Mathematics · 2021
JEE Main · 27 August 2021, Shift 1 · Q81
If A ={x ∈ R:|x-2|>1}, B ={x ∈ R: √(x^2-3)>1}, C ={x ∈ R:|x-4| ≥ 2} and Z is the set of all integers, then the number of subsets of the set ( A ∩ B ∩…
If $\displaystyle \mathrm{A}=\{x \in \mathbf{R}:|x-2|>1\}, \mathrm{B}=\left\{x \in \mathbf{R}: \sqrt{x^2-3}>1\right\}, \mathrm{C}=\{x \in \mathbf{R}:|x-4| \geqslant 2\}$ and $\displaystyle \mathbf{Z}$ is the set of all integers, then the number of subsets of the set $\displaystyle (\mathrm{A} \cap \mathrm{B} \cap \mathrm{C})^{\mathrm{c}} \cap \mathbf{Z}$ is \_\_\_\_.
Official answer
256
More from Sets
- Let _i=1^50 X_i=_i=1^n Y_i=T, where each X_i contains 10 elements and each Y_i contains 5 elements. If each element of the set T is an element of…2020
- Let the set C={(x, y) ∣ x^2-2^y=2023, x, y ∈ N}. Then Σ_(x, y) ∈ C(x+y) is equal to ____.2024
- In a school, there are three types of games to be played. Some of the students play two types of games, but none play all the three games. Which Venn…2021
- A group of 40 students appeared in an examination of 3 subjects - Mathematics, Physics and Chemistry. It was found that all students passed in…2024
- Out of all the patients in a hospital 89 % are found to be suffering from heart ailment and 98\% are suffering from lungs infection. If K\% of them…2021
- Consider the two sets: A={m ∈ R: both the roots of x^2-(m+1) x+m+4=0 are real\} and B=[-3,5). Which of the following is not true?2020
- Let A={(α, β) ∈ R × R:|α-1| ≤ 4 and |β-5| ≤ 6} and B={(α, β) ∈ R × R: 16(α-2)^2+9(β-6)^2 ≤ 144}. Then2025
- Let X={n ∈ N: 1 ≤ n ≤ 50}. If A={n ∈ X: n is a multiple of 2 } and B={n ∈ X: n is a multiple of 7 }, then the number of elements in the smallest…2020
JEE Main 2021 Mathematics question, with the answer from NTA’s final answer key. Where our answers come from.