution
Sum = Mean * Number of Observations = 50 * 10 = 500.
Correct Answer: B — 500
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Q. In a data set, the values are: 1, 2, 3, 4, 5. What is the interquartile range?
Solution
Q1 = 2, Q3 = 4. Interquartile Range = Q3 - Q1 = 4 - 2 = 2.
Correct Answer: B — 2
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Q. In a deck of 52 cards, what is the probability of drawing a heart given that the card drawn is a red card?
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A.
1/2
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B.
1/4
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C.
1/3
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D.
1/5
Solution
There are 26 red cards (hearts and diamonds). The number of hearts is 13. Thus, P(Heart | Red) = 13/26 = 1/2.
Correct Answer: A — 1/2
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Q. In a deck of cards, what is the probability of drawing a heart given that the card drawn is a red card?
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A.
1/2
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B.
1/4
-
C.
1/3
-
D.
1/5
Solution
There are 26 red cards (hearts and diamonds). The number of hearts is 13. Thus, P(Heart | Red) = 13/26 = 1/2.
Correct Answer: A — 1/2
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Q. In a diffraction grating, if the number of slits is increased, what happens to the intensity of the maxima?
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A.
Increases
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B.
Decreases
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C.
Remains the same
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D.
Becomes zero
Solution
Increasing the number of slits increases the intensity of the maxima due to constructive interference.
Correct Answer: A — Increases
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Q. In a diffraction grating, if the number of slits is increased, what happens to the sharpness of the maxima?
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A.
Sharpness increases
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B.
Sharpness decreases
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C.
No effect
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D.
Maxima disappear
Solution
Increasing the number of slits in a diffraction grating increases the sharpness of the maxima due to constructive interference.
Correct Answer: A — Sharpness increases
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Q. In a diffraction grating, if the number of slits is increased, what happens to the angular width of the principal maxima?
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A.
Increases
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B.
Decreases
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C.
Remains the same
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D.
Becomes zero
Solution
Increasing the number of slits increases the sharpness of the maxima, thus decreasing the angular width.
Correct Answer: B — Decreases
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Q. In a diffraction grating, what is the relationship between the angle of diffraction and the order of the maximum?
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A.
Directly proportional
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B.
Inversely proportional
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C.
Independent
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D.
Exponential
Solution
The angle of diffraction is directly proportional to the order of the maximum in a diffraction grating.
Correct Answer: A — Directly proportional
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Q. In a diffraction pattern, how does the intensity of the maxima compare to the minima?
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A.
Maxima are always brighter than minima
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B.
Minima have the same intensity as maxima
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C.
Minima are always darker than maxima
-
D.
Intensity is uniform throughout
Solution
In a diffraction pattern, the minima are always darker than the maxima, which have higher intensity.
Correct Answer: C — Minima are always darker than maxima
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