question_answer

If \[A=\left\{ x\in R:|x|<2 \right\}\] and \[B=\left\{ x\in R:|x-2|\ge 3 \right\};\] then [JEE MAIN Held on 09-01-2020 Evening]

A) \[A-B=[-1,2)\]   

B) \[A\cup B=R-(2,5)\]

C) \[B-A=R-(-2,5)\]

D) \[A\cap B=(-2,-1)\]

Correct Answer: C

Solution :

\[A=\{x:|x|<2\},\] \[B=\{x:|x-2|\le 3\}\] \[A\bigcap B=\left\{ x:x\in \left[ -2,-1 \right) \right.\] \[A\bigcup B=R-\left\{ x:x\in \left[ 2,5 \right) \right\}\] \[A-B=\left\{ x:x\in \left( -1,2 \right) \right\}\] \[B-A=\left( -\infty ,\,-2 \right]\bigcup \left[ 5,\infty  \right)\]