Q. In a forced oscillation, if the amplitude of the oscillation is directly proportional to the driving force, what is the relationship called?
A.
Hooke's Law
B.
Newton's Law
C.
Resonance
D.
Steady state
Show solution
Solution
In forced oscillations, the amplitude is directly proportional to the driving force in the steady state.
Correct Answer:
D
— Steady state
Learn More →
Q. In a forced oscillation, the driving frequency is 2 Hz and the natural frequency of the system is 1.5 Hz. What is the ratio of the driving frequency to the natural frequency?
Show solution
Solution
Ratio = driving frequency / natural frequency = 2 / 1.5 = 1.33
Correct Answer:
C
— 1.33
Learn More →
Q. In a forced oscillation, what happens when the driving frequency matches the natural frequency?
A.
The system oscillates with minimum amplitude
B.
The system oscillates with maximum amplitude
C.
The system stops oscillating
D.
The system oscillates at a different frequency
Show solution
Solution
When the driving frequency matches the natural frequency, resonance occurs, leading to maximum amplitude.
Correct Answer:
B
— The system oscillates with maximum amplitude
Learn More →
Q. In a forced oscillation, what happens when the driving frequency matches the natural frequency of the system?
A.
The system oscillates with minimum amplitude
B.
The system oscillates with maximum amplitude
C.
The system stops oscillating
D.
The system oscillates at a different frequency
Show solution
Solution
When the driving frequency matches the natural frequency, resonance occurs, leading to maximum amplitude.
Correct Answer:
B
— The system oscillates with maximum amplitude
Learn More →
Q. In a forced oscillation, what is the effect of increasing the amplitude of the driving force?
A.
Decreases the amplitude of oscillation
B.
Increases the amplitude of oscillation
C.
Has no effect on amplitude
D.
Causes the system to stop oscillating
Show solution
Solution
Increasing the amplitude of the driving force generally increases the amplitude of the forced oscillation.
Correct Answer:
B
— Increases the amplitude of oscillation
Learn More →
Q. In a forced oscillation, what is the effect of resonance?
A.
Amplitude decreases
B.
Amplitude increases significantly
C.
Frequency decreases
D.
Phase difference becomes zero
Show solution
Solution
At resonance, the driving frequency matches the natural frequency of the system, leading to a significant increase in amplitude.
Correct Answer:
B
— Amplitude increases significantly
Learn More →
Q. In a forced oscillation, what is the term for the maximum amplitude achieved at resonance?
A.
Resonance peak
B.
Damping peak
C.
Natural frequency
D.
Driving frequency
Show solution
Solution
The maximum amplitude achieved at resonance is referred to as the resonance peak.
Correct Answer:
A
— Resonance peak
Learn More →
Q. In a frequency distribution, if the class intervals are 0-10, 10-20, 20-30 and their frequencies are 5, 10, 15, what is the mode?
Show solution
Solution
Mode is the class with the highest frequency, which is 20-30.
Correct Answer:
B
— 20
Learn More →
Q. In a frequency distribution, if the class intervals are 0-10, 10-20, 20-30 and their frequencies are 5, 10, 15 respectively, what is the mode?
Show solution
Solution
The modal class is 20-30 as it has the highest frequency (15).
Correct Answer:
C
— 20
Learn More →
Q. In a frequency distribution, if the class intervals are 0-10, 10-20, 20-30, and the frequencies are 5, 10, 15 respectively, what is the mode?
A.
10
B.
20
C.
30
D.
None of the above
Show solution
Solution
The modal class is 20-30 since it has the highest frequency.
Correct Answer:
B
— 20
Learn More →
Q. In a frequency distribution, if the class intervals are 0-10, 10-20, and 20-30 with frequencies 5, 10, and 15 respectively, what is the mode?
A.
10
B.
20
C.
30
D.
No mode
Show solution
Solution
The modal class is 20-30 since it has the highest frequency (15).
Correct Answer:
B
— 20
Learn More →
Q. In a frequency distribution, if the mode is 10 and appears 15 times, what can be said about the data?
A.
It is uniform
B.
It is bimodal
C.
It is unimodal
D.
It is multimodal
Show solution
Solution
Since there is one mode (10), the data is unimodal.
Correct Answer:
C
— It is unimodal
Learn More →
Q. In a frequency distribution, if the mode is 10 and the highest frequency is 15, what can be said about the data?
A.
It is uniform
B.
It is bimodal
C.
It is unimodal
D.
It is multimodal
Show solution
Solution
Since there is one mode (10), the data is unimodal.
Correct Answer:
C
— It is unimodal
Learn More →
Q. In a frequency distribution, if the mode is 10 and the highest frequency is 5, what can be said about the data?
A.
It is uniform
B.
It is bimodal
C.
It is unimodal
D.
It is multimodal
Show solution
Solution
Since there is one mode (10), the data is unimodal.
Correct Answer:
C
— It is unimodal
Learn More →
Q. In a frequency distribution, if the mode is 12 and the frequency of 12 is 10, what can be inferred about the data?
A.
Data is uniform
B.
Data is skewed
C.
Data has multiple modes
D.
Data is bimodal
Show solution
Solution
A single mode indicates that the data is likely skewed.
Correct Answer:
B
— Data is skewed
Learn More →
Q. In a frequency distribution, the following data is given: 1 (2 times), 2 (3 times), 3 (3 times), 4 (1 time). What is the mode? (2020)
Show solution
Solution
Both 2 and 3 appear 3 times, but since 2 is the smallest, the mode is 2.
Correct Answer:
B
— 2
Learn More →
Q. In a frequency distribution, the following values are recorded: 2, 3, 3, 4, 4, 4, 5, 5. What is the mode?
Show solution
Solution
The number 4 appears 3 times, which is more than any other number, so the mode is 4.
Correct Answer:
C
— 4
Learn More →
Q. In a fruit basket, the ratio of apples to oranges is 2:3. If there are 30 oranges, how many apples are there?
Show solution
Solution
The ratio of apples to oranges is 2:3. If there are 30 oranges, we can set up the proportion: 2/3 = x/30. Solving for x gives us x = 20. Therefore, there are 20 apples.
Correct Answer:
A
— 20
Learn More →
Q. In a fruit basket, the ratio of apples to oranges is 7:5. If there are 35 apples, how many oranges are there?
Show solution
Solution
The ratio of apples to oranges is 7:5. If there are 35 apples, the number of oranges can be calculated as (35 apples * 5 oranges) / 7 apples = 25 oranges.
Correct Answer:
A
— 25
Learn More →
Q. In a function f(x) = ax^2 + bx + c, if a > 0, what can be inferred about the direction of the graph?
A.
The graph opens upwards.
B.
The graph opens downwards.
C.
The graph is a straight line.
D.
The graph is a constant function.
Show solution
Solution
When a > 0 in a quadratic function, the graph opens upwards, indicating that the vertex is the minimum point.
Correct Answer:
A
— The graph opens upwards.
Learn More →
Q. In a function f(x) = ax^2 + bx + c, if a > 0, what can be said about the graph of the function?
A.
It opens upwards.
B.
It opens downwards.
C.
It has a maximum point.
D.
It is a straight line.
Show solution
Solution
If a > 0 in a quadratic function, the graph opens upwards, indicating that it has a minimum point.
Correct Answer:
A
— It opens upwards.
Learn More →
Q. In a function f(x) = ax^2 + bx + c, what does the coefficient 'a' determine about the graph?
A.
The y-intercept of the graph.
B.
The direction of the parabola's opening.
C.
The x-intercepts of the graph.
D.
The slope of the graph.
Show solution
Solution
'a' determines the direction of the parabola's opening; if 'a' is positive, it opens upwards, and if negative, it opens downwards.
Correct Answer:
B
— The direction of the parabola's opening.
Learn More →
Q. In a function f(x) = ax^2 + bx + c, what does the coefficient 'a' determine?
A.
The direction of the parabola's opening.
B.
The y-intercept of the graph.
C.
The slope of the graph.
D.
The x-intercepts of the graph.
Show solution
Solution
The coefficient 'a' in a quadratic function determines whether the parabola opens upwards (a > 0) or downwards (a < 0).
Correct Answer:
A
— The direction of the parabola's opening.
Learn More →
Q. In a function f(x) = ax^2 + bx + c, what does the value of 'a' determine about the graph?
A.
The y-intercept of the graph.
B.
The direction of the parabola.
C.
The x-intercepts of the graph.
D.
The maximum value of the function.
Show solution
Solution
'a' determines the direction of the parabola; if 'a' is positive, it opens upwards, and if negative, it opens downwards.
Correct Answer:
B
— The direction of the parabola.
Learn More →
Q. In a function f(x) = ax^2 + bx + c, what does the value of 'a' determine?
A.
The direction in which the parabola opens.
B.
The x-intercepts of the graph.
C.
The y-intercept of the graph.
D.
The maximum value of the function.
Show solution
Solution
'a' determines the direction of the parabola; if 'a' is positive, it opens upwards, and if negative, it opens downwards.
Correct Answer:
A
— The direction in which the parabola opens.
Learn More →
Q. In a function f(x) = x^3 - 3x, what is the nature of the critical points?
A.
All critical points are local maxima.
B.
All critical points are local minima.
C.
There are both local maxima and minima.
D.
There are no critical points.
Show solution
Solution
The function has critical points where the first derivative is zero, which can be analyzed to find both local maxima and minima.
Correct Answer:
C
— There are both local maxima and minima.
Learn More →
Q. In a function f(x), if f(a) = f(b) for a ≠ b, what can be inferred about the function?
A.
The function is one-to-one.
B.
The function is constant.
C.
The function is quadratic.
D.
The function is increasing.
Show solution
Solution
If f(a) = f(b) for a ≠ b, it indicates that the function is not one-to-one, which means it does not pass the horizontal line test.
Correct Answer:
B
— The function is constant.
Learn More →
Q. In a galvanic cell, if the anode reaction is 2Ag⁺ + 2e⁻ → 2Ag, what is the cathode reaction? (2022)
A.
Cu²⁺ + 2e⁻ → Cu
B.
Zn²⁺ + 2e⁻ → Zn
C.
Fe²⁺ + 2e⁻ → Fe
D.
Pb²⁺ + 2e⁻ → Pb
Show solution
Solution
The cathode reaction must be a reduction reaction, and Cu²⁺ + 2e⁻ → Cu is a common cathode reaction.
Correct Answer:
A
— Cu²⁺ + 2e⁻ → Cu
Learn More →
Q. In a galvanic cell, if the anode reaction is 2H₂ → 4H⁺ + 4e⁻, what is the cathode reaction?
A.
O₂ + 4e⁻ + 4H⁺ → 2H₂O
B.
2H₂O + 4e⁻ → 2H₂ + O₂
C.
4H⁺ + 4e⁻ → 2H₂
D.
2H₂ + O₂ → 2H₂O
Show solution
Solution
The cathode reaction is O₂ + 4e⁻ + 4H⁺ → 2H₂O.
Correct Answer:
A
— O₂ + 4e⁻ + 4H⁺ → 2H₂O
Learn More →
Q. In a galvanic cell, if the anode reaction is Ag⁺ + e⁻ → Ag, what is the cathode reaction?
A.
Cu²⁺ + 2e⁻ → Cu
B.
Zn²⁺ + 2e⁻ → Zn
C.
Fe²⁺ + 2e⁻ → Fe
D.
Pb²⁺ + 2e⁻ → Pb
Show solution
Solution
The cathode reaction must be a reduction; Ag⁺ + e⁻ → Ag is the anode reaction.
Correct Answer:
A
— Cu²⁺ + 2e⁻ → Cu
Learn More →
Showing 13651 to 13680 of 31410 (1047 Pages)
