physics : class11 Function Repetition : Periodic Functions : Oscillations and Waves MCQ Questions and Answers
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Function Repetition
MCQ questions and answers.
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MCQ Questions
1. A function f(t) is periodic with period T. Which relation correctly represents its repetition?
A.
f(t + T) = f(t)
B.
f(t + T) = 0
C.
f(t + T) = T
D.
f(t + T) = -f(t)
Correct Answer:
f(t + T) = f(t)
Explanation:
A periodic function repeats its value after every fixed interval T, so f(t + T) equals f(t).
2. If a function repeats itself after 5 seconds, what is its period?
A.
1 second
B.
5 seconds
C.
10 seconds
D.
25 seconds
Correct Answer:
5 seconds
Explanation:
The period is the smallest time interval after which the function repeats its values. Here, that interval is 5 seconds.
3. For a periodic function with period T, which expression has the same value as f(t)?
A.
f(t + 2T)
B.
f(t + T/2)
C.
f(t - T/2)
D.
f(t + T/3)
Correct Answer:
f(t + 2T)
Explanation:
A periodic function repeats after every integer multiple of its period, so f(t + 2T) equals f(t).
4. A function has a period of 4 units. After how many units will it repeat its value for the first time?
A.
2 units
B.
3 units
C.
4 units
D.
8 units
Correct Answer:
4 units
Explanation:
The period is defined as the smallest positive interval over which the function repeats. Therefore, the first repetition occurs after 4 units.
5. Which statement best describes a periodic function?
A.
It increases continuously without repeating
B.
It repeats the same pattern after a fixed interval
C.
It always has a value of zero
D.
It changes randomly with time
Correct Answer:
It repeats the same pattern after a fixed interval
Explanation:
A periodic function is one whose values and pattern repeat after a fixed interval called the period.
6. If f(t + 6) = f(t) for all values of t, what is a possible period of the function?
A.
3 units
B.
6 units
C.
12 units only
D.
0 units
Correct Answer:
6 units
Explanation:
The given relation shows that the function repeats when t is increased by 6, so 6 units is a period.
7. A periodic function has period 10 seconds. Which equation shows one complete repetition?
A.
f(t + 10) = f(t)
B.
f(t + 10) = 10f(t)
C.
f(t + 10) = f(t) + 10
D.
f(t + 10) = -f(t)
Correct Answer:
f(t + 10) = f(t)
Explanation:
One complete repetition means that the function has the same value after 10 seconds, giving f(t + 10) = f(t).
8. If a function repeats every 2 seconds, how many seconds are needed for it to complete three repetitions?
A.
2 seconds
B.
3 seconds
C.
5 seconds
D.
6 seconds
Correct Answer:
6 seconds
Explanation:
Each repetition takes 2 seconds. Therefore, three repetitions take 3 × 2 = 6 seconds.
9. For a function with period T, which change in the input leaves its value unchanged?
A.
Adding T
B.
Adding T/2 only
C.
Multiplying t by T
D.
Adding 1/T
Correct Answer:
Adding T
Explanation:
By definition of period T, increasing the input by T reproduces the same function value: f(t + T) = f(t).
10. A graph repeats its shape after every 8 units along the horizontal axis. What does 8 units represent?
A.
The amplitude
B.
The period
C.
The average value
D.
The maximum value
Correct Answer:
The period
Explanation:
The horizontal distance over which a graph repeats its shape is called its period.
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