Class 11 Mathematics · Chapter 11 · Test 1
Domain, Range and Periods
40 MCQs Covers domains and ranges, even and odd functions, and the periods of all six trigonometric functions.
40 questions · 35 min · 40 marks
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Sample questions
The first 5 of 40. Try each one, then tap to see the answer.
Question 1
What is the domain of y = sin x?
- A[−1, 1]
- BR = (−∞, ∞)
- CR except odd multiples of π/2
- DR except multiples of π
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Answer: B
Sine is defined for every real number, so its domain is R. Its range is [−1, 1].
Question 2
What is the range of y = cos x?
- A(−∞, ∞)
- B(−∞, −1] ∪ [1, ∞)
- C[0, 1]
- D[−1, 1]
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Answer: D
The values of cosine always lie between −1 and 1, inclusive.
Question 3
What is the domain of y = tan x?
- AR except x = (2n + 1)π/2, n ∈ Z
- BR except x = nπ, n ∈ Z
- CR
- D[−1, 1]
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Answer: A
tan x = sin x / cos x is undefined where cos x = 0, i.e. at odd multiples of π/2.
Question 4
What is the range of y = tan x?
- A[−1, 1]
- B(−∞, −1] ∪ [1, ∞)
- C(−∞, ∞)
- D[0, ∞)
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Answer: C
Tangent takes every real value, so its range is R.
Question 5
What is the domain of y = cot x?
- AR except x = (2n + 1)π/2, n ∈ Z
- BR except x = nπ, n ∈ Z
- CR
- D(−∞, −1] ∪ [1, ∞)
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Answer: B
cot x = cos x / sin x is undefined where sin x = 0, i.e. at multiples of π.
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