Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
BITSAT 2010
Exam
BITSAT
Year
2010
Subject
Mathematics
Chapter
Sets and Relations

BITSAT 2010 · Mathematics · Sets and Relations

Let ( A= \ x: x ∈ R,| x| 1\ ); ( B= \ x: x ∈ R,| x-1| ≥ 1\ and A...

Let (A=\mathrm{A}=\{x: x \in R,∣\mathrm{R},|x| \lt 1\}); (B=\mathrm{B}=\{x: x \in R,∣\mathrm{R},|x-1| \geq 1\} \text{ and } \mathrm{A} \cup\mathrm{B}=\mathrm{R}−D, -\mathrm{D} \text{, } then the set (D\mathrm{D} is

Options

  1. A(\{x: 1 < x \leq 2\})
  2. B(\{x: 1 \leq x < 2\})
  3. C(\{x: 1 \leq x \leq 2\})
  4. DNone of these

Correct answer

B. (\{x: 1 \leq x < 2\})

Step-by-step solution

A=[x:x∈R,−1<x<1]B=[x:x∈R:x−1≤−1 or x−1≥1]=[x:x∈R:x≤0 or x≥2]∴A∪B=R−D,\begin{aligned}& \mathrm{A}=[x: x \in \mathrm{R},-1 < x < 1] \\ & \mathrm{B}=[x: x \in \mathrm{R}: x-1 \leq-1 \text{ or }x-1 \geq 1] \\ &=[x: x \in\mathbb{R}: x \leq 0 \text{ or }x \geq 2] \\ & \therefore A \cup B=R-D, \end{aligned}) where (D=[x: x \in \mathbb{R}, 1 \leq x < 2])
Practice Sets and Relations on Quantrex Academy →

More from Sets and Relations

In a statistical investigation of 1003 families of Calcutta, it was found that 63… BITSAT 2024Let R be the relation "is congruent to" on the set of all triangles in a plane is BITSAT 2024Number of subsets of set of letter of word 'MONOTONE'. BITSAT 2024In an examination, 62 \% of the candidates failed in English, 42% in Mathematics and 20%… BITSAT 2024If n( A)=1000, n( B)=500 and if n( A B) ≥ 1 and n( A B)=p , then BITSAT 2023A set A has 3 elements and another set B has 6 elements. Then BITSAT 2023If A=\ x: x is a multiple of 4 \ and, B=\ x: x is a multiple of 6 \ , then A B consists… BITSAT 2022In a statistical investigation of 1003 families of Calcutta, it was found that 63… BITSAT 2020Let A = 1, 2, 3, 4, 5 and R be a relation defined by R = ( x, y ) : x, y ∈ A, x + y = 5 .… BITSAT 2017Let A and B be two sets such that A X = B X = ϕ and A X = B X for same set X . Then, BITSAT 2017Two finite sets have m and n elements. The number of subsets of the first set is 112 more… BITSAT 2016Universal set, U=\ x x^ 5 -6 x^ 4 +11 x^ 3 -6 x^ 2 =0\ A=\ x x^ 2 -5 x+6=0\ B=\ x ^ 2… BITSAT 2015If ρ=\ (x, y) x^ 2 +y^ 2 =1 ; x, y ∈ ℝ\ . Then, ρ is BITSAT 2015The set (A B) (B A) is equal to] BITSAT 2014Let R=\ (3,3),(6,6),(9,9),(12,12),(6,12), (3,9),(3,12),(3,6) be a relation on the set A=\… BITSAT 2014A class has 175 students. The following data shows the number of students obtaining one… BITSAT 2013 Full Sets and Relations list Sets and Relations JEE Maths PYQsJEE Mathematics PYQs All BITSAT PYQs