Skip to main content
Back to FUNCTIONS

JEE MATHEMATICS MCQ: FUNCTIONS

1 Easy
1 of 1
Analyzing +4 | -1
Let the sets AA and BB denote the domain and range respectively of the function f(x)=1⌈x⌉−xf(x)=\frac{1}{\sqrt{\lceil x\rceil-x}}, where ⌈x⌉\lceil x\rceil denotes the smallest integer greater than or equal to xx. Then among the statements

(S1):A∩B=(1,∞)−N(\mathrm{S} 1): A \cap B=(1, \infty)-\mathbb{N} and

(S2):A∪B=(1,∞)(\mathrm{S} 2): A \cup B=(1, \infty)
View answer and explanation
Correct option: C
Neither (S1) nor (S2) is true
The correct answer is C (Neither (S1) nor (S2) is true) because the function is not defined for any real number x, making both the domain and range empty sets.

More Questions from FUNCTIONS

Practice All Chapter MCQs →
If f:(−∞,2]⟶(−∞,4]f:(-\infty, 2] \longrightarrow(-\infty, 4], where f(x)=x(4−x)f(x)=x(4-x), then f−1(x)f^{-1}(x) is given by: If g(f(x))=∣sin⁡x∣g(f(x))=|\sin x| and f(g(x))=(sin⁡x)2f(g(x))=(\sin \sqrt{x})^2, then Let f:(2,  3)→(0,  1)f:\left( {2,\;3} \right) \to \left( {0,\;1} \right) be defined by f(x)=x−[x]f\left( x \right) = x - \left[ x \right], then f−1(x){f^{ - 1}}\left( x \right) equals Let f:R→Rf: R \rightarrow R be defined as f(x)=x4f(x)=x^4, Choose the correct answer. Which of the following functions are odd functions Let f(x)=(x+1)2−1(x≥−1)f(x)=(x+1)^2-1(x \geq-1). Then the set S={x:f(x)=f−1(x)}S=\left\{x: f(x)=f^{-1}(x)\right\} contains
Type at least 2 characters or jump directly:
🩺 NEET MCQs 🔬 JEE MCQs 🎯 JEE College Predictor Study guides 📊 Dashboard
🔓

Save your learning progress

Sign in with a free account to save your practice answers and quiz results, then return to them when you revise.

Continue with Free Account →